Ekman_Pumping

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```					Oct 30: Ekman pumping and wind stress curl

Balance between Coriolis and the vertical friction mixing of momentum, or
stress, leads to Ekman currents. Integrating this balance vertically (in
practice over the top few tens of meters) gives us the Ekman transport:

1  x                    1  y
 fv                   ;   fu 
 z                       z
0
take  dz         ...
D

x                     y
get V E                   ; UE           in m 2 s 1
f                     f

These components of Ekman transport describe depth integrated flow (in
m2s-1) (i.e. velocity times depth) that is 900 to the right (left) of the wind
stress in the northern (southern) hemisphere.

The units of m2 s-1 can be thought of as the total transport (m3 s-1) per meter
perpendicular to the current.

Conveniently, the details of the eddy viscosity profile (the vertical rate of
momentum mixing) are irrelevant to this transport result.

In an infinite ocean, uniform winds would generate uniform Ekman
transports and the ocean currents would be the same everywhere.

But the ocean is not infinite, and winds are variable, so Ekman transports are
not spatially uniform, which leads to converge and divergence of the surface
currents.

Ekman pumping.

Q: Recalling what you know about the global patterns of winds, what
latitudes would you expect to be characterized by converging Ekman
transports and therefore downward Ekman pumping?

A: The region between the Trades and Westerlies
The net influence of converging or diverging horizontal Ekman transports
can be quantified by considering the conservation of mass equation:

u v w
0


D
  
x y z
dz  0

                             w
0            0          0

Du dz      Dv dz        dz  w D  w( D)  wE
0

x          y            D z

U E VE
     wE
x   y

Figure 3.24 Ocean Circulation: Ekman pumping (convergence and
divergence)

Recall that the Ekman transport components are related to the wind stress:

y                  x
UE           and VE  
f                  f
U E VE    y          x    
                           wE
x   y  x  f

 y  f
    


         
       curl     wE
f        f


curl      0
Where          f    the Ekman pumping velocity wE is negative, i.e. there is a
convergence of Ekman transports that pump water downward into the ocean
interior.

This downward Ekman pumping between the Trades and Westerlies
generates a depressed thermocline in the center of the subtropical gyres.

This is the case in both hemispheres, because the sign of curl wind stress and
f both differ, so we < 0.

The baroclinic pressure gradients associated with this drive the large scale
gyre circulations, and conservation of mass closes the gyre circulations with
intense poleward western boundary currents.

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