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