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h 1. z. LNM. h 2. y. Across Channel Momentum Balance. Geostrophic balance (frictionless, steady and linear motion) in the lower layer. h. h 1. LNM. h 2. z. y. Geostrophic Balance in the upper layer. Geostrophic Balance in the lower layer:. h. h 1. LNM. h 2. z. y. - PowerPoint PPT Presentation
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Across Channel Momentum Balance
Geostrophic balance (frictionless, steady and linear motion) in the lower layer
2211)( ghghzp
22
1fu
y
p
yh
gyh
gfu 22
11
22
1
y
z
LNM
h1
h2
11 u
22 u
zv
Azy
vA
yxv
Axy
pfu
zv
wyv
vxv
utv
zyx1
Geostrophic Balance in the upper layer
y
gfu
11
11
21
but
hhyy
yh
yh
ygfu
211
yh
gfu
yh
211
yh
gyh
gfu 22
11
22
1
Geostrophic Balance in the lower layer:
y
z
LNM
h1
h2
11 u
22 u
yh
gfu
yh
211
yh
gyh
gfu 22
11
22
1
y
hg
y
h
g
fugfu 2
221
12
2
1
ggy
hfufu 12
21122
12
22112
g
uuf
y
hMargules’ Relation
How about ?y
h
1
g
fu
g
fu
g
fu
y
h
g
fu
y
h 22111211
21112 1 and :that Note
1222212211
'1 uu
gf
gfu
gfu
gfu
gfu
121
'uu
gf
yh
With one can determine2121 ,,, uuy
hy
hyy
hy
h
2121 ,,
y
z
LNM
h1
h2
11 u
22 u
Effects of the Earth’s Rotation
Observed slope: 2m in 10 km
2 / 104 = 2 x 10-4
12
22112
g
uuf
y
h
f = 8.8e-5u1 = 0.08u2 = -0.025rho1 = 1020rho2 = 1024
42 103.2 yh
Could you draw the pressure field (isobars) associated with these salinity (density) fields?
12
22112
guuf
yh
u1 = 0.10 m/su2 = -0.05 m/s
ρ1 = 1017 kg/m3
ρ2 = 1022 kg/m3
f = 8.8 e-5 s-1
42 107.2 yh
u1 = 0.08 m/su2 = -0.06 m/s
ρ1 = 1021 kg/m3
ρ2 = 1023 kg/m3
f = 8.8 e-5 s-1
42 104.6 yh
Observed =2 m in 8 km =2.5 x 10-4
Observed =7 m in 8 km =8.8 x 10-4
Generally, the outflow modified by rotation will be restricted by theinternal radius of deformation R, derived from geostrophy:
zx
gfv
Scaling:
22
2
'
'
f
HgL
L
HgLf
Internal Radius of Deformationor
Internal Rossby Radius
fC
f
HgL i
'
L