Coriolis Force and Ekman Flow in Oceanic Gyres

1. Question: Why 45o, physics or math? Physics: Coriolis force is balanced by vertical mixing (friction) for Ekman flow If Az is constant, and are perpendicular to each other 45o relation is not likely to hold Only if B=0, i.e., as z- 45o relation holds for boundary layer solution

2. Question: Why 45o, physics or math? Physics: Coriolis force is balanced by vertical mixing (friction) for Ekman flow If Az is not constant, and are not likely perpendicular to each other 45o relation is not likely to hold even for boundary layer solution

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

4. What generate the gyre circulation?

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

6. http://www.aoml.noaa.gov/phod/dac/gdp_drifter.php

7. Surface current observations

8. Surface current observations

14. http://www.aoml.noaa.gov/phod/dac/drifter_climatology.html A climatology of near-surface currents and SST for the world, at one degree resolution, derived from satellite-tracked surface drifting buoy observations. Most recent data included: 1 January 2011. Reference: Lumpkin, R. and Z. Garraffo, 2005: Evaluating the Decomposition of Tropical Atlantic Drifter Observations. J. Atmos. Oceanic Techn. I 22, 1403-1415. Lumpkin, R. and S. L. Garzoli, 2005: Near-surface Circulation in the Tropical Atlantic Ocean. Deep-Sea Res. I 52(3),495-518, 10.1016/j.dsr.2004.09.001.

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

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

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

20. Relation between surface winds and subtropical gyres

21. 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. 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

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

26. 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”

27. is the total meridional mass transport Geostrophic transport Ekman transport Order of magnitude example: At 35oN, -4 s-1, 2  10-11 m-1 s-1, assume x10-1 Nm-2 y=0

28. then

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

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

33. 1 Sverdrup (Sv) =106 m3/s

35. A More General Form of Sverdrup Equation Surface stress curl Bottom stress curl Bottom topography effect Vanish if the bottom is flat Or flow follows topographic contour