Steady State General Ocean Circulation
“steady state” means: constant in time, no accelerations
or
Sum of all forces = 0
Outline:
1. Ekman dynamics (Coriolis~Friction)
2. Geostrophic dynamics (Coriolis~Pressure gradients)
3. Ekman+Geostrophy with Coriolis as f=f0+by
The
subtropical
gyre
circulation
is a
geostrophic
flow (with
many
eddies)
From WHP Pacific Atlas (Talley, 2007)
http://www-pord.ucsd.edu/whp_atlas
Geostrophy
Coriolis balances pressure gradient
Geostrophic Degeneracy
Ekman balance:
Coriolis ~ Friction
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a-1=(2Az/f) is a vertical decay scale
~ 20m-60m
from Stewart, 2005
Ekman velocity spiral
•
•
•
•
Surface velocity to the right of the wind (northern hemisphere, due to Coriolis)
Surface layer pushes next layer down slightly the right, and slightly weaker current
Next layer pushes next layer, slightly to right and slightly weaker current
Producing a “spiral” of the current vectors, to right in northern hemisphere,
decreasing speed with increasing depth
• Details of the spiral depend on the vertical viscosity (how frictional the flow is,
and also whether “friction” depends on depth)
Ekman transport
The wind stress on the ocean surface is the vector
 = ( (x) , (y) )
Integrate the Coriolis/friction balances in the vertical
x: -fv = /z(AVu/z) -> -fVEK= AVu/z = (x) /
y: fu = /z(AVv/z) -> fUEK= AVv/z = (y) /
•UEK and VEK are the “Ekman transport” ∫udz, ∫vdz
•Ekman “transport” is exactly to the right of the wind stress
(northern hemisphere ).
•Ekman transport does not depend on the size or structure of AV
(but the detailed structure of the spiral DOES depend on it)
Ekman layer “transport”
• “Transport”: 90° to wind, to right in northern hemisphere
• UEk= /f (units are m2/s, not m3/s so technically this is not a
transport; need to sum horizontally along a section to get a transport).
• Typical size: for wind stress 0.1 N/m2, UEk= 1 m2/s. Integrate over
width of ocean, say 5000 km, get total transport of 5 x 106 m3/sec = 5
Sv.
Ekman layer depth
• Depth: depends on eddy viscosity AV (why?)
Dek = (2AV/f)1/2
• Eddy viscosity is about 0.05 m2/sec in turbulent
surface layer, so Ekman layer depth is 20 to 60 m
for latitudes 80° to 10°.
Ekman layer velocity
• Velocity: spirals with depths and magnitude depends on
eddy viscosity. If AV is constant, surface velocity is 45° to
wind
• For eddy viscosity 0.05 m2/sec, and wind stress of 1
dyne/cm2 (.1 N/m2), surface velocity is 3 cm/sec at 45°N.
Observations of Ekman layer
Direct current measurements in California
Current region revealed excellent Ekmantype spiral (Chereskin, JGR, 1995)
Global surface wind velocity
Westward
Eastward
Ekman divergence (Ekman upwelling) at
equator and at land boundaries
Equatorial
Land boundary
(southern hemisphere, like Peru)
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Ekman transport convergence
and divergence
Ekman transport convergence
and divergence
Ekman
Pumping
Geostrophic
flow
Vertical velocity at base of Ekman layer: order (10-4cm/sec)
(Compare with typical horizontal velocities of 1-10 cm/sec)
Pacific winds (mean)
• Ekman pumping
Gray: downwelling
White: upwelling
from Talley 2006
Ekman Pumping
continuity
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vertical integral
Ekman transports
Convergence in
Ekman transport
Recall
MEx = y/f
MEy = -x/f
Vertical velocity
Ekman pumping
Ekman transport 90 degrees to wind