# 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)

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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=f 0 +  y

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 from Stewart, 2005 a -1 =  (2A z /f) is a vertical decay scale ~ 20m-60m

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(A V  u/  z) -> -fV EK = A V  u/  z =  (x) /  y: fu =  /  z(A V  v/  z) -> fU EK = A V  v/  z =  (y) /  U EK and V EK 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 A V (but the detailed structure of the spiral DOES depend on it)

Ekman layer “transport” “Transport”: 90° to wind, to right in northern hemisphere U Ek =  /  f (units are m 2 /s, not m 3 /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/m 2, U Ek = 1 m 2 /s. Integrate over width of ocean, say 5000 km, get total transport of 5 x 10 6 m 3 /sec = 5 Sv.

Ekman layer depth Depth: depends on eddy viscosity A V (why?) D ek = (2A V /f) 1/2 Eddy viscosity is about 0.05 m 2 /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 A V is constant, surface velocity is 45° to wind For eddy viscosity 0.05 m 2 /sec, and wind stress of 1 dyne/cm 2 (.1 N/m 2 ), surface velocity is 3 cm/sec at 45°N.

Observations of Ekman layer Direct current measurements in California Current region revealed excellent Ekman- type spiral (Chereskin, JGR, 1995)

Global surface wind velocity WestwardEastward

Ekman divergence (Ekman upwelling) at equator and at land boundaries Equatorial Land boundary (southern hemisphere, like Peru)

Ekman transport convergence and divergence

Vertical velocity at base of Ekman layer: order (10 -4 cm/sec) (Compare with typical horizontal velocities of 1-10 cm/sec) Ekman Pumping Geostrophic flow

Pacific winds (mean) Ekman pumping Gray: downwelling White: upwelling from Talley 2006

Ekman Pumping continuity vertical integral Ekman transports Convergence in Ekman transport Vertical velocity Ekman pumping Recall M Ex =  y /  fEkman transport 90 degrees to wind M Ey = -  x /  f

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