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Ocean currents II
Wind-water interaction and drag forces Ekman transport circular and geostrophic flow General ocean flow pattern
Wind-Water surface interaction Water motion at the surface of the ocean (mixed layer) is driven by wind effects Friction causes drag effects on the water transferring momentum from the atmospheric winds to the ocean surface water
The drag force Wind generates vertical and horizontal motion in the water triggering convective motion causing turbulent mixing down to about 100m depth which defines the isothermal mixed layer The drag force FD on the water depends on wind velocity v
wavesofemergencethelyparticular
androughnesssurfaceondepending
areasectionalcrossACninteractiowaterwindfor
factoressdimensionltcoefficiendragCvACF
D
DaDD
0020
2
Katsushika Hokusai The Great Wave off Kanagawa
The Beaufort Scale is an empirical measure describing wind speed based on the observed sea conditions (1 knot = 0514 ms = 185 kmh)
For land and city people Bft 6 Bft 8
Bft 9 Bft 10 Bft 11 Bft 12
Bft 7
s
mBv 238360
A strong breeze of B=6 corresponds to wind speed of v=39 to 49 kmh at which long waves begin to form and white foam crests become frequent The drag force can be calculated to
2
2
2
3
3
2
5187518751212000010
0010512451200
mNAForNAs
mmA
m
kgF
Cs
m
h
kmv
m
kgvACF
DD
DaaDD
For a strong gale (B=12) v=35 ms the drag stress on the water will be
00250351200
367535120000250
3
2
2
3
Da
D
Cs
mv
m
kg
mNs
m
m
kgAF
Conversion from scale to wind velocity
Ekman transport The frictional drag force of wind with velocity v or wind stress x generating a water velocity u is balanced by the Coriolis force but drag decreases with depth z
sm
kgdz
fdzf
f
transportofdirectionvectordefines
ftermsvectorin
zuf
zz
zzz
Am
AF
D
D
0
0
ˆˆ
ˆ
ˆ
1ˆ
1
uM
Mzuz
z
τuz
uz
z
τuz
Ek
Ek
D
D
kg
N
mass
force
zA
mparameterCoriolissf
A
mufuAmAFvCAF ccaDDD
1
2
sin2
sin2
Ekman mass transport vector
dep
th v
ecto
r
Since the horizontal wind direction u moving the water is perpendicular to the depth vector z the direction of the frictional drag force D is perpendicular to both vectors and the magnitude is
zufz
f
MfMfz
D
EkEkD
sin2
90sin1 0
zuM
depth thdensity wi waterof increase linear moreless a is assumption
sm
kgdz
Ek
0
uMEk
Ekman transport
Example for Ekman transport What drag force (pressure) does it take at a latitude of 35oN to move water over a depth of 10 m within 1 minute by 100 m to the right
22
15
3
15015
150
1837000020101834
000201060
1001200
10183435sin1029272
10292735sin2
m
N
sm
kg
sm
kgsMfz
sm
kgm
s
m
m
kgzuM
ssf
sfMfz
EkD
Ek
EkD
Weak force done by winds of Basymp2 with h
km
s
m
m
kgsm
kg
Cv
D
D 339130
00101200
1
3
2
Typical surface wind stress conditions
Annual mean wind stress on the ocean in units (Nm2) The green shade represents the magnitude of the stress Typical wind stress values in the Westerlies reach asymp 01 to 02 Nm2 The strongest stress component can be observed for the Roaring Forties the weakest component is in the Doldrums
sin2
2
vC
f
zMMfz aDD
EkEkD
Calculate the mass transport MEk for a typical wind stress of D = 025 Nm2
at the southern latitude of 40oS
sm
kg
s
m
N
fM
ssf
sf
DEk
3
15
2
15015
150
1067210379
250
1037940sin1029272
10292740sin2
About 2 tons of water are shifted within 1 sec by 1 meter to the left
Determine the wind velocity for a typical drag coefficient CD=0002
h
km
s
m
m
kgsm
kgs
C
Mfv
C
Mfv
aD
Ek
aD
Ek 1290
12000020
1013210379
3
315
2
About B=1-2 on the Beauford Scale
Impact on ocean currents The direction of Ekman transport depends on the hemisphere In the northern hemisphere this transport is at a 90o angle to the right of the wind direction and in the southern hemisphere it occurs at a 90o angle to the left of the wind direction This generates gyres circular motions in ocean basins limited by continental coasts
Reality is more complex because of additional forces due to friction and temperature effects which add to the eddy formation phenomenon
Reality is more complex because of additional forces due to the drag forces provided by the atmospheric wind circulation and by the friction forces exerted by deeper water layers
Humboldt Current The cold Peruvian current (an eastern boundary current) flows towards the equator along the coast of Ecuador and Peru It flows with a speed of 01 to 015[ms] In the absence of an El Nintildeo prevailing surface winds cause Ekman transport to the left or away from the coast with subsequent upwelling of cold water
Kon Tiki Heyerdahlrsquos thesis of populating Polynesia from the East rather than from the North-West by taking advantage of Humboldt current for sea travel
Pressure conditions Pressure gradient towards ocean depth can be expressed in terms of the salinity and temperature dependence of ocean water density
PaatmP
zsurface
zgPzP
PTSneglecting
PTSgz
P
gdz
dP
surface
refsurface
ref
5101
PakmPkmz
PakmPkmz
Pamm
kg
s
mPamPmz
7
7
6
32
5
10444
1011
10100100081910100100
Flow at larger depth is directed by the pressure gradient and the Coriolis force ldquogeostrophic flowrdquo
Approximately a linear increase of pressure with depth ndash in contrast the atmosphere displays an exponential decrease of pressure with altitude
Geostrophic flow
A geostrophic current is an oceanic flow in which the pressure gradient force is balanced by the Coriolis effect The direction of geostrophic flow is parallel to the isobars with the high pressure to the right of the flow in the Northern Hemisphere and the high pressure to the left in the Southern Hemisphere
Fluid or gaseous media move from high pressure to low pressure regions The force pushing the water is called the pressure gradient force Fp In a geostrophic flow water moves along the lines of equal pressure (isobars) instead of moving from a high pressure to low pressure region This occurs due to Earthrsquos rotation that cause the Coriolis force Fc The Coriolis force acts at right angles to the flow When it balances the pressure gradient force (Fp=Fc) the resulting flow becomes the geostrophic flow
Flow velocity Variations of pressure conditions or isobars with depth are associated with temperature and salinity conditions and can cause horizontal flow The pressure gradient is balanced by the Coriolis force This allows an estimate of the flow speed
Pzu
Puz
ˆ1
01
ˆ
f
velocityflowayielding
fFF pc
With f being the Coriolis parameter and g the earth acceleration L represents the distance over which the salinity and temperature dependent density anomaly changes Between 20oN and 40oN Lasymp2000km
L
z
f
gu
ref
surface
The pressure gradient is also affected along coastlines with upwards sloping ground level
Geostrophic ocean flow
With f being the Coriolis parameter and g the earth acceleration L represents the distance over which the salinity and temperature dependent density anomaly changes Between 20oN and 40oN Lasymp2000km
L
z
f
gu
ref
surface
Consider the gulf stream as a sample The is a pressure or density with depth that in combination with the previously discussed Coriolis force affects the direction and determines the surface flow velocity
Overall agreement within the range of local speed variations The maximum speed is observed at the western boundaries of the Gulf stream with v asymp 1ms while in the interior of the gyre the speed is much lower vasymp10cms
s
m
m
m
kg
m
kgs
s
m
u
sfsf
m
kg
m
kg
m
kg
L
z
f
gu
surface
ref
surface
13
3
15
2
15150
333
1030000002
041000
1000102927
819
10292710292730sin2
42226
Estimate the gulf stream surface velocity usurface assuming a distance between 20oN and 40oN of L=2000 km for a depth of z=1000 m
Gulf stream flow velocity
Ocean current simulation for different temperature zones
NASAGoddard Space Flight Center Scientific Visualization Studio
The flow pattern is complex and the flow velocity varies greatly Both observables are defined by coastal boundaries drag forces at the surface density gradients at deep depths and the Coriolis force
Single water drop flow
Geostrophic flow induced variations in ocean surface height
The curvature of the flow and the horizontal velocity gradient across the flow causes a pressure gradient perpendicular to the flow direction which translate into variations of the ocean surface height
6
2
614
101
819
1010110
L
m
s
ms
mms
g
uLf
kmLsfs
mufor 10001010 14
Ocean Surface Height
Example Gulf of Mexico
httpwwwaomlnoaagovphoddhosaltimetryphp
Flow pattern Water height
Altitude anomalies
Maps of sea level obtained from satellite altimetry measurements are used to derive surface ocean currents Higher values of sea level (oranges and reds) are associated with gyres and warm eddies while lower values are associated to colder features Drifter trajectories illustrate circulation features Sea height anomaly maps show the difference of sea level from average conditions while sea height maps show absolute values of the sea level
Changing average sea altitude levels
Based on observational data such as tide level measurements and satellite based altimetry
Sea level trend between 1992 and 2009 with respect to a reference level based on satellite altitude measurements Yellow and red regions show rising sea level while green and blue regions show falling sea level
Wind-Water surface interaction Water motion at the surface of the ocean (mixed layer) is driven by wind effects Friction causes drag effects on the water transferring momentum from the atmospheric winds to the ocean surface water
The drag force Wind generates vertical and horizontal motion in the water triggering convective motion causing turbulent mixing down to about 100m depth which defines the isothermal mixed layer The drag force FD on the water depends on wind velocity v
wavesofemergencethelyparticular
androughnesssurfaceondepending
areasectionalcrossACninteractiowaterwindfor
factoressdimensionltcoefficiendragCvACF
D
DaDD
0020
2
Katsushika Hokusai The Great Wave off Kanagawa
The Beaufort Scale is an empirical measure describing wind speed based on the observed sea conditions (1 knot = 0514 ms = 185 kmh)
For land and city people Bft 6 Bft 8
Bft 9 Bft 10 Bft 11 Bft 12
Bft 7
s
mBv 238360
A strong breeze of B=6 corresponds to wind speed of v=39 to 49 kmh at which long waves begin to form and white foam crests become frequent The drag force can be calculated to
2
2
2
3
3
2
5187518751212000010
0010512451200
mNAForNAs
mmA
m
kgF
Cs
m
h
kmv
m
kgvACF
DD
DaaDD
For a strong gale (B=12) v=35 ms the drag stress on the water will be
00250351200
367535120000250
3
2
2
3
Da
D
Cs
mv
m
kg
mNs
m
m
kgAF
Conversion from scale to wind velocity
Ekman transport The frictional drag force of wind with velocity v or wind stress x generating a water velocity u is balanced by the Coriolis force but drag decreases with depth z
sm
kgdz
fdzf
f
transportofdirectionvectordefines
ftermsvectorin
zuf
zz
zzz
Am
AF
D
D
0
0
ˆˆ
ˆ
ˆ
1ˆ
1
uM
Mzuz
z
τuz
uz
z
τuz
Ek
Ek
D
D
kg
N
mass
force
zA
mparameterCoriolissf
A
mufuAmAFvCAF ccaDDD
1
2
sin2
sin2
Ekman mass transport vector
dep
th v
ecto
r
Since the horizontal wind direction u moving the water is perpendicular to the depth vector z the direction of the frictional drag force D is perpendicular to both vectors and the magnitude is
zufz
f
MfMfz
D
EkEkD
sin2
90sin1 0
zuM
depth thdensity wi waterof increase linear moreless a is assumption
sm
kgdz
Ek
0
uMEk
Ekman transport
Example for Ekman transport What drag force (pressure) does it take at a latitude of 35oN to move water over a depth of 10 m within 1 minute by 100 m to the right
22
15
3
15015
150
1837000020101834
000201060
1001200
10183435sin1029272
10292735sin2
m
N
sm
kg
sm
kgsMfz
sm
kgm
s
m
m
kgzuM
ssf
sfMfz
EkD
Ek
EkD
Weak force done by winds of Basymp2 with h
km
s
m
m
kgsm
kg
Cv
D
D 339130
00101200
1
3
2
Typical surface wind stress conditions
Annual mean wind stress on the ocean in units (Nm2) The green shade represents the magnitude of the stress Typical wind stress values in the Westerlies reach asymp 01 to 02 Nm2 The strongest stress component can be observed for the Roaring Forties the weakest component is in the Doldrums
sin2
2
vC
f
zMMfz aDD
EkEkD
Calculate the mass transport MEk for a typical wind stress of D = 025 Nm2
at the southern latitude of 40oS
sm
kg
s
m
N
fM
ssf
sf
DEk
3
15
2
15015
150
1067210379
250
1037940sin1029272
10292740sin2
About 2 tons of water are shifted within 1 sec by 1 meter to the left
Determine the wind velocity for a typical drag coefficient CD=0002
h
km
s
m
m
kgsm
kgs
C
Mfv
C
Mfv
aD
Ek
aD
Ek 1290
12000020
1013210379
3
315
2
About B=1-2 on the Beauford Scale
Impact on ocean currents The direction of Ekman transport depends on the hemisphere In the northern hemisphere this transport is at a 90o angle to the right of the wind direction and in the southern hemisphere it occurs at a 90o angle to the left of the wind direction This generates gyres circular motions in ocean basins limited by continental coasts
Reality is more complex because of additional forces due to friction and temperature effects which add to the eddy formation phenomenon
Reality is more complex because of additional forces due to the drag forces provided by the atmospheric wind circulation and by the friction forces exerted by deeper water layers
Humboldt Current The cold Peruvian current (an eastern boundary current) flows towards the equator along the coast of Ecuador and Peru It flows with a speed of 01 to 015[ms] In the absence of an El Nintildeo prevailing surface winds cause Ekman transport to the left or away from the coast with subsequent upwelling of cold water
Kon Tiki Heyerdahlrsquos thesis of populating Polynesia from the East rather than from the North-West by taking advantage of Humboldt current for sea travel
Pressure conditions Pressure gradient towards ocean depth can be expressed in terms of the salinity and temperature dependence of ocean water density
PaatmP
zsurface
zgPzP
PTSneglecting
PTSgz
P
gdz
dP
surface
refsurface
ref
5101
PakmPkmz
PakmPkmz
Pamm
kg
s
mPamPmz
7
7
6
32
5
10444
1011
10100100081910100100
Flow at larger depth is directed by the pressure gradient and the Coriolis force ldquogeostrophic flowrdquo
Approximately a linear increase of pressure with depth ndash in contrast the atmosphere displays an exponential decrease of pressure with altitude
Geostrophic flow
A geostrophic current is an oceanic flow in which the pressure gradient force is balanced by the Coriolis effect The direction of geostrophic flow is parallel to the isobars with the high pressure to the right of the flow in the Northern Hemisphere and the high pressure to the left in the Southern Hemisphere
Fluid or gaseous media move from high pressure to low pressure regions The force pushing the water is called the pressure gradient force Fp In a geostrophic flow water moves along the lines of equal pressure (isobars) instead of moving from a high pressure to low pressure region This occurs due to Earthrsquos rotation that cause the Coriolis force Fc The Coriolis force acts at right angles to the flow When it balances the pressure gradient force (Fp=Fc) the resulting flow becomes the geostrophic flow
Flow velocity Variations of pressure conditions or isobars with depth are associated with temperature and salinity conditions and can cause horizontal flow The pressure gradient is balanced by the Coriolis force This allows an estimate of the flow speed
Pzu
Puz
ˆ1
01
ˆ
f
velocityflowayielding
fFF pc
With f being the Coriolis parameter and g the earth acceleration L represents the distance over which the salinity and temperature dependent density anomaly changes Between 20oN and 40oN Lasymp2000km
L
z
f
gu
ref
surface
The pressure gradient is also affected along coastlines with upwards sloping ground level
Geostrophic ocean flow
With f being the Coriolis parameter and g the earth acceleration L represents the distance over which the salinity and temperature dependent density anomaly changes Between 20oN and 40oN Lasymp2000km
