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Across Channel Momentum Balance
Geostrophic balance (frictionless, steady and linear motion) in the lower layer
)()( 22112 zhgghzp
22
2
1fu
y
p
y
hg
y
hgfu 2
21
12
21
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 yg
ygfu
11
1
1
21
but
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y
h
y
h
yg
fu
211
yh
gfu
yh
211
y
hg
y
hgfu 2
21
12
21
Geostrophic Balance in the lower layer:
y
z
LNM
h1
h2
11 u
22 u
h
yh
gfu
yh
211
y
hg
y
hgfu 2
21
12
21
y
hg
y
h
g
fugfu 2
221
12
2
1
ggy
hfufu 12
21122
12
22112
g
uuf
y
hMargules’ Relation
y
z
LNM
h1
h2
11 u
22 u
h
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
Seno Ballena
Estrecho de Magallanes
Ejemplo
Efectos de Rotación
Seno Ballena
Estrecho de Magallanes
Seno Ballena
Dept
h (m
)
rojo – flujo hacia afuera
azul – flujo hacia adentro
Dic 2003
Dic 2004
Flujo Promedio
Framework established:
Along estuary: pressure gradient balanced by friction
Across estuary: geostrophic balance
inducedRiver
2
2
inducedDensity
3
3
2
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