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

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

4. Surface current observations

5. Surface current observations

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

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

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

12. Relation between surface winds and subtropical gyres

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

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

16. 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
(1)
(2)
Integrating vertically from –h to 0 for both (1) and (2), we have
(neglecting bottom stress and surface height change)
(3)
(4)
where
are total zonal and meridional transport of mass
sum of geostrophic and ageostropic transports

17. (3) and (4) can be written as
Define
We have
(3) and (4) can be written as
(6)
(5)
Differentiating
, we have

18. We have Sverdrup equation
Using continuity equation
And define
We have Sverdrup equation
Vertical component of the wind stress curl If
The line provides a natural boundary that separate the circulation into “gyres”

19. is the total meridional mass transport
Geostrophic transport
Ekman transport
Order of magnitude example:
At 35oN, -4 s-1, 2  m-1 s-1, assume x10-1 Nm-2 y=0

20. Alternative derivation of Sverdrup Relation
Construct vorticity equation from geostrophic balance
(1)
Assume =constant
(2) 
Integrating over the whole ocean depth, we have

21. where
is the entrainment rate from the surface Ekman layer
at 45oN
The Sverdrup transport is the total of geostrophic and Ekman transport.
The indirectly driven Vg may be much larger than VE.

22. then

23. set x =0 at the eastern boundary,
Since
, we have
set x =0 at the eastern boundary,
Further assume
In the trade wind and equatorial zones, the 2nd derivative term dominates:

26. Mass Transport Since Let , ,  where  is stream function.
Problem: only one boundary condition can be satisfied.

27. 1 Sverdrup (Sv) =106 m3/s