L
z
f
gu
ref
surface
Consider the gulf stream as a sample The is a pressure or density with depth that in combination with the previously discussed Coriolis force affects the direction and determines the surface flow velocity
Overall agreement within the range of local speed variations The maximum speed is observed at the western boundaries of the Gulf stream with v asymp 1ms while in the interior of the gyre the speed is much lower vasymp10cms
s
m
m
m
kg
m
kgs
s
m
u
sfsf
m
kg
m
kg
m
kg
L
z
f
gu
surface
ref
surface
13
3
15
2
15150
333
1030000002
041000
1000102927
819
10292710292730sin2
42226
Estimate the gulf stream surface velocity usurface assuming a distance between 20oN and 40oN of L=2000 km for a depth of z=1000 m
Gulf stream flow velocity
Ocean current simulation for different temperature zones
NASAGoddard Space Flight Center Scientific Visualization Studio
The flow pattern is complex and the flow velocity varies greatly Both observables are defined by coastal boundaries drag forces at the surface density gradients at deep depths and the Coriolis force
Single water drop flow
Geostrophic flow induced variations in ocean surface height
The curvature of the flow and the horizontal velocity gradient across the flow causes a pressure gradient perpendicular to the flow direction which translate into variations of the ocean surface height
6
2
614
101
819
1010110
L
m
s
ms
mms
g
uLf
kmLsfs
mufor 10001010 14
Ocean Surface Height
Example Gulf of Mexico
httpwwwaomlnoaagovphoddhosaltimetryphp
Flow pattern Water height
Altitude anomalies
Maps of sea level obtained from satellite altimetry measurements are used to derive surface ocean currents Higher values of sea level (oranges and reds) are associated with gyres and warm eddies while lower values are associated to colder features Drifter trajectories illustrate circulation features Sea height anomaly maps show the difference of sea level from average conditions while sea height maps show absolute values of the sea level
Changing average sea altitude levels
Based on observational data such as tide level measurements and satellite based altimetry
Sea level trend between 1992 and 2009 with respect to a reference level based on satellite altitude measurements Yellow and red regions show rising sea level while green and blue regions show falling sea level
The drag force Wind generates vertical and horizontal motion in the water triggering convective motion causing turbulent mixing down to about 100m depth which defines the isothermal mixed layer The drag force FD on the water depends on wind velocity v
wavesofemergencethelyparticular
androughnesssurfaceondepending
areasectionalcrossACninteractiowaterwindfor
factoressdimensionltcoefficiendragCvACF
D
DaDD
0020
2
Katsushika Hokusai The Great Wave off Kanagawa
The Beaufort Scale is an empirical measure describing wind speed based on the observed sea conditions (1 knot = 0514 ms = 185 kmh)
For land and city people Bft 6 Bft 8
Bft 9 Bft 10 Bft 11 Bft 12
Bft 7
s
mBv 238360
A strong breeze of B=6 corresponds to wind speed of v=39 to 49 kmh at which long waves begin to form and white foam crests become frequent The drag force can be calculated to
2
2
2
3
3
2
5187518751212000010
0010512451200
mNAForNAs
mmA
m
kgF
Cs
m
h
kmv
m
kgvACF
DD
DaaDD
For a strong gale (B=12) v=35 ms the drag stress on the water will be
00250351200
367535120000250
3
2
2
3
Da
D
Cs
mv
m
kg
mNs
m
m
kgAF
Conversion from scale to wind velocity
Ekman transport The frictional drag force of wind with velocity v or wind stress x generating a water velocity u is balanced by the Coriolis force but drag decreases with depth z
sm
kgdz
fdzf
f
transportofdirectionvectordefines
ftermsvectorin
zuf
zz
zzz
Am
AF
D
D
0
0
ˆˆ
ˆ
ˆ
1ˆ
1
uM
Mzuz
z
τuz
uz
z
τuz
Ek
Ek
D
D
kg
N
mass
force
zA
mparameterCoriolissf
A
mufuAmAFvCAF ccaDDD
1
2
sin2
sin2
Ekman mass transport vector
dep
th v
ecto
r
Since the horizontal wind direction u moving the water is perpendicular to the depth vector z the direction of the frictional drag force D is perpendicular to both vectors and the magnitude is
zufz
f
MfMfz
D
EkEkD
sin2
90sin1 0
zuM
depth thdensity wi waterof increase linear moreless a is assumption
sm
kgdz
Ek
0
uMEk
Ekman transport
Example for Ekman transport What drag force (pressure) does it take at a latitude of 35oN to move water over a depth of 10 m within 1 minute by 100 m to the right
22
15
3
15015
150
1837000020101834
000201060
1001200
10183435sin1029272
10292735sin2
m
N
sm
kg
sm
kgsMfz
sm
kgm
s
m
m
kgzuM
ssf
sfMfz
EkD
Ek
EkD
Weak force done by winds of Basymp2 with h
km
s
m
m
kgsm
kg
Cv
D
D 339130
00101200
1
3
2
Typical surface wind stress conditions
Annual mean wind stress on the ocean in units (Nm2) The green shade represents the magnitude of the stress Typical wind stress values in the Westerlies reach asymp 01 to 02 Nm2 The strongest stress component can be observed for the Roaring Forties the weakest component is in the Doldrums
sin2
2
vC
f
zMMfz aDD
EkEkD
Calculate the mass transport MEk for a typical wind stress of D = 025 Nm2
at the southern latitude of 40oS
sm
kg
s
m
N
fM
ssf
sf
DEk
3
15
2
15015
150
1067210379
250
1037940sin1029272
10292740sin2
About 2 tons of water are shifted within 1 sec by 1 meter to the left
Determine the wind velocity for a typical drag coefficient CD=0002
h
km
s
m
m
kgsm
kgs
C
Mfv
C
Mfv
aD
Ek
aD
Ek 1290
12000020
1013210379
3
315
2
About B=1-2 on the Beauford Scale
Impact on ocean currents The direction of Ekman transport depends on the hemisphere In the northern hemisphere this transport is at a 90o angle to the right of the wind direction and in the southern hemisphere it occurs at a 90o angle to the left of the wind direction This generates gyres circular motions in ocean basins limited by continental coasts
Reality is more complex because of additional forces due to friction and temperature effects which add to the eddy formation phenomenon
Reality is more complex because of additional forces due to the drag forces provided by the atmospheric wind circulation and by the friction forces exerted by deeper water layers
Humboldt Current The cold Peruvian current (an eastern boundary current) flows towards the equator along the coast of Ecuador and Peru It flows with a speed of 01 to 015[ms] In the absence of an El Nintildeo prevailing surface winds cause Ekman transport to the left or away from the coast with subsequent upwelling of cold water
Kon Tiki Heyerdahlrsquos thesis of populating Polynesia from the East rather than from the North-West by taking advantage of Humboldt current for sea travel
Pressure conditions Pressure gradient towards ocean depth can be expressed in terms of the salinity and temperature dependence of ocean water density
PaatmP
zsurface
zgPzP
PTSneglecting
PTSgz
P
gdz
dP
surface
refsurface
ref
5101
PakmPkmz
PakmPkmz
Pamm
kg
s
mPamPmz
7
7
6
32
5
10444
1011
10100100081910100100
Flow at larger depth is directed by the pressure gradient and the Coriolis force ldquogeostrophic flowrdquo
Approximately a linear increase of pressure with depth ndash in contrast the atmosphere displays an exponential decrease of pressure with altitude
Geostrophic flow
A geostrophic current is an oceanic flow in which the pressure gradient force is balanced by the Coriolis effect The direction of geostrophic flow is parallel to the isobars with the high pressure to the right of the flow in the Northern Hemisphere and the high pressure to the left in the Southern Hemisphere
Fluid or gaseous media move from high pressure to low pressure regions The force pushing the water is called the pressure gradient force Fp In a geostrophic flow water moves along the lines of equal pressure (isobars) instead of moving from a high pressure to low pressure region This occurs due to Earthrsquos rotation that cause the Coriolis force Fc The Coriolis force acts at right angles to the flow When it balances the pressure gradient force (Fp=Fc) the resulting flow becomes the geostrophic flow
Flow velocity Variations of pressure conditions or isobars with depth are associated with temperature and salinity conditions and can cause horizontal flow The pressure gradient is balanced by the Coriolis force This allows an estimate of the flow speed
Pzu
Puz
ˆ1
01
ˆ
f
velocityflowayielding
fFF pc
With f being the Coriolis parameter and g the earth acceleration L represents the distance over which the salinity and temperature dependent density anomaly changes Between 20oN and 40oN Lasymp2000km
L
z
f
gu
ref
surface
The pressure gradient is also affected along coastlines with upwards sloping ground level
Geostrophic ocean flow
With f being the Coriolis parameter and g the earth acceleration L represents the distance over which the salinity and temperature dependent density anomaly changes Between 20oN and 40oN Lasymp2000km
L
z
f
gu
ref
surface
Consider the gulf stream as a sample The is a pressure or density with depth that in combination with the previously discussed Coriolis force affects the direction and determines the surface flow velocity
Overall agreement within the range of local speed variations The maximum speed is observed at the western boundaries of the Gulf stream with v asymp 1ms while in the interior of the gyre the speed is much lower vasymp10cms
s
m
m
m
kg
m
kgs
s
m
u
sfsf
m
kg
m
kg
m
kg
L
z
f
gu
surface
ref
surface
13
3
15
2
15150
333
1030000002
041000
1000102927
819
10292710292730sin2
42226
Estimate the gulf stream surface velocity usurface assuming a distance between 20oN and 40oN of L=2000 km for a depth of z=1000 m
Gulf stream flow velocity
Ocean current simulation for different temperature zones
NASAGoddard Space Flight Center Scientific Visualization Studio
The flow pattern is complex and the flow velocity varies greatly Both observables are defined by coastal boundaries drag forces at the surface density gradients at deep depths and the Coriolis force
Single water drop flow
Geostrophic flow induced variations in ocean surface height
The curvature of the flow and the horizontal velocity gradient across the flow causes a pressure gradient perpendicular to the flow direction which translate into variations of the ocean surface height
6
2
614
101
819
1010110
L
m
s
ms
mms
g
uLf
kmLsfs
mufor 10001010 14
Ocean Surface Height
Example Gulf of Mexico
httpwwwaomlnoaagovphoddhosaltimetryphp
Flow pattern Water height
Altitude anomalies
Maps of sea level obtained from satellite altimetry measurements are used to derive surface ocean currents Higher values of sea level (oranges and reds) are associated with gyres and warm eddies while lower values are associated to colder features Drifter trajectories illustrate circulation features Sea height anomaly maps show the difference of sea level from average conditions while sea height maps show absolute values of the sea level
Changing average sea altitude levels
Based on observational data such as tide level measurements and satellite based altimetry
Sea level trend between 1992 and 2009 with respect to a reference level based on satellite altitude measurements Yellow and red regions show rising sea level while green and blue regions show falling sea level
The Beaufort Scale is an empirical measure describing wind speed based on the observed sea conditions (1 knot = 0514 ms = 185 kmh)
For land and city people Bft 6 Bft 8
Bft 9 Bft 10 Bft 11 Bft 12
Bft 7
s
mBv 238360
A strong breeze of B=6 corresponds to wind speed of v=39 to 49 kmh at which long waves begin to form and white foam crests become frequent The drag force can be calculated to
2
2
2
3
3
2
5187518751212000010
0010512451200
mNAForNAs
mmA
m
kgF
Cs
m
h
kmv
m
kgvACF
DD
DaaDD
For a strong gale (B=12) v=35 ms the drag stress on the water will be
00250351200
367535120000250
3
2
2
3
Da
D
Cs
mv
m
kg
mNs
m
m
kgAF
Conversion from scale to wind velocity
Ekman transport The frictional drag force of wind with velocity v or wind stress x generating a water velocity u is balanced by the Coriolis force but drag decreases with depth z
sm
kgdz
fdzf
f
transportofdirectionvectordefines
ftermsvectorin
zuf
zz
zzz
Am
AF
D
D
0
0
ˆˆ
ˆ
ˆ
1ˆ
1
uM
Mzuz
z
τuz
uz
z
τuz
Ek
Ek
D
D
kg
N
mass
force
zA
mparameterCoriolissf
A
mufuAmAFvCAF ccaDDD
1
2
sin2
sin2
Ekman mass transport vector
dep
th v
ecto
r
Since the horizontal wind direction u moving the water is perpendicular to the depth vector z the direction of the frictional drag force D is perpendicular to both vectors and the magnitude is
zufz
f
MfMfz
D
EkEkD
sin2
90sin1 0
zuM
depth thdensity wi waterof increase linear moreless a is assumption
sm
kgdz
Ek
0
uMEk
Ekman transport
Example for Ekman transport What drag force (pressure) does it take at a latitude of 35oN to move water over a depth of 10 m within 1 minute by 100 m to the right
22
15
3
15015
150
1837000020101834
000201060
1001200
10183435sin1029272
10292735sin2
m
N
sm
kg
sm
kgsMfz
sm
kgm
s
m
m
kgzuM
ssf
sfMfz
EkD
Ek
EkD
Weak force done by winds of Basymp2 with h
km
s
m
m
kgsm
kg
Cv
D
D 339130
00101200
1
3
2
Typical surface wind stress conditions
Annual mean wind stress on the ocean in units (Nm2) The green shade represents the magnitude of the stress Typical wind stress values in the Westerlies reach asymp 01 to 02 Nm2 The strongest stress component can be observed for the Roaring Forties the weakest component is in the Doldrums
sin2
2
vC
f
zMMfz aDD
EkEkD
Calculate the mass transport MEk for a typical wind stress of D = 025 Nm2
at the southern latitude of 40oS
sm
kg
s
m
N
fM
ssf
sf
DEk
3
15
2
15015
150
1067210379
250
1037940sin1029272
10292740sin2
About 2 tons of water are shifted within 1 sec by 1 meter to the left
Determine the wind velocity for a typical drag coefficient CD=0002
h
km
s
m
m
kgsm
kgs
C
Mfv
C
Mfv
aD
Ek
aD
Ek 1290
12000020
1013210379
3
315
2
About B=1-2 on the Beauford Scale
Impact on ocean currents The direction of Ekman transport depends on the hemisphere In the northern hemisphere this transport is at a 90o angle to the right of the wind direction and in the southern hemisphere it occurs at a 90o angle to the left of the wind direction This generates gyres circular motions in ocean basins limited by continental coasts
Reality is more complex because of additional forces due to friction and temperature effects which add to the eddy formation phenomenon
Reality is more complex because of additional forces due to the drag forces provided by the atmospheric wind circulation and by the friction forces exerted by deeper water layers
Humboldt Current The cold Peruvian current (an eastern boundary current) flows towards the equator along the coast of Ecuador and Peru It flows with a speed of 01 to 015[ms] In the absence of an El Nintildeo prevailing surface winds cause Ekman transport to the left or away from the coast with subsequent upwelling of cold water
Kon Tiki Heyerdahlrsquos thesis of populating Polynesia from the East rather than from the North-West by taking advantage of Humboldt current for sea travel
Pressure conditions Pressure gradient towards ocean depth can be expressed in terms of the salinity and temperature dependence of ocean water density
PaatmP
zsurface
zgPzP
PTSneglecting
PTSgz
P
gdz
dP
surface
refsurface
ref
5101
PakmPkmz
PakmPkmz
Pamm
kg
s
mPamPmz
7
7
6
32
5
10444
1011
10100100081910100100
Flow at larger depth is directed by the pressure gradient and the Coriolis force ldquogeostrophic flowrdquo
Approximately a linear increase of pressure with depth ndash in contrast the atmosphere displays an exponential decrease of pressure with altitude
Geostrophic flow
A geostrophic current is an oceanic flow in which the pressure gradient force is balanced by the Coriolis effect The direction of geostrophic flow is parallel to the isobars with the high pressure to the right of the flow in the Northern Hemisphere and the high pressure to the left in the Southern Hemisphere
