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Ekman Layer and Wind-Driven Ocean Circulation

Learn about the Ekman layer at the bottom of the sea and the associated wind-driven circulation, including the Sverdrup Relation and Vorticity Equation. Discover how surface currents are measured and observe major oceanic gyres. Surface wind patterns influence subtropical gyres and currents like the North Equatorial Counter Current.

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Ekman Layer and Wind-Driven Ocean Circulation

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  1. 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. Ekman layer at the bottom of the sea 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.

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

  7. We have Since

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

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

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

  11. Surface current observations

  12. Surface current observations

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

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

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

  16. Relation between surface winds and subtropical gyres

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

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

  19. 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 and Using continuity equation , Sverdrup relation we have

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