1. 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) or
As z-(into the interior) or

2. General solution:
If z, VE0, i.e., A=0
If z=0, VE=-Vg=B
We have
Let

3. Let

4. Solution
For z0,

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

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

8. We have
Since

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

10. Wind-driven circulation II
●Wind pattern and oceanic gyres
●Sverdrup Relation
●Vorticity Equation

13. Surface current measurement from ship drift
Current measurements are harder to make than T&S
The data are much sparse.

14. Surface current observations

15. Surface current observations

18. Drifting Buoy Data Assembly Center, Miami, Florida
Atlantic Oceanographic and Meteorological Laboratory, NOAA

19. Annual Mean Surface Current Pacific Ocean, 1995-2003
Drifting Buoy Data Assembly Center, Miami, Florida
Atlantic Oceanographic and Meteorological Laboratory, NOAA

21. Schematic picture of the major surface currents of the world oceans
Note the anticyclonic circulation in the subtropics (the subtropical gyres)

22. Relation between surface winds and subtropical gyres

23. Surface winds and oceanic gyres: A more realistic view
Note that the North Equatorial Counter Current (NECC) is against the direction of prevailing wind.

24. Mean surface current tropical Atlantic Ocean
Note the North Equatorial Counter Current (NECC)

25. Consider the following balance in an ocean of depth h of flat bottom
Sverdrup Relation
Consider the following balance in an ocean of depth h of flat bottom ,
Integrating vertically from –h to 0, we have
(neglecting bottom stress and surface height change)
(1)
(2)
where
and
Differentiating
, we have
Using continuity equation
and ,
Sverdrup relation
we have