Fluid or gaseous media move from high pressure to low pressure regions The force pushing the water is called the pressure gradient force Fp In a geostrophic flow water moves along the lines of equal pressure (isobars) instead of moving from a high pressure to low pressure region This occurs due to Earthrsquos rotation that cause the Coriolis force Fc The Coriolis force acts at right angles to the flow When it balances the pressure gradient force (Fp=Fc) the resulting flow becomes the geostrophic flow
Flow velocity Variations of pressure conditions or isobars with depth are associated with temperature and salinity conditions and can cause horizontal flow The pressure gradient is balanced by the Coriolis force This allows an estimate of the flow speed
Pzu
Puz
ˆ1
01
ˆ
f
velocityflowayielding
fFF pc
With f being the Coriolis parameter and g the earth acceleration L represents the distance over which the salinity and temperature dependent density anomaly changes Between 20oN and 40oN Lasymp2000km
L
z
f
gu
ref
surface
The pressure gradient is also affected along coastlines with upwards sloping ground level
Geostrophic ocean flow
With f being the Coriolis parameter and g the earth acceleration L represents the distance over which the salinity and temperature dependent density anomaly changes Between 20oN and 40oN Lasymp2000km
L
z
f
gu
ref
surface
Consider the gulf stream as a sample The is a pressure or density with depth that in combination with the previously discussed Coriolis force affects the direction and determines the surface flow velocity
Overall agreement within the range of local speed variations The maximum speed is observed at the western boundaries of the Gulf stream with v asymp 1ms while in the interior of the gyre the speed is much lower vasymp10cms
s
m
m
m
kg
m
kgs
s
m
u
sfsf
m
kg
m
kg
m
kg
L
z
f
gu
surface
ref
surface
13
3
15
2
15150
333
1030000002
041000
1000102927
819
10292710292730sin2
42226
Estimate the gulf stream surface velocity usurface assuming a distance between 20oN and 40oN of L=2000 km for a depth of z=1000 m
Gulf stream flow velocity
Ocean current simulation for different temperature zones
NASAGoddard Space Flight Center Scientific Visualization Studio
The flow pattern is complex and the flow velocity varies greatly Both observables are defined by coastal boundaries drag forces at the surface density gradients at deep depths and the Coriolis force
Single water drop flow
Geostrophic flow induced variations in ocean surface height
The curvature of the flow and the horizontal velocity gradient across the flow causes a pressure gradient perpendicular to the flow direction which translate into variations of the ocean surface height
6
2
614
101
819
1010110
L
m
s
ms
mms
g
uLf
kmLsfs
mufor 10001010 14
Ocean Surface Height
Example Gulf of Mexico
httpwwwaomlnoaagovphoddhosaltimetryphp
Flow pattern Water height
Altitude anomalies
Maps of sea level obtained from satellite altimetry measurements are used to derive surface ocean currents Higher values of sea level (oranges and reds) are associated with gyres and warm eddies while lower values are associated to colder features Drifter trajectories illustrate circulation features Sea height anomaly maps show the difference of sea level from average conditions while sea height maps show absolute values of the sea level
Changing average sea altitude levels
Based on observational data such as tide level measurements and satellite based altimetry
Sea level trend between 1992 and 2009 with respect to a reference level based on satellite altitude measurements Yellow and red regions show rising sea level while green and blue regions show falling sea level
For land and city people Bft 6 Bft 8
Bft 9 Bft 10 Bft 11 Bft 12
Bft 7
s
mBv 238360
A strong breeze of B=6 corresponds to wind speed of v=39 to 49 kmh at which long waves begin to form and white foam crests become frequent The drag force can be calculated to
2
2
2
3
3
2
5187518751212000010
0010512451200
mNAForNAs
mmA
m
kgF
Cs
m
h
kmv
m
kgvACF
DD
DaaDD
For a strong gale (B=12) v=35 ms the drag stress on the water will be
00250351200
367535120000250
3
2
2
3
Da
D
Cs
mv
m
kg
mNs
m
m
kgAF
Conversion from scale to wind velocity
Ekman transport The frictional drag force of wind with velocity v or wind stress x generating a water velocity u is balanced by the Coriolis force but drag decreases with depth z
sm
kgdz
fdzf
f
transportofdirectionvectordefines
ftermsvectorin
zuf
zz
zzz
Am
AF
D
D
0
0
ˆˆ
ˆ
ˆ
1ˆ
1
uM
Mzuz
z
τuz
uz
z
τuz
Ek
Ek
D
D
kg
N
mass
force
zA
mparameterCoriolissf
A
mufuAmAFvCAF ccaDDD
1
2
sin2
sin2
Ekman mass transport vector
dep
th v
ecto
r
Since the horizontal wind direction u moving the water is perpendicular to the depth vector z the direction of the frictional drag force D is perpendicular to both vectors and the magnitude is
zufz
f
MfMfz
D
EkEkD
sin2
90sin1 0
zuM
depth thdensity wi waterof increase linear moreless a is assumption
sm
kgdz
Ek
0
uMEk
Ekman transport
Example for Ekman transport What drag force (pressure) does it take at a latitude of 35oN to move water over a depth of 10 m within 1 minute by 100 m to the right
22
15
3
15015
150
1837000020101834
000201060
1001200
10183435sin1029272
10292735sin2
m
N
sm
kg
sm
kgsMfz
sm
kgm
s
m
m
kgzuM
ssf
sfMfz
EkD
Ek
EkD
Weak force done by winds of Basymp2 with h
km
s
m
m
kgsm
kg
Cv
D
D 339130
00101200
1
3
2
Typical surface wind stress conditions
Annual mean wind stress on the ocean in units (Nm2) The green shade represents the magnitude of the stress Typical wind stress values in the Westerlies reach asymp 01 to 02 Nm2 The strongest stress component can be observed for the Roaring Forties the weakest component is in the Doldrums
sin2
2
vC
f
zMMfz aDD
EkEkD
Calculate the mass transport MEk for a typical wind stress of D = 025 Nm2
at the southern latitude of 40oS
sm
kg
s
m
N
fM
ssf
sf
DEk
3
15
2
15015
150
1067210379
250
1037940sin1029272
10292740sin2
About 2 tons of water are shifted within 1 sec by 1 meter to the left
Determine the wind velocity for a typical drag coefficient CD=0002
h
km
s
m
m
kgsm
kgs
C
Mfv
C
Mfv
aD
Ek
aD
Ek 1290
12000020
1013210379
3
315
2
About B=1-2 on the Beauford Scale
Impact on ocean currents The direction of Ekman transport depends on the hemisphere In the northern hemisphere this transport is at a 90o angle to the right of the wind direction and in the southern hemisphere it occurs at a 90o angle to the left of the wind direction This generates gyres circular motions in ocean basins limited by continental coasts
Reality is more complex because of additional forces due to friction and temperature effects which add to the eddy formation phenomenon
Reality is more complex because of additional forces due to the drag forces provided by the atmospheric wind circulation and by the friction forces exerted by deeper water layers
Humboldt Current The cold Peruvian current (an eastern boundary current) flows towards the equator along the coast of Ecuador and Peru It flows with a speed of 01 to 015[ms] In the absence of an El Nintildeo prevailing surface winds cause Ekman transport to the left or away from the coast with subsequent upwelling of cold water
Kon Tiki Heyerdahlrsquos thesis of populating Polynesia from the East rather than from the North-West by taking advantage of Humboldt current for sea travel
Pressure conditions Pressure gradient towards ocean depth can be expressed in terms of the salinity and temperature dependence of ocean water density
PaatmP
zsurface
zgPzP
PTSneglecting
PTSgz
P
gdz
dP
surface
refsurface
ref
5101
PakmPkmz
PakmPkmz
Pamm
kg
s
mPamPmz
7
7
6
32
5
10444
1011
10100100081910100100
Flow at larger depth is directed by the pressure gradient and the Coriolis force ldquogeostrophic flowrdquo
Approximately a linear increase of pressure with depth ndash in contrast the atmosphere displays an exponential decrease of pressure with altitude
Geostrophic flow
A geostrophic current is an oceanic flow in which the pressure gradient force is balanced by the Coriolis effect The direction of geostrophic flow is parallel to the isobars with the high pressure to the right of the flow in the Northern Hemisphere and the high pressure to the left in the Southern Hemisphere
Fluid or gaseous media move from high pressure to low pressure regions The force pushing the water is called the pressure gradient force Fp In a geostrophic flow water moves along the lines of equal pressure (isobars) instead of moving from a high pressure to low pressure region This occurs due to Earthrsquos rotation that cause the Coriolis force Fc The Coriolis force acts at right angles to the flow When it balances the pressure gradient force (Fp=Fc) the resulting flow becomes the geostrophic flow
Flow velocity Variations of pressure conditions or isobars with depth are associated with temperature and salinity conditions and can cause horizontal flow The pressure gradient is balanced by the Coriolis force This allows an estimate of the flow speed
Pzu
Puz
ˆ1
01
ˆ
f
velocityflowayielding
fFF pc
With f being the Coriolis parameter and g the earth acceleration L represents the distance over which the salinity and temperature dependent density anomaly changes Between 20oN and 40oN Lasymp2000km
L
z
f
gu
ref
surface
The pressure gradient is also affected along coastlines with upwards sloping ground level
Geostrophic ocean flow
With f being the Coriolis parameter and g the earth acceleration L represents the distance over which the salinity and temperature dependent density anomaly changes Between 20oN and 40oN Lasymp2000km
L
z
f
gu
ref
surface
Consider the gulf stream as a sample The is a pressure or density with depth that in combination with the previously discussed Coriolis force affects the direction and determines the surface flow velocity
Overall agreement within the range of local speed variations The maximum speed is observed at the western boundaries of the Gulf stream with v asymp 1ms while in the interior of the gyre the speed is much lower vasymp10cms
s
m
m
m
kg
m
kgs
s
m
u
sfsf
m
kg
m
kg
m
kg
L
z
f
gu
surface
ref
surface
13
3
15
2
15150
333
1030000002
041000
1000102927
819
10292710292730sin2
42226
Estimate the gulf stream surface velocity usurface assuming a distance between 20oN and 40oN of L=2000 km for a depth of z=1000 m
Gulf stream flow velocity
Ocean current simulation for different temperature zones
NASAGoddard Space Flight Center Scientific Visualization Studio
The flow pattern is complex and the flow velocity varies greatly Both observables are defined by coastal boundaries drag forces at the surface density gradients at deep depths and the Coriolis force
Single water drop flow
Geostrophic flow induced variations in ocean surface height
The curvature of the flow and the horizontal velocity gradient across the flow causes a pressure gradient perpendicular to the flow direction which translate into variations of the ocean surface height
6
2
614
101
819
1010110
L
m
s
ms
mms
g
uLf
kmLsfs
mufor 10001010 14
Ocean Surface Height
Example Gulf of Mexico
httpwwwaomlnoaagovphoddhosaltimetryphp
Flow pattern Water height
Altitude anomalies
Maps of sea level obtained from satellite altimetry measurements are used to derive surface ocean currents Higher values of sea level (oranges and reds) are associated with gyres and warm eddies while lower values are associated to colder features Drifter trajectories illustrate circulation features Sea height anomaly maps show the difference of sea level from average conditions while sea height maps show absolute values of the sea level
Changing average sea altitude levels
Based on observational data such as tide level measurements and satellite based altimetry
Sea level trend between 1992 and 2009 with respect to a reference level based on satellite altitude measurements Yellow and red regions show rising sea level while green and blue regions show falling sea level
s
mBv 238360
A strong breeze of B=6 corresponds to wind speed of v=39 to 49 kmh at which long waves begin to form and white foam crests become frequent The drag force can be calculated to
2
2
2
3
3
2
5187518751212000010
0010512451200
mNAForNAs
mmA
m
kgF
Cs
m
h
kmv
m
kgvACF
DD
DaaDD
For a strong gale (B=12) v=35 ms the drag stress on the water will be
00250351200
367535120000250
3
2
2
3
Da
D
Cs
mv
m
kg
mNs
m
m
kgAF
Conversion from scale to wind velocity
Ekman transport The frictional drag force of wind with velocity v or wind stress x generating a water velocity u is balanced by the Coriolis force but drag decreases with depth z
sm
kgdz
fdzf
f
transportofdirectionvectordefines
ftermsvectorin
zuf
zz
zzz
Am
AF
D
D
0
0
ˆˆ
ˆ
ˆ
1ˆ
1
uM
Mzuz
z
τuz
uz
z
τuz
Ek
Ek
D
D
kg
N
mass
force
zA
mparameterCoriolissf
A
mufuAmAFvCAF ccaDDD
1
2
sin2
sin2
Ekman mass transport vector
dep
th v
ecto
r
Since the horizontal wind direction u moving the water is perpendicular to the depth vector z the direction of the frictional drag force D is perpendicular to both vectors and the magnitude is
zufz
f
MfMfz
D
EkEkD
sin2
90sin1 0
zuM
depth thdensity wi waterof increase linear moreless a is assumption
sm
kgdz
Ek
0
uMEk
Ekman transport
Example for Ekman transport What drag force (pressure) does it take at a latitude of 35oN to move water over a depth of 10 m within 1 minute by 100 m to the right
22
15
3
15015
150
1837000020101834
000201060
1001200
10183435sin1029272
10292735sin2
m
N
sm
kg
sm
kgsMfz
sm
kgm
s
m
m
kgzuM
ssf
sfMfz
EkD
Ek
EkD
Weak force done by winds of Basymp2 with h
km
s
m
m
kgsm
kg
Cv
D
D 339130
00101200
1
3
2
Typical surface wind stress conditions
Annual mean wind stress on the ocean in units (Nm2) The green shade represents the magnitude of the stress Typical wind stress values in the Westerlies reach asymp 01 to 02 Nm2 The strongest stress component can be observed for the Roaring Forties the weakest component is in the Doldrums
sin2
2
vC
f
zMMfz aDD
EkEkD
Calculate the mass transport MEk for a typical wind stress of D = 025 Nm2
at the southern latitude of 40oS
sm
kg
s
m
N
fM
ssf
sf
DEk
3
15
2
15015
150
1067210379
250
1037940sin1029272
10292740sin2
About 2 tons of water are shifted within 1 sec by 1 meter to the left
Determine the wind velocity for a typical drag coefficient CD=0002
h
km
s
m
m
kgsm
kgs
C
Mfv
C
Mfv
aD
Ek
aD
Ek 1290
12000020
1013210379
3
315
2
About B=1-2 on the Beauford Scale
Impact on ocean currents The direction of Ekman transport depends on the hemisphere In the northern hemisphere this transport is at a 90o angle to the right of the wind direction and in the southern hemisphere it occurs at a 90o angle to the left of the wind direction This generates gyres circular motions in ocean basins limited by continental coasts
Reality is more complex because of additional forces due to friction and temperature effects which add to the eddy formation phenomenon
Reality is more complex because of additional forces due to the drag forces provided by the atmospheric wind circulation and by the friction forces exerted by deeper water layers
Humboldt Current The cold Peruvian current (an eastern boundary current) flows towards the equator along the coast of Ecuador and Peru It flows with a speed of 01 to 015[ms] In the absence of an El Nintildeo prevailing surface winds cause Ekman transport to the left or away from the coast with subsequent upwelling of cold water
Kon Tiki Heyerdahlrsquos thesis of populating Polynesia from the East rather than from the North-West by taking advantage of Humboldt current for sea travel
Pressure conditions Pressure gradient towards ocean depth can be expressed in terms of the salinity and temperature dependence of ocean water density
PaatmP
zsurface
zgPzP
PTSneglecting
PTSgz
P
gdz
dP
surface
refsurface
ref
5101
PakmPkmz
PakmPkmz
Pamm
kg
s
mPamPmz
7
7
6
32
5
10444
1011
10100100081910100100
Flow at larger depth is directed by the pressure gradient and the Coriolis force ldquogeostrophic flowrdquo
