Define Current decreases exponentially with depth. At the same time, its direction changes clockwise with depth (The Ekman spiral). we have,. and At the sea surface (z=0), t he surface current flows at 45 o to the right of the wind direction At D E, the current magnitude is 4% of the surface current and its direction is opposite to that of the surface current. D E (≈100 m in mid-latitude) is regarded as the depth of the Ekman layer. D E is not the mixed layer depth (h m ). The latter also depends on past history, surface heat flux (heat balance) and the stability of the underlying water. In reality, D E < h m because h m can be affected by strong wind burst of short period. Depends on constant A z =>

(,,  ) (2) Relationship between W and D E. Ekman ’ s empirical formula between W and V o., outside ±10 o latitude  (3) There is large uncertainty in C D (1.3 to 1.5 x ±20% for wind speed up to about 15 m/s). C D itself is actually a function of W. (1) Relationship between surface wind speed W and (V o, D E ). Wind stress magnitude has an error range of 2-5%.(4) Other properties

(1) D E is not the mixed layer depth (h m ). The latter also depends on past history, surface heat flux (heat balance) and the stability of the underlying water. In reality, D E < h m because h m can be affected by strong wind burst of short period. (2) A z = const and steady state assumptions are questionable. (3) Lack of data to test the theory. (The Ekman spiral has been observed in laboratory but difficult to observe in fields). (4) Vertically integrated Ekman transport does not strongly depend on the specific form of A z. More comments

Progressive vector diagram, using daily averaged currents relative to the flow at 48 m, at a subset of depths from a moored ADCP at 37.1°N, 127.6°W in the California Current, deployed as part of the Eastern Boundary Currents experiment. Daily averaged wind vectors are plotted at midnight UT along the 8-m relative to 48-m displacement curve. Wind velocity scale is shown at bottom left. (Chereskin, T. K., 1995: Evidence for an Ekman balance in the California Current. J. Geophys. Res., 100, )

Surface Drifter Current Measurements a platform designed to move with the ocean current

Ekman Transport Integrating from surface z=  to z=-2D E (e -2DE =0.002), we have by the Ekman current. Since, we have Starting from a more general form of the Ekman equation (without assuming A Z or even a specific form for vertical turbulent flux) where and are the zonal and meridional mass transports by the 

Ekman transport is to the right of the direction of the surface winds

Ekman pumping Integrating the continuity equation is transport into or out of the bottom of the Ekman layer to the ocean’s interior (Ekman pumping). through the layer: Where and are volume transports. Assume and let, we have, upwelling Water pumped into the Ekman layer by the surface wind induced upwelling is from meters, which is colder and reduces SST., downwelling

Upwelling/downwelling are generated by curls of wind stress

Coastal and equatorial upwelling Coastal upwelling: Along the eastern coasts of the Pacific and Atlantic Oceans the Trade Winds blow nearly parallel to the coast towards the Doldrums. The Ekman transport is therefore directed offshore, forcing water up from below (usually from m depth). Equatorial Upwelling: In the Pacific and Atlantic Oceans the Doldrums are located at 5°N, so the southern hemisphere Trade Winds are present on either side of the equator. The Ekman layer transport is directed to the south in the southern hemisphere, to the north in the northern hemisphere. This causes a surface divergence at the equator and forces water to upwell (from about m).

An example of coastal upwelling Water property sections in a coastal upwelling region, indicating upward water movement within about 200 km from the coast. (This particular example comes from the Benguela Current upwelling region, off the coast of Namibia.) The coast is on the right, outside the graphs; the edge of the shelf can just be seen rising to about 200 m depth at the right of each graph. Note how all contours rise towards the surface as the coast is approached; they rise steeply in the last 200 km. On the shelf the water is colder, less saline and richer in nutrients as a result of upwelling.

Cold SST associated with the coastal and equatorial upwelling

Ekman layer at the bottom of the sea For convenience, assume the bottom of the sea is flat and located at z=0, the governing equation and its general solution are the same as the surface case. Boundary conditions Z=0 (bottom of the sea) As z  -  (into the interior) or

General solution: If z , V E  0, i.e., A=0 If z=0, V E =-V g =B Let We have

Let

Solution For z  0,

The direction of the total currents where The near bottom the total current is 45 o to the left of the geostrophic current.

Ekman Transport

Transport at the top of the bottom Ekman layer Assume, the solution can be written as Using the continuity equation

We have Since

Given the integral i.e.,  The vertical velocity at the top of the bottom boundary layer Ekman pumping at the bottom.