Across Channel Momentum Balance

Geostrophic balance (frictionless, steady and linear motion) in the lower layer

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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

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211

yh

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yh

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hg

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hgfu 2

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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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R

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z

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x

4

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232

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120

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