Approximately a linear increase of pressure with depth ndash in contrast the atmosphere displays an exponential decrease of pressure with altitude
Geostrophic flow
A geostrophic current is an oceanic flow in which the pressure gradient force is balanced by the Coriolis effect The direction of geostrophic flow is parallel to the isobars with the high pressure to the right of the flow in the Northern Hemisphere and the high pressure to the left in the Southern Hemisphere
Fluid or gaseous media move from high pressure to low pressure regions The force pushing the water is called the pressure gradient force Fp In a geostrophic flow water moves along the lines of equal pressure (isobars) instead of moving from a high pressure to low pressure region This occurs due to Earthrsquos rotation that cause the Coriolis force Fc The Coriolis force acts at right angles to the flow When it balances the pressure gradient force (Fp=Fc) the resulting flow becomes the geostrophic flow
Flow velocity Variations of pressure conditions or isobars with depth are associated with temperature and salinity conditions and can cause horizontal flow The pressure gradient is balanced by the Coriolis force This allows an estimate of the flow speed
Pzu
Puz
ˆ1
01
ˆ
f
velocityflowayielding
fFF pc
With f being the Coriolis parameter and g the earth acceleration L represents the distance over which the salinity and temperature dependent density anomaly changes Between 20oN and 40oN Lasymp2000km
L
z
f
gu
ref
surface
The pressure gradient is also affected along coastlines with upwards sloping ground level
Geostrophic ocean flow
With f being the Coriolis parameter and g the earth acceleration L represents the distance over which the salinity and temperature dependent density anomaly changes Between 20oN and 40oN Lasymp2000km
L
z
f
gu
ref
surface
Consider the gulf stream as a sample The is a pressure or density with depth that in combination with the previously discussed Coriolis force affects the direction and determines the surface flow velocity
Overall agreement within the range of local speed variations The maximum speed is observed at the western boundaries of the Gulf stream with v asymp 1ms while in the interior of the gyre the speed is much lower vasymp10cms
s
m
m
m
kg
m
kgs
s
m
u
sfsf
m
kg
m
kg
m
kg
L
z
f
gu
surface
ref
surface
13
3
15
2
15150
333
1030000002
041000
1000102927
819
10292710292730sin2
42226
Estimate the gulf stream surface velocity usurface assuming a distance between 20oN and 40oN of L=2000 km for a depth of z=1000 m
Gulf stream flow velocity
Ocean current simulation for different temperature zones
NASAGoddard Space Flight Center Scientific Visualization Studio
The flow pattern is complex and the flow velocity varies greatly Both observables are defined by coastal boundaries drag forces at the surface density gradients at deep depths and the Coriolis force
Single water drop flow
Geostrophic flow induced variations in ocean surface height
The curvature of the flow and the horizontal velocity gradient across the flow causes a pressure gradient perpendicular to the flow direction which translate into variations of the ocean surface height
6
2
614
101
819
1010110
L
m
s
ms
mms
g
uLf
kmLsfs
mufor 10001010 14
Ocean Surface Height
Example Gulf of Mexico
httpwwwaomlnoaagovphoddhosaltimetryphp
Flow pattern Water height
Altitude anomalies
Maps of sea level obtained from satellite altimetry measurements are used to derive surface ocean currents Higher values of sea level (oranges and reds) are associated with gyres and warm eddies while lower values are associated to colder features Drifter trajectories illustrate circulation features Sea height anomaly maps show the difference of sea level from average conditions while sea height maps show absolute values of the sea level
Changing average sea altitude levels
Based on observational data such as tide level measurements and satellite based altimetry
Sea level trend between 1992 and 2009 with respect to a reference level based on satellite altitude measurements Yellow and red regions show rising sea level while green and blue regions show falling sea level
Ekman transport The frictional drag force of wind with velocity v or wind stress x generating a water velocity u is balanced by the Coriolis force but drag decreases with depth z
sm
kgdz
fdzf
f
transportofdirectionvectordefines
ftermsvectorin
zuf
zz
zzz
Am
AF
D
D
0
0
ˆˆ
ˆ
ˆ
1ˆ
1
uM
Mzuz
z
τuz
uz
z
τuz
Ek
Ek
D
D
kg
N
mass
force
zA
mparameterCoriolissf
A
mufuAmAFvCAF ccaDDD
1
2
sin2
sin2
Ekman mass transport vector
dep
th v
ecto
r
Since the horizontal wind direction u moving the water is perpendicular to the depth vector z the direction of the frictional drag force D is perpendicular to both vectors and the magnitude is
zufz
f
MfMfz
D
EkEkD
sin2
90sin1 0
zuM
depth thdensity wi waterof increase linear moreless a is assumption
sm
kgdz
Ek
0
uMEk
Ekman transport
Example for Ekman transport What drag force (pressure) does it take at a latitude of 35oN to move water over a depth of 10 m within 1 minute by 100 m to the right
22
15
3
15015
150
1837000020101834
000201060
1001200
10183435sin1029272
10292735sin2
m
N
sm
kg
sm
kgsMfz
sm
kgm
s
m
m
kgzuM
ssf
sfMfz
EkD
Ek
EkD
Weak force done by winds of Basymp2 with h
km
s
m
m
kgsm
kg
Cv
D
D 339130
00101200
1
3
2
Typical surface wind stress conditions
Annual mean wind stress on the ocean in units (Nm2) The green shade represents the magnitude of the stress Typical wind stress values in the Westerlies reach asymp 01 to 02 Nm2 The strongest stress component can be observed for the Roaring Forties the weakest component is in the Doldrums
sin2
2
vC
f
zMMfz aDD
EkEkD
Calculate the mass transport MEk for a typical wind stress of D = 025 Nm2
at the southern latitude of 40oS
sm
kg
s
m
N
fM
ssf
sf
DEk
3
15
2
15015
150
1067210379
250
1037940sin1029272
10292740sin2
About 2 tons of water are shifted within 1 sec by 1 meter to the left
Determine the wind velocity for a typical drag coefficient CD=0002
h
km
s
m
m
kgsm
kgs
C
Mfv
C
Mfv
aD
Ek
aD
Ek 1290
12000020
1013210379
3
315
2
About B=1-2 on the Beauford Scale
Impact on ocean currents The direction of Ekman transport depends on the hemisphere In the northern hemisphere this transport is at a 90o angle to the right of the wind direction and in the southern hemisphere it occurs at a 90o angle to the left of the wind direction This generates gyres circular motions in ocean basins limited by continental coasts
Reality is more complex because of additional forces due to friction and temperature effects which add to the eddy formation phenomenon
Reality is more complex because of additional forces due to the drag forces provided by the atmospheric wind circulation and by the friction forces exerted by deeper water layers
Humboldt Current The cold Peruvian current (an eastern boundary current) flows towards the equator along the coast of Ecuador and Peru It flows with a speed of 01 to 015[ms] In the absence of an El Nintildeo prevailing surface winds cause Ekman transport to the left or away from the coast with subsequent upwelling of cold water
Kon Tiki Heyerdahlrsquos thesis of populating Polynesia from the East rather than from the North-West by taking advantage of Humboldt current for sea travel
Pressure conditions Pressure gradient towards ocean depth can be expressed in terms of the salinity and temperature dependence of ocean water density
PaatmP
zsurface
zgPzP
PTSneglecting
PTSgz
P
gdz
dP
surface
refsurface
ref
5101
PakmPkmz
PakmPkmz
Pamm
kg
s
mPamPmz
7
7
6
32
5
10444
1011
10100100081910100100
Flow at larger depth is directed by the pressure gradient and the Coriolis force ldquogeostrophic flowrdquo
Approximately a linear increase of pressure with depth ndash in contrast the atmosphere displays an exponential decrease of pressure with altitude
Geostrophic flow
A geostrophic current is an oceanic flow in which the pressure gradient force is balanced by the Coriolis effect The direction of geostrophic flow is parallel to the isobars with the high pressure to the right of the flow in the Northern Hemisphere and the high pressure to the left in the Southern Hemisphere
Fluid or gaseous media move from high pressure to low pressure regions The force pushing the water is called the pressure gradient force Fp In a geostrophic flow water moves along the lines of equal pressure (isobars) instead of moving from a high pressure to low pressure region This occurs due to Earthrsquos rotation that cause the Coriolis force Fc The Coriolis force acts at right angles to the flow When it balances the pressure gradient force (Fp=Fc) the resulting flow becomes the geostrophic flow
Flow velocity Variations of pressure conditions or isobars with depth are associated with temperature and salinity conditions and can cause horizontal flow The pressure gradient is balanced by the Coriolis force This allows an estimate of the flow speed
Pzu
Puz
ˆ1
01
ˆ
f
velocityflowayielding
fFF pc
With f being the Coriolis parameter and g the earth acceleration L represents the distance over which the salinity and temperature dependent density anomaly changes Between 20oN and 40oN Lasymp2000km
L
z
f
gu
ref
surface
The pressure gradient is also affected along coastlines with upwards sloping ground level
Geostrophic ocean flow
With f being the Coriolis parameter and g the earth acceleration L represents the distance over which the salinity and temperature dependent density anomaly changes Between 20oN and 40oN Lasymp2000km
L
z
f
gu
ref
surface
Consider the gulf stream as a sample The is a pressure or density with depth that in combination with the previously discussed Coriolis force affects the direction and determines the surface flow velocity
Overall agreement within the range of local speed variations The maximum speed is observed at the western boundaries of the Gulf stream with v asymp 1ms while in the interior of the gyre the speed is much lower vasymp10cms
s
m
m
m
kg
m
kgs
s
m
u
sfsf
m
kg
m
kg
m
kg
L
z
f
gu
surface
ref
surface
13
3
15
2
15150
333
1030000002
041000
1000102927
819
10292710292730sin2
42226
Estimate the gulf stream surface velocity usurface assuming a distance between 20oN and 40oN of L=2000 km for a depth of z=1000 m
Gulf stream flow velocity
Ocean current simulation for different temperature zones
NASAGoddard Space Flight Center Scientific Visualization Studio
The flow pattern is complex and the flow velocity varies greatly Both observables are defined by coastal boundaries drag forces at the surface density gradients at deep depths and the Coriolis force
Single water drop flow
Geostrophic flow induced variations in ocean surface height
The curvature of the flow and the horizontal velocity gradient across the flow causes a pressure gradient perpendicular to the flow direction which translate into variations of the ocean surface height
6
2
614
101
819
1010110
L
m
s
ms
mms
g
uLf
kmLsfs
mufor 10001010 14
Ocean Surface Height
Example Gulf of Mexico
httpwwwaomlnoaagovphoddhosaltimetryphp
Flow pattern Water height
Altitude anomalies
Maps of sea level obtained from satellite altimetry measurements are used to derive surface ocean currents Higher values of sea level (oranges and reds) are associated with gyres and warm eddies while lower values are associated to colder features Drifter trajectories illustrate circulation features Sea height anomaly maps show the difference of sea level from average conditions while sea height maps show absolute values of the sea level
Changing average sea altitude levels
Based on observational data such as tide level measurements and satellite based altimetry
Sea level trend between 1992 and 2009 with respect to a reference level based on satellite altitude measurements Yellow and red regions show rising sea level while green and blue regions show falling sea level
dep
th v
ecto
r
Since the horizontal wind direction u moving the water is perpendicular to the depth vector z the direction of the frictional drag force D is perpendicular to both vectors and the magnitude is
zufz
f
MfMfz
D
EkEkD
sin2
90sin1 0
zuM
depth thdensity wi waterof increase linear moreless a is assumption
sm
kgdz
Ek
0
uMEk
Ekman transport
Example for Ekman transport What drag force (pressure) does it take at a latitude of 35oN to move water over a depth of 10 m within 1 minute by 100 m to the right
22
15
3
15015
150
1837000020101834
000201060
1001200
10183435sin1029272
10292735sin2
m
N
sm
kg
sm
kgsMfz
sm
kgm
s
m
m
kgzuM
ssf
sfMfz
EkD
Ek
EkD
Weak force done by winds of Basymp2 with h
km
s
m
m
kgsm
kg
Cv
D
D 339130
00101200
1
3
2
Typical surface wind stress conditions
Annual mean wind stress on the ocean in units (Nm2) The green shade represents the magnitude of the stress Typical wind stress values in the Westerlies reach asymp 01 to 02 Nm2 The strongest stress component can be observed for the Roaring Forties the weakest component is in the Doldrums
sin2
2
vC
f
zMMfz aDD
EkEkD
Calculate the mass transport MEk for a typical wind stress of D = 025 Nm2
at the southern latitude of 40oS
sm
kg
s
m
N
fM
ssf
sf
DEk
3
15
2
15015
150
1067210379
250
1037940sin1029272
10292740sin2
About 2 tons of water are shifted within 1 sec by 1 meter to the left
Determine the wind velocity for a typical drag coefficient CD=0002
h
km
s
m
m
kgsm
kgs
C
Mfv
C
Mfv
aD
Ek
aD
Ek 1290
12000020
1013210379
3
315
2
About B=1-2 on the Beauford Scale
Impact on ocean currents The direction of Ekman transport depends on the hemisphere In the northern hemisphere this transport is at a 90o angle to the right of the wind direction and in the southern hemisphere it occurs at a 90o angle to the left of the wind direction This generates gyres circular motions in ocean basins limited by continental coasts
Reality is more complex because of additional forces due to friction and temperature effects which add to the eddy formation phenomenon
Reality is more complex because of additional forces due to the drag forces provided by the atmospheric wind circulation and by the friction forces exerted by deeper water layers
Humboldt Current The cold Peruvian current (an eastern boundary current) flows towards the equator along the coast of Ecuador and Peru It flows with a speed of 01 to 015[ms] In the absence of an El Nintildeo prevailing surface winds cause Ekman transport to the left or away from the coast with subsequent upwelling of cold water
Kon Tiki Heyerdahlrsquos thesis of populating Polynesia from the East rather than from the North-West by taking advantage of Humboldt current for sea travel
Pressure conditions Pressure gradient towards ocean depth can be expressed in terms of the salinity and temperature dependence of ocean water density
PaatmP
zsurface
zgPzP
PTSneglecting
PTSgz
P
gdz
dP
surface
refsurface
ref
5101
PakmPkmz
PakmPkmz
Pamm
kg
s
mPamPmz
7
7
6
32
5
10444
1011
10100100081910100100
Flow at larger depth is directed by the pressure gradient and the Coriolis force ldquogeostrophic flowrdquo
Approximately a linear increase of pressure with depth ndash in contrast the atmosphere displays an exponential decrease of pressure with altitude
Geostrophic flow
A geostrophic current is an oceanic flow in which the pressure gradient force is balanced by the Coriolis effect The direction of geostrophic flow is parallel to the isobars with the high pressure to the right of the flow in the Northern Hemisphere and the high pressure to the left in the Southern Hemisphere
Fluid or gaseous media move from high pressure to low pressure regions The force pushing the water is called the pressure gradient force Fp In a geostrophic flow water moves along the lines of equal pressure (isobars) instead of moving from a high pressure to low pressure region This occurs due to Earthrsquos rotation that cause the Coriolis force Fc The Coriolis force acts at right angles to the flow When it balances the pressure gradient force (Fp=Fc) the resulting flow becomes the geostrophic flow
