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+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

QuickTime™ and aTIFF (Uncompressed) decompressor

are needed to see this picture.

Geostrophy

Coriolis balances pressure gradient

Geostrophic Degeneracy

Ekman balance: Coriolis ~ FrictionQuickTime™ and a decompressor

are needed to see this picture.

QuickTime™ and a decompressor

are needed to see this picture.

from Stewart, 2005

QuickTime™ and a decompressor

are needed to see this picture.

QuickTime™ and a decompressor

are needed to see this picture.

a-1=(2Az/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 transportThe wind stress on the ocean surface is the vector

= ( (x) , (y) )

Integrate the Coriolis/friction balances in the vertical

x: -fv = /z(AVu/z) -> -fVEK= AVu/z = (x) /y: fu = /z(AVv/z) -> fUEK= AVv/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 Ekman-type spiral (Chereskin, JGR, 1995)

Global surface wind velocity

Westward Eastward

Ekman divergence (Ekman upwelling) at equator and at land boundaries

QuickTime™ and aTIFF (Uncompressed) decompressor

are needed to see this picture.QuickTime™ and aTIFF (Uncompressed) decompressor

are needed to see this picture.

Equatorial Land boundary

(southern hemisphere, like Peru)

Ekman transport convergence and divergence

Ekman transport convergence and divergence

Vertical velocity at base of Ekman layer: order (10-4cm/sec)

(Compare with typical horizontal velocities of 1-10 cm/sec)

EkmanPumping

Geostrophicflow

Pacific winds (mean) • Ekman pumping Gray: downwelling White: upwelling

from Talley 2006

Ekman Pumping

QuickTime™ and a decompressor

are needed to see this picture.

continuity

vertical integral

Ekman transports

Convergence inEkman transport

Vertical velocityEkman pumping

Recall MEx = y/f Ekman transport 90 degrees to windMEy = -x/f