Flow velocity Variations of pressure conditions or isobars with depth are associated with temperature and salinity conditions and can cause horizontal flow The pressure gradient is balanced by the Coriolis force This allows an estimate of the flow speed
Pzu
Puz
ˆ1
01
ˆ
f
velocityflowayielding
fFF pc
With f being the Coriolis parameter and g the earth acceleration L represents the distance over which the salinity and temperature dependent density anomaly changes Between 20oN and 40oN Lasymp2000km
L
z
f
gu
ref
surface
The pressure gradient is also affected along coastlines with upwards sloping ground level
Geostrophic ocean flow
With f being the Coriolis parameter and g the earth acceleration L represents the distance over which the salinity and temperature dependent density anomaly changes Between 20oN and 40oN Lasymp2000km
L
z
f
gu
ref
surface
Consider the gulf stream as a sample The is a pressure or density with depth that in combination with the previously discussed Coriolis force affects the direction and determines the surface flow velocity
Overall agreement within the range of local speed variations The maximum speed is observed at the western boundaries of the Gulf stream with v asymp 1ms while in the interior of the gyre the speed is much lower vasymp10cms
s
m
m
m
kg
m
kgs
s
m
u
sfsf
m
kg
m
kg
m
kg
L
z
f
gu
surface
ref
surface
13
3
15
2
15150
333
1030000002
041000
1000102927
819
10292710292730sin2
42226
Estimate the gulf stream surface velocity usurface assuming a distance between 20oN and 40oN of L=2000 km for a depth of z=1000 m
Gulf stream flow velocity
Ocean current simulation for different temperature zones
NASAGoddard Space Flight Center Scientific Visualization Studio
The flow pattern is complex and the flow velocity varies greatly Both observables are defined by coastal boundaries drag forces at the surface density gradients at deep depths and the Coriolis force
Single water drop flow
Geostrophic flow induced variations in ocean surface height
The curvature of the flow and the horizontal velocity gradient across the flow causes a pressure gradient perpendicular to the flow direction which translate into variations of the ocean surface height
6
2
614
101
819
1010110
L
m
s
ms
mms
g
uLf
kmLsfs
mufor 10001010 14
Ocean Surface Height
Example Gulf of Mexico
httpwwwaomlnoaagovphoddhosaltimetryphp
Flow pattern Water height
Altitude anomalies
Maps of sea level obtained from satellite altimetry measurements are used to derive surface ocean currents Higher values of sea level (oranges and reds) are associated with gyres and warm eddies while lower values are associated to colder features Drifter trajectories illustrate circulation features Sea height anomaly maps show the difference of sea level from average conditions while sea height maps show absolute values of the sea level
Changing average sea altitude levels
Based on observational data such as tide level measurements and satellite based altimetry
Sea level trend between 1992 and 2009 with respect to a reference level based on satellite altitude measurements Yellow and red regions show rising sea level while green and blue regions show falling sea level
Example for Ekman transport What drag force (pressure) does it take at a latitude of 35oN to move water over a depth of 10 m within 1 minute by 100 m to the right
22
15
3
15015
150
1837000020101834
000201060
1001200
10183435sin1029272
10292735sin2
m
N
sm
kg
sm
kgsMfz
sm
kgm
s
m
m
kgzuM
ssf
sfMfz
EkD
Ek
EkD
Weak force done by winds of Basymp2 with h
km
s
m
m
kgsm
kg
Cv
D
D 339130
00101200
1
3
2
Typical surface wind stress conditions
Annual mean wind stress on the ocean in units (Nm2) The green shade represents the magnitude of the stress Typical wind stress values in the Westerlies reach asymp 01 to 02 Nm2 The strongest stress component can be observed for the Roaring Forties the weakest component is in the Doldrums
sin2
2
vC
f
zMMfz aDD
EkEkD
Calculate the mass transport MEk for a typical wind stress of D = 025 Nm2
at the southern latitude of 40oS
sm
kg
s
m
N
fM
ssf
sf
DEk
3
15
2
15015
150
1067210379
250
1037940sin1029272
10292740sin2
About 2 tons of water are shifted within 1 sec by 1 meter to the left
Determine the wind velocity for a typical drag coefficient CD=0002
h
km
s
m
m
kgsm
kgs
C
Mfv
C
Mfv
aD
Ek
aD
Ek 1290
12000020
1013210379
3
315
2
About B=1-2 on the Beauford Scale
Impact on ocean currents The direction of Ekman transport depends on the hemisphere In the northern hemisphere this transport is at a 90o angle to the right of the wind direction and in the southern hemisphere it occurs at a 90o angle to the left of the wind direction This generates gyres circular motions in ocean basins limited by continental coasts
Reality is more complex because of additional forces due to friction and temperature effects which add to the eddy formation phenomenon
Reality is more complex because of additional forces due to the drag forces provided by the atmospheric wind circulation and by the friction forces exerted by deeper water layers
Humboldt Current The cold Peruvian current (an eastern boundary current) flows towards the equator along the coast of Ecuador and Peru It flows with a speed of 01 to 015[ms] In the absence of an El Nintildeo prevailing surface winds cause Ekman transport to the left or away from the coast with subsequent upwelling of cold water
Kon Tiki Heyerdahlrsquos thesis of populating Polynesia from the East rather than from the North-West by taking advantage of Humboldt current for sea travel
Pressure conditions Pressure gradient towards ocean depth can be expressed in terms of the salinity and temperature dependence of ocean water density
PaatmP
zsurface
zgPzP
PTSneglecting
PTSgz
P
gdz
dP
surface
refsurface
ref
5101
PakmPkmz
PakmPkmz
Pamm
kg
s
mPamPmz
7
7
6
32
5
10444
1011
10100100081910100100
Flow at larger depth is directed by the pressure gradient and the Coriolis force ldquogeostrophic flowrdquo
Approximately a linear increase of pressure with depth ndash in contrast the atmosphere displays an exponential decrease of pressure with altitude
Geostrophic flow
A geostrophic current is an oceanic flow in which the pressure gradient force is balanced by the Coriolis effect The direction of geostrophic flow is parallel to the isobars with the high pressure to the right of the flow in the Northern Hemisphere and the high pressure to the left in the Southern Hemisphere
Fluid or gaseous media move from high pressure to low pressure regions The force pushing the water is called the pressure gradient force Fp In a geostrophic flow water moves along the lines of equal pressure (isobars) instead of moving from a high pressure to low pressure region This occurs due to Earthrsquos rotation that cause the Coriolis force Fc The Coriolis force acts at right angles to the flow When it balances the pressure gradient force (Fp=Fc) the resulting flow becomes the geostrophic flow
Flow velocity Variations of pressure conditions or isobars with depth are associated with temperature and salinity conditions and can cause horizontal flow The pressure gradient is balanced by the Coriolis force This allows an estimate of the flow speed
Pzu
Puz
ˆ1
01
ˆ
f
velocityflowayielding
fFF pc
With f being the Coriolis parameter and g the earth acceleration L represents the distance over which the salinity and temperature dependent density anomaly changes Between 20oN and 40oN Lasymp2000km
L
z
f
gu
ref
surface
The pressure gradient is also affected along coastlines with upwards sloping ground level
Geostrophic ocean flow
With f being the Coriolis parameter and g the earth acceleration L represents the distance over which the salinity and temperature dependent density anomaly changes Between 20oN and 40oN Lasymp2000km
L
z
f
gu
ref
surface
Consider the gulf stream as a sample The is a pressure or density with depth that in combination with the previously discussed Coriolis force affects the direction and determines the surface flow velocity
Overall agreement within the range of local speed variations The maximum speed is observed at the western boundaries of the Gulf stream with v asymp 1ms while in the interior of the gyre the speed is much lower vasymp10cms
s
m
m
m
kg
m
kgs
s
m
u
sfsf
m
kg
m
kg
m
kg
L
z
f
gu
surface
ref
surface
13
3
15
2
15150
333
1030000002
041000
1000102927
819
10292710292730sin2
42226
Estimate the gulf stream surface velocity usurface assuming a distance between 20oN and 40oN of L=2000 km for a depth of z=1000 m
Gulf stream flow velocity
Ocean current simulation for different temperature zones
NASAGoddard Space Flight Center Scientific Visualization Studio
The flow pattern is complex and the flow velocity varies greatly Both observables are defined by coastal boundaries drag forces at the surface density gradients at deep depths and the Coriolis force
Single water drop flow
Geostrophic flow induced variations in ocean surface height
The curvature of the flow and the horizontal velocity gradient across the flow causes a pressure gradient perpendicular to the flow direction which translate into variations of the ocean surface height
6
2
614
101
819
1010110
L
m
s
ms
mms
g
uLf
kmLsfs
mufor 10001010 14
Ocean Surface Height
Example Gulf of Mexico
httpwwwaomlnoaagovphoddhosaltimetryphp
Flow pattern Water height
Altitude anomalies
Maps of sea level obtained from satellite altimetry measurements are used to derive surface ocean currents Higher values of sea level (oranges and reds) are associated with gyres and warm eddies while lower values are associated to colder features Drifter trajectories illustrate circulation features Sea height anomaly maps show the difference of sea level from average conditions while sea height maps show absolute values of the sea level
Changing average sea altitude levels
Based on observational data such as tide level measurements and satellite based altimetry
Sea level trend between 1992 and 2009 with respect to a reference level based on satellite altitude measurements Yellow and red regions show rising sea level while green and blue regions show falling sea level
Typical surface wind stress conditions
Annual mean wind stress on the ocean in units (Nm2) The green shade represents the magnitude of the stress Typical wind stress values in the Westerlies reach asymp 01 to 02 Nm2 The strongest stress component can be observed for the Roaring Forties the weakest component is in the Doldrums
sin2
2
vC
f
zMMfz aDD
EkEkD
Calculate the mass transport MEk for a typical wind stress of D = 025 Nm2
at the southern latitude of 40oS
sm
kg
s
m
N
fM
ssf
sf
DEk
3
15
2
15015
150
1067210379
250
1037940sin1029272
10292740sin2
About 2 tons of water are shifted within 1 sec by 1 meter to the left
Determine the wind velocity for a typical drag coefficient CD=0002
h
km
s
m
m
kgsm
kgs
C
Mfv
C
Mfv
aD
Ek
aD
Ek 1290
12000020
1013210379
3
315
2
About B=1-2 on the Beauford Scale
Impact on ocean currents The direction of Ekman transport depends on the hemisphere In the northern hemisphere this transport is at a 90o angle to the right of the wind direction and in the southern hemisphere it occurs at a 90o angle to the left of the wind direction This generates gyres circular motions in ocean basins limited by continental coasts
Reality is more complex because of additional forces due to friction and temperature effects which add to the eddy formation phenomenon
Reality is more complex because of additional forces due to the drag forces provided by the atmospheric wind circulation and by the friction forces exerted by deeper water layers
Humboldt Current The cold Peruvian current (an eastern boundary current) flows towards the equator along the coast of Ecuador and Peru It flows with a speed of 01 to 015[ms] In the absence of an El Nintildeo prevailing surface winds cause Ekman transport to the left or away from the coast with subsequent upwelling of cold water
Kon Tiki Heyerdahlrsquos thesis of populating Polynesia from the East rather than from the North-West by taking advantage of Humboldt current for sea travel
Pressure conditions Pressure gradient towards ocean depth can be expressed in terms of the salinity and temperature dependence of ocean water density
PaatmP
zsurface
zgPzP
PTSneglecting
PTSgz
P
gdz
dP
surface
refsurface
ref
5101
PakmPkmz
PakmPkmz
Pamm
kg
s
mPamPmz
7
7
6
32
5
10444
1011
10100100081910100100
Flow at larger depth is directed by the pressure gradient and the Coriolis force ldquogeostrophic flowrdquo
Approximately a linear increase of pressure with depth ndash in contrast the atmosphere displays an exponential decrease of pressure with altitude
Geostrophic flow
A geostrophic current is an oceanic flow in which the pressure gradient force is balanced by the Coriolis effect The direction of geostrophic flow is parallel to the isobars with the high pressure to the right of the flow in the Northern Hemisphere and the high pressure to the left in the Southern Hemisphere
Fluid or gaseous media move from high pressure to low pressure regions The force pushing the water is called the pressure gradient force Fp In a geostrophic flow water moves along the lines of equal pressure (isobars) instead of moving from a high pressure to low pressure region This occurs due to Earthrsquos rotation that cause the Coriolis force Fc The Coriolis force acts at right angles to the flow When it balances the pressure gradient force (Fp=Fc) the resulting flow becomes the geostrophic flow
Flow velocity Variations of pressure conditions or isobars with depth are associated with temperature and salinity conditions and can cause horizontal flow The pressure gradient is balanced by the Coriolis force This allows an estimate of the flow speed
Pzu
Puz
ˆ1
01
ˆ
f
velocityflowayielding
fFF pc
With f being the Coriolis parameter and g the earth acceleration L represents the distance over which the salinity and temperature dependent density anomaly changes Between 20oN and 40oN Lasymp2000km
L
z
f
gu
ref
surface
The pressure gradient is also affected along coastlines with upwards sloping ground level
Geostrophic ocean flow
With f being the Coriolis parameter and g the earth acceleration L represents the distance over which the salinity and temperature dependent density anomaly changes Between 20oN and 40oN Lasymp2000km
L
z
f
gu
ref
surface
Consider the gulf stream as a sample The is a pressure or density with depth that in combination with the previously discussed Coriolis force affects the direction and determines the surface flow velocity
Overall agreement within the range of local speed variations The maximum speed is observed at the western boundaries of the Gulf stream with v asymp 1ms while in the interior of the gyre the speed is much lower vasymp10cms
s
m
m
m
kg
m
kgs
s
m
u
sfsf
m
kg
m
kg
m
kg
L
z
f
gu
surface
ref
surface
13
3
15
2
15150
333
1030000002
041000
1000102927
819
10292710292730sin2
42226
Estimate the gulf stream surface velocity usurface assuming a distance between 20oN and 40oN of L=2000 km for a depth of z=1000 m
Gulf stream flow velocity
Ocean current simulation for different temperature zones
NASAGoddard Space Flight Center Scientific Visualization Studio
The flow pattern is complex and the flow velocity varies greatly Both observables are defined by coastal boundaries drag forces at the surface density gradients at deep depths and the Coriolis force
Single water drop flow
Geostrophic flow induced variations in ocean surface height
The curvature of the flow and the horizontal velocity gradient across the flow causes a pressure gradient perpendicular to the flow direction which translate into variations of the ocean surface height
6
2
614
101
819
1010110
L
m
s
ms
mms
g
uLf
kmLsfs
mufor 10001010 14
Ocean Surface Height
Example Gulf of Mexico
httpwwwaomlnoaagovphoddhosaltimetryphp
Flow pattern Water height
Altitude anomalies
Maps of sea level obtained from satellite altimetry measurements are used to derive surface ocean currents Higher values of sea level (oranges and reds) are associated with gyres and warm eddies while lower values are associated to colder features Drifter trajectories illustrate circulation features Sea height anomaly maps show the difference of sea level from average conditions while sea height maps show absolute values of the sea level
Changing average sea altitude levels
Based on observational data such as tide level measurements and satellite based altimetry
Sea level trend between 1992 and 2009 with respect to a reference level based on satellite altitude measurements Yellow and red regions show rising sea level while green and blue regions show falling sea level
sin2
2
vC
f
zMMfz aDD
EkEkD
Calculate the mass transport MEk for a typical wind stress of D = 025 Nm2
at the southern latitude of 40oS
sm
kg
s
m
N
fM
ssf
sf
DEk
3
15
2
15015
150
1067210379
250
1037940sin1029272
10292740sin2
About 2 tons of water are shifted within 1 sec by 1 meter to the left
Determine the wind velocity for a typical drag coefficient CD=0002
h
km
s
m
m
kgsm
kgs
C
Mfv
C
Mfv
aD
Ek
aD
Ek 1290
12000020
1013210379
3
315
2
About B=1-2 on the Beauford Scale
Impact on ocean currents The direction of Ekman transport depends on the hemisphere In the northern hemisphere this transport is at a 90o angle to the right of the wind direction and in the southern hemisphere it occurs at a 90o angle to the left of the wind direction This generates gyres circular motions in ocean basins limited by continental coasts
Reality is more complex because of additional forces due to friction and temperature effects which add to the eddy formation phenomenon
Reality is more complex because of additional forces due to the drag forces provided by the atmospheric wind circulation and by the friction forces exerted by deeper water layers
Humboldt Current The cold Peruvian current (an eastern boundary current) flows towards the equator along the coast of Ecuador and Peru It flows with a speed of 01 to 015[ms] In the absence of an El Nintildeo prevailing surface winds cause Ekman transport to the left or away from the coast with subsequent upwelling of cold water
Kon Tiki Heyerdahlrsquos thesis of populating Polynesia from the East rather than from the North-West by taking advantage of Humboldt current for sea travel
Pressure conditions Pressure gradient towards ocean depth can be expressed in terms of the salinity and temperature dependence of ocean water density
PaatmP
zsurface
zgPzP
PTSneglecting
PTSgz
P
gdz
dP
surface
refsurface
ref
5101
PakmPkmz
PakmPkmz
Pamm
kg
s
mPamPmz
7
7
6
32
5
10444
1011
10100100081910100100
Flow at larger depth is directed by the pressure gradient and the Coriolis force ldquogeostrophic flowrdquo
Approximately a linear increase of pressure with depth ndash in contrast the atmosphere displays an exponential decrease of pressure with altitude
Geostrophic flow
A geostrophic current is an oceanic flow in which the pressure gradient force is balanced by the Coriolis effect The direction of geostrophic flow is parallel to the isobars with the high pressure to the right of the flow in the Northern Hemisphere and the high pressure to the left in the Southern Hemisphere
Fluid or gaseous media move from high pressure to low pressure regions The force pushing the water is called the pressure gradient force Fp In a geostrophic flow water moves along the lines of equal pressure (isobars) instead of moving from a high pressure to low pressure region This occurs due to Earthrsquos rotation that cause the Coriolis force Fc The Coriolis force acts at right angles to the flow When it balances the pressure gradient force (Fp=Fc) the resulting flow becomes the geostrophic flow
Flow velocity Variations of pressure conditions or isobars with depth are associated with temperature and salinity conditions and can cause horizontal flow The pressure gradient is balanced by the Coriolis force This allows an estimate of the flow speed
Pzu
Puz
ˆ1
01
ˆ
f
velocityflowayielding
fFF pc
With f being the Coriolis parameter and g the earth acceleration L represents the distance over which the salinity and temperature dependent density anomaly changes Between 20oN and 40oN Lasymp2000km
L
z
f
gu
ref
surface
The pressure gradient is also affected along coastlines with upwards sloping ground level
Geostrophic ocean flow
With f being the Coriolis parameter and g the earth acceleration L represents the distance over which the salinity and temperature dependent density anomaly changes Between 20oN and 40oN Lasymp2000km
L
z
f
gu
ref
surface
Consider the gulf stream as a sample The is a pressure or density with depth that in combination with the previously discussed Coriolis force affects the direction and determines the surface flow velocity
Overall agreement within the range of local speed variations The maximum speed is observed at the western boundaries of the Gulf stream with v asymp 1ms while in the interior of the gyre the speed is much lower vasymp10cms
s
m
m
m
kg
m
kgs
s
m
u
sfsf
m
kg
m
kg
m
kg
L
z
f
gu
surface
ref
surface
13
3
15
2
15150
333
1030000002
041000
1000102927
819
10292710292730sin2
42226
Estimate the gulf stream surface velocity usurface assuming a distance between 20oN and 40oN of L=2000 km for a depth of z=1000 m
Gulf stream flow velocity
Ocean current simulation for different temperature zones
NASAGoddard Space Flight Center Scientific Visualization Studio
The flow pattern is complex and the flow velocity varies greatly Both observables are defined by coastal boundaries drag forces at the surface density gradients at deep depths and the Coriolis force
Single water drop flow
Geostrophic flow induced variations in ocean surface height
The curvature of the flow and the horizontal velocity gradient across the flow causes a pressure gradient perpendicular to the flow direction which translate into variations of the ocean surface height
6
2
614
101
819
1010110
L
m
s
ms
mms
g
uLf
kmLsfs
mufor 10001010 14
Ocean Surface Height
Example Gulf of Mexico
httpwwwaomlnoaagovphoddhosaltimetryphp
Flow pattern Water height
Altitude anomalies
Maps of sea level obtained from satellite altimetry measurements are used to derive surface ocean currents Higher values of sea level (oranges and reds) are associated with gyres and warm eddies while lower values are associated to colder features Drifter trajectories illustrate circulation features Sea height anomaly maps show the difference of sea level from average conditions while sea height maps show absolute values of the sea level
Changing average sea altitude levels
Based on observational data such as tide level measurements and satellite based altimetry
Sea level trend between 1992 and 2009 with respect to a reference level based on satellite altitude measurements Yellow and red regions show rising sea level while green and blue regions show falling sea level
Impact on ocean currents The direction of Ekman transport depends on the hemisphere In the northern hemisphere this transport is at a 90o angle to the right of the wind direction and in the southern hemisphere it occurs at a 90o angle to the left of the wind direction This generates gyres circular motions in ocean basins limited by continental coasts
Reality is more complex because of additional forces due to friction and temperature effects which add to the eddy formation phenomenon
Reality is more complex because of additional forces due to the drag forces provided by the atmospheric wind circulation and by the friction forces exerted by deeper water layers
Humboldt Current The cold Peruvian current (an eastern boundary current) flows towards the equator along the coast of Ecuador and Peru It flows with a speed of 01 to 015[ms] In the absence of an El Nintildeo prevailing surface winds cause Ekman transport to the left or away from the coast with subsequent upwelling of cold water
Kon Tiki Heyerdahlrsquos thesis of populating Polynesia from the East rather than from the North-West by taking advantage of Humboldt current for sea travel
Pressure conditions Pressure gradient towards ocean depth can be expressed in terms of the salinity and temperature dependence of ocean water density
PaatmP
zsurface
zgPzP
PTSneglecting
PTSgz
P
gdz
dP
surface
refsurface
ref
5101
PakmPkmz
PakmPkmz
Pamm
kg
s
mPamPmz
7
7
6
32
5
10444
1011
10100100081910100100
Flow at larger depth is directed by the pressure gradient and the Coriolis force ldquogeostrophic flowrdquo
Approximately a linear increase of pressure with depth ndash in contrast the atmosphere displays an exponential decrease of pressure with altitude
Geostrophic flow
A geostrophic current is an oceanic flow in which the pressure gradient force is balanced by the Coriolis effect The direction of geostrophic flow is parallel to the isobars with the high pressure to the right of the flow in the Northern Hemisphere and the high pressure to the left in the Southern Hemisphere
Fluid or gaseous media move from high pressure to low pressure regions The force pushing the water is called the pressure gradient force Fp In a geostrophic flow water moves along the lines of equal pressure (isobars) instead of moving from a high pressure to low pressure region This occurs due to Earthrsquos rotation that cause the Coriolis force Fc The Coriolis force acts at right angles to the flow When it balances the pressure gradient force (Fp=Fc) the resulting flow becomes the geostrophic flow
Flow velocity Variations of pressure conditions or isobars with depth are associated with temperature and salinity conditions and can cause horizontal flow The pressure gradient is balanced by the Coriolis force This allows an estimate of the flow speed
Pzu
Puz
ˆ1
01
ˆ
f
velocityflowayielding
fFF pc
With f being the Coriolis parameter and g the earth acceleration L represents the distance over which the salinity and temperature dependent density anomaly changes Between 20oN and 40oN Lasymp2000km
L
z
f
gu
ref
surface
The pressure gradient is also affected along coastlines with upwards sloping ground level
Geostrophic ocean flow
With f being the Coriolis parameter and g the earth acceleration L represents the distance over which the salinity and temperature dependent density anomaly changes Between 20oN and 40oN Lasymp2000km
L
z
f
gu
ref
surface
Consider the gulf stream as a sample The is a pressure or density with depth that in combination with the previously discussed Coriolis force affects the direction and determines the surface flow velocity
Overall agreement within the range of local speed variations The maximum speed is observed at the western boundaries of the Gulf stream with v asymp 1ms while in the interior of the gyre the speed is much lower vasymp10cms
s
m
m
m
kg
m
kgs
s
m
u
sfsf
m
kg
m
kg
m
kg
L
z
f
gu
surface
ref
surface
13
3
15
2
15150
333
1030000002
041000
1000102927
819
10292710292730sin2
42226
Estimate the gulf stream surface velocity usurface assuming a distance between 20oN and 40oN of L=2000 km for a depth of z=1000 m
Gulf stream flow velocity
Ocean current simulation for different temperature zones
NASAGoddard Space Flight Center Scientific Visualization Studio
The flow pattern is complex and the flow velocity varies greatly Both observables are defined by coastal boundaries drag forces at the surface density gradients at deep depths and the Coriolis force
Single water drop flow
Geostrophic flow induced variations in ocean surface height
The curvature of the flow and the horizontal velocity gradient across the flow causes a pressure gradient perpendicular to the flow direction which translate into variations of the ocean surface height
6
2
614
101
819
1010110
L
m
s
ms
mms
g
uLf
kmLsfs
mufor 10001010 14
Ocean Surface Height
Example Gulf of Mexico
httpwwwaomlnoaagovphoddhosaltimetryphp
Flow pattern Water height
Altitude anomalies
Maps of sea level obtained from satellite altimetry measurements are used to derive surface ocean currents Higher values of sea level (oranges and reds) are associated with gyres and warm eddies while lower values are associated to colder features Drifter trajectories illustrate circulation features Sea height anomaly maps show the difference of sea level from average conditions while sea height maps show absolute values of the sea level
Changing average sea altitude levels
Based on observational data such as tide level measurements and satellite based altimetry
Sea level trend between 1992 and 2009 with respect to a reference level based on satellite altitude measurements Yellow and red regions show rising sea level while green and blue regions show falling sea level
Reality is more complex because of additional forces due to friction and temperature effects which add to the eddy formation phenomenon
Reality is more complex because of additional forces due to the drag forces provided by the atmospheric wind circulation and by the friction forces exerted by deeper water layers
Humboldt Current The cold Peruvian current (an eastern boundary current) flows towards the equator along the coast of Ecuador and Peru It flows with a speed of 01 to 015[ms] In the absence of an El Nintildeo prevailing surface winds cause Ekman transport to the left or away from the coast with subsequent upwelling of cold water
Kon Tiki Heyerdahlrsquos thesis of populating Polynesia from the East rather than from the North-West by taking advantage of Humboldt current for sea travel
Pressure conditions Pressure gradient towards ocean depth can be expressed in terms of the salinity and temperature dependence of ocean water density
PaatmP
zsurface
zgPzP
PTSneglecting
PTSgz
P
gdz
dP
surface
refsurface
ref
5101
PakmPkmz
PakmPkmz
Pamm
kg
s
mPamPmz
7
7
6
32
5
10444
1011
10100100081910100100
Flow at larger depth is directed by the pressure gradient and the Coriolis force ldquogeostrophic flowrdquo
Approximately a linear increase of pressure with depth ndash in contrast the atmosphere displays an exponential decrease of pressure with altitude
Geostrophic flow
A geostrophic current is an oceanic flow in which the pressure gradient force is balanced by the Coriolis effect The direction of geostrophic flow is parallel to the isobars with the high pressure to the right of the flow in the Northern Hemisphere and the high pressure to the left in the Southern Hemisphere
Fluid or gaseous media move from high pressure to low pressure regions The force pushing the water is called the pressure gradient force Fp In a geostrophic flow water moves along the lines of equal pressure (isobars) instead of moving from a high pressure to low pressure region This occurs due to Earthrsquos rotation that cause the Coriolis force Fc The Coriolis force acts at right angles to the flow When it balances the pressure gradient force (Fp=Fc) the resulting flow becomes the geostrophic flow
Flow velocity Variations of pressure conditions or isobars with depth are associated with temperature and salinity conditions and can cause horizontal flow The pressure gradient is balanced by the Coriolis force This allows an estimate of the flow speed
Pzu
Puz
ˆ1
01
ˆ
f
velocityflowayielding
fFF pc
With f being the Coriolis parameter and g the earth acceleration L represents the distance over which the salinity and temperature dependent density anomaly changes Between 20oN and 40oN Lasymp2000km
L
z
f
gu
ref
surface
The pressure gradient is also affected along coastlines with upwards sloping ground level
Geostrophic ocean flow
With f being the Coriolis parameter and g the earth acceleration L represents the distance over which the salinity and temperature dependent density anomaly changes Between 20oN and 40oN Lasymp2000km
L
z
f
gu
ref
surface
Consider the gulf stream as a sample The is a pressure or density with depth that in combination with the previously discussed Coriolis force affects the direction and determines the surface flow velocity
Overall agreement within the range of local speed variations The maximum speed is observed at the western boundaries of the Gulf stream with v asymp 1ms while in the interior of the gyre the speed is much lower vasymp10cms
s
m
m
m
kg
m
kgs
s
m
u
sfsf
m
kg
m
kg
m
kg
L
z
f
gu
surface
ref
surface
13
3
15
2
15150
333
1030000002
041000
1000102927
819
10292710292730sin2
42226
Estimate the gulf stream surface velocity usurface assuming a distance between 20oN and 40oN of L=2000 km for a depth of z=1000 m
Gulf stream flow velocity
Ocean current simulation for different temperature zones
NASAGoddard Space Flight Center Scientific Visualization Studio
The flow pattern is complex and the flow velocity varies greatly Both observables are defined by coastal boundaries drag forces at the surface density gradients at deep depths and the Coriolis force
Single water drop flow
Geostrophic flow induced variations in ocean surface height
The curvature of the flow and the horizontal velocity gradient across the flow causes a pressure gradient perpendicular to the flow direction which translate into variations of the ocean surface height
6
2
614
101
819
1010110
L
m
s
ms
mms
g
uLf
kmLsfs
mufor 10001010 14
Ocean Surface Height
Example Gulf of Mexico
httpwwwaomlnoaagovphoddhosaltimetryphp
Flow pattern Water height
Altitude anomalies
Maps of sea level obtained from satellite altimetry measurements are used to derive surface ocean currents Higher values of sea level (oranges and reds) are associated with gyres and warm eddies while lower values are associated to colder features Drifter trajectories illustrate circulation features Sea height anomaly maps show the difference of sea level from average conditions while sea height maps show absolute values of the sea level
Changing average sea altitude levels
Based on observational data such as tide level measurements and satellite based altimetry
Sea level trend between 1992 and 2009 with respect to a reference level based on satellite altitude measurements Yellow and red regions show rising sea level while green and blue regions show falling sea level
Humboldt Current The cold Peruvian current (an eastern boundary current) flows towards the equator along the coast of Ecuador and Peru It flows with a speed of 01 to 015[ms] In the absence of an El Nintildeo prevailing surface winds cause Ekman transport to the left or away from the coast with subsequent upwelling of cold water
Kon Tiki Heyerdahlrsquos thesis of populating Polynesia from the East rather than from the North-West by taking advantage of Humboldt current for sea travel
Pressure conditions Pressure gradient towards ocean depth can be expressed in terms of the salinity and temperature dependence of ocean water density
PaatmP
zsurface
zgPzP
PTSneglecting
PTSgz
P
gdz
dP
surface
refsurface
ref
5101
PakmPkmz
PakmPkmz
Pamm
kg
s
mPamPmz
7
7
6
32
5
10444
1011
10100100081910100100
Flow at larger depth is directed by the pressure gradient and the Coriolis force ldquogeostrophic flowrdquo
Approximately a linear increase of pressure with depth ndash in contrast the atmosphere displays an exponential decrease of pressure with altitude
Geostrophic flow
A geostrophic current is an oceanic flow in which the pressure gradient force is balanced by the Coriolis effect The direction of geostrophic flow is parallel to the isobars with the high pressure to the right of the flow in the Northern Hemisphere and the high pressure to the left in the Southern Hemisphere
Fluid or gaseous media move from high pressure to low pressure regions The force pushing the water is called the pressure gradient force Fp In a geostrophic flow water moves along the lines of equal pressure (isobars) instead of moving from a high pressure to low pressure region This occurs due to Earthrsquos rotation that cause the Coriolis force Fc The Coriolis force acts at right angles to the flow When it balances the pressure gradient force (Fp=Fc) the resulting flow becomes the geostrophic flow
Flow velocity Variations of pressure conditions or isobars with depth are associated with temperature and salinity conditions and can cause horizontal flow The pressure gradient is balanced by the Coriolis force This allows an estimate of the flow speed
Pzu
Puz
ˆ1
01
ˆ
f
velocityflowayielding
fFF pc
With f being the Coriolis parameter and g the earth acceleration L represents the distance over which the salinity and temperature dependent density anomaly changes Between 20oN and 40oN Lasymp2000km
L
z
f
gu
ref
surface
The pressure gradient is also affected along coastlines with upwards sloping ground level
Geostrophic ocean flow
With f being the Coriolis parameter and g the earth acceleration L represents the distance over which the salinity and temperature dependent density anomaly changes Between 20oN and 40oN Lasymp2000km
L
z
f
gu
ref
surface
Consider the gulf stream as a sample The is a pressure or density with depth that in combination with the previously discussed Coriolis force affects the direction and determines the surface flow velocity
Overall agreement within the range of local speed variations The maximum speed is observed at the western boundaries of the Gulf stream with v asymp 1ms while in the interior of the gyre the speed is much lower vasymp10cms
s
m
m
m
kg
m
kgs
s
m
u
sfsf
m
kg
m
kg
m
kg
L
z
f
gu
surface
ref
surface
13
3
15
2
15150
333
1030000002
041000
1000102927
819
10292710292730sin2
42226
Estimate the gulf stream surface velocity usurface assuming a distance between 20oN and 40oN of L=2000 km for a depth of z=1000 m
Gulf stream flow velocity
Ocean current simulation for different temperature zones
NASAGoddard Space Flight Center Scientific Visualization Studio
The flow pattern is complex and the flow velocity varies greatly Both observables are defined by coastal boundaries drag forces at the surface density gradients at deep depths and the Coriolis force
Single water drop flow
Geostrophic flow induced variations in ocean surface height
The curvature of the flow and the horizontal velocity gradient across the flow causes a pressure gradient perpendicular to the flow direction which translate into variations of the ocean surface height
6
2
614
101
819
1010110
L
m
s
ms
mms
g
uLf
kmLsfs
mufor 10001010 14
Ocean Surface Height
Example Gulf of Mexico
httpwwwaomlnoaagovphoddhosaltimetryphp
Flow pattern Water height
Altitude anomalies
Maps of sea level obtained from satellite altimetry measurements are used to derive surface ocean currents Higher values of sea level (oranges and reds) are associated with gyres and warm eddies while lower values are associated to colder features Drifter trajectories illustrate circulation features Sea height anomaly maps show the difference of sea level from average conditions while sea height maps show absolute values of the sea level
Changing average sea altitude levels
Based on observational data such as tide level measurements and satellite based altimetry
Sea level trend between 1992 and 2009 with respect to a reference level based on satellite altitude measurements Yellow and red regions show rising sea level while green and blue regions show falling sea level
Pressure conditions Pressure gradient towards ocean depth can be expressed in terms of the salinity and temperature dependence of ocean water density
PaatmP
zsurface
zgPzP
PTSneglecting
PTSgz
P
gdz
dP
surface
refsurface
ref
5101
PakmPkmz
PakmPkmz
Pamm
kg
s
mPamPmz
7
7
6
32
5
10444
1011
10100100081910100100
Flow at larger depth is directed by the pressure gradient and the Coriolis force ldquogeostrophic flowrdquo
Approximately a linear increase of pressure with depth ndash in contrast the atmosphere displays an exponential decrease of pressure with altitude
Geostrophic flow
A geostrophic current is an oceanic flow in which the pressure gradient force is balanced by the Coriolis effect The direction of geostrophic flow is parallel to the isobars with the high pressure to the right of the flow in the Northern Hemisphere and the high pressure to the left in the Southern Hemisphere
Fluid or gaseous media move from high pressure to low pressure regions The force pushing the water is called the pressure gradient force Fp In a geostrophic flow water moves along the lines of equal pressure (isobars) instead of moving from a high pressure to low pressure region This occurs due to Earthrsquos rotation that cause the Coriolis force Fc The Coriolis force acts at right angles to the flow When it balances the pressure gradient force (Fp=Fc) the resulting flow becomes the geostrophic flow
Flow velocity Variations of pressure conditions or isobars with depth are associated with temperature and salinity conditions and can cause horizontal flow The pressure gradient is balanced by the Coriolis force This allows an estimate of the flow speed
Pzu
Puz
ˆ1
01
ˆ
f
velocityflowayielding
fFF pc
With f being the Coriolis parameter and g the earth acceleration L represents the distance over which the salinity and temperature dependent density anomaly changes Between 20oN and 40oN Lasymp2000km
L
z
f
gu
ref
surface
The pressure gradient is also affected along coastlines with upwards sloping ground level
Geostrophic ocean flow
With f being the Coriolis parameter and g the earth acceleration L represents the distance over which the salinity and temperature dependent density anomaly changes Between 20oN and 40oN Lasymp2000km
L
z
f
gu
ref
surface
Consider the gulf stream as a sample The is a pressure or density with depth that in combination with the previously discussed Coriolis force affects the direction and determines the surface flow velocity
Overall agreement within the range of local speed variations The maximum speed is observed at the western boundaries of the Gulf stream with v asymp 1ms while in the interior of the gyre the speed is much lower vasymp10cms
s
m
m
m
kg
m
kgs
s
m
u
sfsf
m
kg
m
kg
m
kg
L
z
f
gu
surface
ref
surface
13
3
15
2
15150
333
1030000002
041000
1000102927
819
10292710292730sin2
42226
Estimate the gulf stream surface velocity usurface assuming a distance between 20oN and 40oN of L=2000 km for a depth of z=1000 m
Gulf stream flow velocity
Ocean current simulation for different temperature zones
NASAGoddard Space Flight Center Scientific Visualization Studio
The flow pattern is complex and the flow velocity varies greatly Both observables are defined by coastal boundaries drag forces at the surface density gradients at deep depths and the Coriolis force
Single water drop flow
Geostrophic flow induced variations in ocean surface height
The curvature of the flow and the horizontal velocity gradient across the flow causes a pressure gradient perpendicular to the flow direction which translate into variations of the ocean surface height
6
2
614
101
819
1010110
L
m
s
ms
mms
g
uLf
kmLsfs
mufor 10001010 14
Ocean Surface Height
Example Gulf of Mexico
httpwwwaomlnoaagovphoddhosaltimetryphp
Flow pattern Water height
Altitude anomalies
Maps of sea level obtained from satellite altimetry measurements are used to derive surface ocean currents Higher values of sea level (oranges and reds) are associated with gyres and warm eddies while lower values are associated to colder features Drifter trajectories illustrate circulation features Sea height anomaly maps show the difference of sea level from average conditions while sea height maps show absolute values of the sea level
Changing average sea altitude levels
Based on observational data such as tide level measurements and satellite based altimetry
Sea level trend between 1992 and 2009 with respect to a reference level based on satellite altitude measurements Yellow and red regions show rising sea level while green and blue regions show falling sea level
Geostrophic flow
A geostrophic current is an oceanic flow in which the pressure gradient force is balanced by the Coriolis effect The direction of geostrophic flow is parallel to the isobars with the high pressure to the right of the flow in the Northern Hemisphere and the high pressure to the left in the Southern Hemisphere
Fluid or gaseous media move from high pressure to low pressure regions The force pushing the water is called the pressure gradient force Fp In a geostrophic flow water moves along the lines of equal pressure (isobars) instead of moving from a high pressure to low pressure region This occurs due to Earthrsquos rotation that cause the Coriolis force Fc The Coriolis force acts at right angles to the flow When it balances the pressure gradient force (Fp=Fc) the resulting flow becomes the geostrophic flow
Flow velocity Variations of pressure conditions or isobars with depth are associated with temperature and salinity conditions and can cause horizontal flow The pressure gradient is balanced by the Coriolis force This allows an estimate of the flow speed
Pzu
Puz
ˆ1
01
ˆ
f
velocityflowayielding
fFF pc
With f being the Coriolis parameter and g the earth acceleration L represents the distance over which the salinity and temperature dependent density anomaly changes Between 20oN and 40oN Lasymp2000km
L
z
f
gu
ref
surface
The pressure gradient is also affected along coastlines with upwards sloping ground level
Geostrophic ocean flow
With f being the Coriolis parameter and g the earth acceleration L represents the distance over which the salinity and temperature dependent density anomaly changes Between 20oN and 40oN Lasymp2000km
L
z
f
gu
ref
surface
Consider the gulf stream as a sample The is a pressure or density with depth that in combination with the previously discussed Coriolis force affects the direction and determines the surface flow velocity
Overall agreement within the range of local speed variations The maximum speed is observed at the western boundaries of the Gulf stream with v asymp 1ms while in the interior of the gyre the speed is much lower vasymp10cms
s
m
m
m
kg
m
kgs
s
m
u
sfsf
m
kg
m
kg
m
kg
L
z
f
gu
surface
ref
surface
13
3
15
2
15150
333
1030000002
041000
1000102927
819
10292710292730sin2
42226
Estimate the gulf stream surface velocity usurface assuming a distance between 20oN and 40oN of L=2000 km for a depth of z=1000 m
Gulf stream flow velocity
Ocean current simulation for different temperature zones
NASAGoddard Space Flight Center Scientific Visualization Studio
The flow pattern is complex and the flow velocity varies greatly Both observables are defined by coastal boundaries drag forces at the surface density gradients at deep depths and the Coriolis force
Single water drop flow
Geostrophic flow induced variations in ocean surface height
The curvature of the flow and the horizontal velocity gradient across the flow causes a pressure gradient perpendicular to the flow direction which translate into variations of the ocean surface height
6
2
614
101
819
1010110
L
m
s
ms
mms
g
uLf
kmLsfs
mufor 10001010 14
Ocean Surface Height
Example Gulf of Mexico
httpwwwaomlnoaagovphoddhosaltimetryphp
Flow pattern Water height
Altitude anomalies
Maps of sea level obtained from satellite altimetry measurements are used to derive surface ocean currents Higher values of sea level (oranges and reds) are associated with gyres and warm eddies while lower values are associated to colder features Drifter trajectories illustrate circulation features Sea height anomaly maps show the difference of sea level from average conditions while sea height maps show absolute values of the sea level
Changing average sea altitude levels
Based on observational data such as tide level measurements and satellite based altimetry
Sea level trend between 1992 and 2009 with respect to a reference level based on satellite altitude measurements Yellow and red regions show rising sea level while green and blue regions show falling sea level
Flow velocity Variations of pressure conditions or isobars with depth are associated with temperature and salinity conditions and can cause horizontal flow The pressure gradient is balanced by the Coriolis force This allows an estimate of the flow speed
Pzu
Puz
ˆ1
01
ˆ
f
velocityflowayielding
fFF pc
With f being the Coriolis parameter and g the earth acceleration L represents the distance over which the salinity and temperature dependent density anomaly changes Between 20oN and 40oN Lasymp2000km
L
z
f
gu
ref
surface
The pressure gradient is also affected along coastlines with upwards sloping ground level
Geostrophic ocean flow
With f being the Coriolis parameter and g the earth acceleration L represents the distance over which the salinity and temperature dependent density anomaly changes Between 20oN and 40oN Lasymp2000km
L
z
f
gu
ref
surface
Consider the gulf stream as a sample The is a pressure or density with depth that in combination with the previously discussed Coriolis force affects the direction and determines the surface flow velocity
Overall agreement within the range of local speed variations The maximum speed is observed at the western boundaries of the Gulf stream with v asymp 1ms while in the interior of the gyre the speed is much lower vasymp10cms
s
m
m
m
kg
m
kgs
s
m
u
sfsf
m
kg
m
kg
m
kg
L
z
f
gu
surface
ref
surface
13
3
15
2
15150
333
1030000002
041000
1000102927
819
10292710292730sin2
42226
Estimate the gulf stream surface velocity usurface assuming a distance between 20oN and 40oN of L=2000 km for a depth of z=1000 m
Gulf stream flow velocity
Ocean current simulation for different temperature zones
NASAGoddard Space Flight Center Scientific Visualization Studio
The flow pattern is complex and the flow velocity varies greatly Both observables are defined by coastal boundaries drag forces at the surface density gradients at deep depths and the Coriolis force
Single water drop flow
Geostrophic flow induced variations in ocean surface height
The curvature of the flow and the horizontal velocity gradient across the flow causes a pressure gradient perpendicular to the flow direction which translate into variations of the ocean surface height
6
2
614
101
819
1010110
L
m
s
ms
mms
g
uLf
kmLsfs
mufor 10001010 14
Ocean Surface Height
Example Gulf of Mexico
httpwwwaomlnoaagovphoddhosaltimetryphp
Flow pattern Water height
Altitude anomalies
Maps of sea level obtained from satellite altimetry measurements are used to derive surface ocean currents Higher values of sea level (oranges and reds) are associated with gyres and warm eddies while lower values are associated to colder features Drifter trajectories illustrate circulation features Sea height anomaly maps show the difference of sea level from average conditions while sea height maps show absolute values of the sea level
Changing average sea altitude levels
Based on observational data such as tide level measurements and satellite based altimetry
Sea level trend between 1992 and 2009 with respect to a reference level based on satellite altitude measurements Yellow and red regions show rising sea level while green and blue regions show falling sea level
Geostrophic ocean flow
With f being the Coriolis parameter and g the earth acceleration L represents the distance over which the salinity and temperature dependent density anomaly changes Between 20oN and 40oN Lasymp2000km
L
z
f
gu
ref
surface
Consider the gulf stream as a sample The is a pressure or density with depth that in combination with the previously discussed Coriolis force affects the direction and determines the surface flow velocity
Overall agreement within the range of local speed variations The maximum speed is observed at the western boundaries of the Gulf stream with v asymp 1ms while in the interior of the gyre the speed is much lower vasymp10cms
s
m
m
m
kg
m
kgs
s
m
u
sfsf
m
kg
m
kg
m
kg
L
z
f
gu
surface
ref
surface
13
3
15
2
15150
333
1030000002
041000
1000102927
819
10292710292730sin2
42226
Estimate the gulf stream surface velocity usurface assuming a distance between 20oN and 40oN of L=2000 km for a depth of z=1000 m
Gulf stream flow velocity
Ocean current simulation for different temperature zones
NASAGoddard Space Flight Center Scientific Visualization Studio
The flow pattern is complex and the flow velocity varies greatly Both observables are defined by coastal boundaries drag forces at the surface density gradients at deep depths and the Coriolis force
Single water drop flow
Geostrophic flow induced variations in ocean surface height
The curvature of the flow and the horizontal velocity gradient across the flow causes a pressure gradient perpendicular to the flow direction which translate into variations of the ocean surface height
6
2
614
101
819
1010110
L
m
s
ms
mms
g
uLf
kmLsfs
mufor 10001010 14
Ocean Surface Height
Example Gulf of Mexico
httpwwwaomlnoaagovphoddhosaltimetryphp
Flow pattern Water height
Altitude anomalies
Maps of sea level obtained from satellite altimetry measurements are used to derive surface ocean currents Higher values of sea level (oranges and reds) are associated with gyres and warm eddies while lower values are associated to colder features Drifter trajectories illustrate circulation features Sea height anomaly maps show the difference of sea level from average conditions while sea height maps show absolute values of the sea level
Changing average sea altitude levels
Based on observational data such as tide level measurements and satellite based altimetry
Sea level trend between 1992 and 2009 with respect to a reference level based on satellite altitude measurements Yellow and red regions show rising sea level while green and blue regions show falling sea level
Overall agreement within the range of local speed variations The maximum speed is observed at the western boundaries of the Gulf stream with v asymp 1ms while in the interior of the gyre the speed is much lower vasymp10cms
s
m
m
m
kg
m
kgs
s
m
u
sfsf
m
kg
m
kg
m
kg
L
z
f
gu
surface
ref
surface
13
3
15
2
15150
333
1030000002
041000
1000102927
819
10292710292730sin2
42226
Estimate the gulf stream surface velocity usurface assuming a distance between 20oN and 40oN of L=2000 km for a depth of z=1000 m
Gulf stream flow velocity
Ocean current simulation for different temperature zones
NASAGoddard Space Flight Center Scientific Visualization Studio
The flow pattern is complex and the flow velocity varies greatly Both observables are defined by coastal boundaries drag forces at the surface density gradients at deep depths and the Coriolis force
Single water drop flow
Geostrophic flow induced variations in ocean surface height
The curvature of the flow and the horizontal velocity gradient across the flow causes a pressure gradient perpendicular to the flow direction which translate into variations of the ocean surface height
6
2
614
101
819
1010110
L
m
s
ms
mms
g
uLf
kmLsfs
mufor 10001010 14
Ocean Surface Height
Example Gulf of Mexico
httpwwwaomlnoaagovphoddhosaltimetryphp
Flow pattern Water height
Altitude anomalies
Maps of sea level obtained from satellite altimetry measurements are used to derive surface ocean currents Higher values of sea level (oranges and reds) are associated with gyres and warm eddies while lower values are associated to colder features Drifter trajectories illustrate circulation features Sea height anomaly maps show the difference of sea level from average conditions while sea height maps show absolute values of the sea level
Changing average sea altitude levels
Based on observational data such as tide level measurements and satellite based altimetry
Sea level trend between 1992 and 2009 with respect to a reference level based on satellite altitude measurements Yellow and red regions show rising sea level while green and blue regions show falling sea level
Gulf stream flow velocity
Ocean current simulation for different temperature zones
NASAGoddard Space Flight Center Scientific Visualization Studio
The flow pattern is complex and the flow velocity varies greatly Both observables are defined by coastal boundaries drag forces at the surface density gradients at deep depths and the Coriolis force
Single water drop flow
Geostrophic flow induced variations in ocean surface height
The curvature of the flow and the horizontal velocity gradient across the flow causes a pressure gradient perpendicular to the flow direction which translate into variations of the ocean surface height
6
2
614
101
819
1010110
L
m
s
ms
mms
g
uLf
kmLsfs
mufor 10001010 14
Ocean Surface Height
Example Gulf of Mexico
httpwwwaomlnoaagovphoddhosaltimetryphp
Flow pattern Water height
Altitude anomalies
Maps of sea level obtained from satellite altimetry measurements are used to derive surface ocean currents Higher values of sea level (oranges and reds) are associated with gyres and warm eddies while lower values are associated to colder features Drifter trajectories illustrate circulation features Sea height anomaly maps show the difference of sea level from average conditions while sea height maps show absolute values of the sea level
Changing average sea altitude levels
Based on observational data such as tide level measurements and satellite based altimetry
Sea level trend between 1992 and 2009 with respect to a reference level based on satellite altitude measurements Yellow and red regions show rising sea level while green and blue regions show falling sea level
Ocean current simulation for different temperature zones
NASAGoddard Space Flight Center Scientific Visualization Studio
The flow pattern is complex and the flow velocity varies greatly Both observables are defined by coastal boundaries drag forces at the surface density gradients at deep depths and the Coriolis force
Single water drop flow
Geostrophic flow induced variations in ocean surface height
The curvature of the flow and the horizontal velocity gradient across the flow causes a pressure gradient perpendicular to the flow direction which translate into variations of the ocean surface height
6
2
614
101
819
1010110
L
m
s
ms
mms
g
uLf
kmLsfs
mufor 10001010 14
Ocean Surface Height
Example Gulf of Mexico
httpwwwaomlnoaagovphoddhosaltimetryphp
Flow pattern Water height
Altitude anomalies
Maps of sea level obtained from satellite altimetry measurements are used to derive surface ocean currents Higher values of sea level (oranges and reds) are associated with gyres and warm eddies while lower values are associated to colder features Drifter trajectories illustrate circulation features Sea height anomaly maps show the difference of sea level from average conditions while sea height maps show absolute values of the sea level
Changing average sea altitude levels
Based on observational data such as tide level measurements and satellite based altimetry
Sea level trend between 1992 and 2009 with respect to a reference level based on satellite altitude measurements Yellow and red regions show rising sea level while green and blue regions show falling sea level
The flow pattern is complex and the flow velocity varies greatly Both observables are defined by coastal boundaries drag forces at the surface density gradients at deep depths and the Coriolis force
Single water drop flow
Geostrophic flow induced variations in ocean surface height
The curvature of the flow and the horizontal velocity gradient across the flow causes a pressure gradient perpendicular to the flow direction which translate into variations of the ocean surface height
6
2
614
101
819
1010110
L
m
s
ms
mms
g
uLf
kmLsfs
mufor 10001010 14
Ocean Surface Height
Example Gulf of Mexico
httpwwwaomlnoaagovphoddhosaltimetryphp
Flow pattern Water height
Altitude anomalies
Maps of sea level obtained from satellite altimetry measurements are used to derive surface ocean currents Higher values of sea level (oranges and reds) are associated with gyres and warm eddies while lower values are associated to colder features Drifter trajectories illustrate circulation features Sea height anomaly maps show the difference of sea level from average conditions while sea height maps show absolute values of the sea level
Changing average sea altitude levels
Based on observational data such as tide level measurements and satellite based altimetry
Sea level trend between 1992 and 2009 with respect to a reference level based on satellite altitude measurements Yellow and red regions show rising sea level while green and blue regions show falling sea level
Geostrophic flow induced variations in ocean surface height
The curvature of the flow and the horizontal velocity gradient across the flow causes a pressure gradient perpendicular to the flow direction which translate into variations of the ocean surface height
6
2
614
101
819
1010110
L
m
s
ms
mms
g
uLf
kmLsfs
mufor 10001010 14
Ocean Surface Height
Example Gulf of Mexico
httpwwwaomlnoaagovphoddhosaltimetryphp
Flow pattern Water height
Altitude anomalies
Maps of sea level obtained from satellite altimetry measurements are used to derive surface ocean currents Higher values of sea level (oranges and reds) are associated with gyres and warm eddies while lower values are associated to colder features Drifter trajectories illustrate circulation features Sea height anomaly maps show the difference of sea level from average conditions while sea height maps show absolute values of the sea level
Changing average sea altitude levels
Based on observational data such as tide level measurements and satellite based altimetry
Sea level trend between 1992 and 2009 with respect to a reference level based on satellite altitude measurements Yellow and red regions show rising sea level while green and blue regions show falling sea level
6
2
614
101
819
1010110
L
m
s
ms
mms
g
uLf
kmLsfs
mufor 10001010 14
Ocean Surface Height
Example Gulf of Mexico
httpwwwaomlnoaagovphoddhosaltimetryphp
Flow pattern Water height
Altitude anomalies
Maps of sea level obtained from satellite altimetry measurements are used to derive surface ocean currents Higher values of sea level (oranges and reds) are associated with gyres and warm eddies while lower values are associated to colder features Drifter trajectories illustrate circulation features Sea height anomaly maps show the difference of sea level from average conditions while sea height maps show absolute values of the sea level
Changing average sea altitude levels
Based on observational data such as tide level measurements and satellite based altimetry
Sea level trend between 1992 and 2009 with respect to a reference level based on satellite altitude measurements Yellow and red regions show rising sea level while green and blue regions show falling sea level
Example Gulf of Mexico
httpwwwaomlnoaagovphoddhosaltimetryphp
Flow pattern Water height
Altitude anomalies
Maps of sea level obtained from satellite altimetry measurements are used to derive surface ocean currents Higher values of sea level (oranges and reds) are associated with gyres and warm eddies while lower values are associated to colder features Drifter trajectories illustrate circulation features Sea height anomaly maps show the difference of sea level from average conditions while sea height maps show absolute values of the sea level
Changing average sea altitude levels
Based on observational data such as tide level measurements and satellite based altimetry
Sea level trend between 1992 and 2009 with respect to a reference level based on satellite altitude measurements Yellow and red regions show rising sea level while green and blue regions show falling sea level
Changing average sea altitude levels
Based on observational data such as tide level measurements and satellite based altimetry
Sea level trend between 1992 and 2009 with respect to a reference level based on satellite altitude measurements Yellow and red regions show rising sea level while green and blue regions show falling sea level