The thickness of the Ekman layer is arbitrary because the Ekman currents decrease exponentially with depth. Ekman proposed that the thickness be the depth DE at which the current velocity is opposite the velocity at the surface, which occurs at a depth $ D_E = \pi/a $, and the Ekman layer depth is:

$$ D_E = \sqrt{\frac{2\pi A_z}{f}} $$

where $ D_E $ is the Ekman layer depth, $ A_z $ the coefficient of eddy viscosity and f the Coriolis Parameter. History

Here an summary of the most important Equations:

The horizontal variability of the wind blowing on the sea surface leads to horizontal variability of the Ekman transports. Because mass must be conserved, the spatial variability of the transports must lead to vertical velocities at the top of the Ekman layer. This leads to a vertical geostrophic current in the ocean's interior. Applications in Oceanography

1. Upwelling Steady winds blowing on the sea surface produce an Ekman layer that transports water at right angles to the wind direction. Any spatial variability of the wind, or winds blowing along some coasts, can lead to upwelling. This includes coastal upwelling regimes which provide the nutrient supply for some of the largest fishing markets on the planet, as well as equatorial upwelling where, in both hemispheres, a trade wind component towards the west causes a net transport of water towards the pole, and a trade wind component towards the east causes a net transport of water away from the pole.
2. Cyclonic winds On smaller scales, cyclonic winds induce Ekman transport which causes net divergence and upwelling, or Ekman suction, while anti-cyclonic winds cause net convergence and downwelling, or Ekman pumping.
3. Ocean Gyres Ekman transport is also a factor in the circulation of the ocean gyres. Ekman transport causes water to flow toward the center of the subtropical gyres, creating a sloped sea-surface, and initiating geostrophic flow. This is the reason for the formation of the Ocean Garbage Patches. They form as material is captured in the currents, wind-driven surface currents gradually move floating debris toward the center, trapping it in the region.

Colling, A., Ocean Circulation, Open University Course Team. Second Edition. 2001. ISBN 978-0-7506-5278-0

Knauss, J.A., Introduction to Physical Oceanography, Waveland Press. Second Edition. 2005. ISBN 978-1-57766-429-1

Münnich, M. (2014): Introduction to Physical Oceanography:Lecture 8

Stewart, R. H., Introduction To Physical Oceanography, Department of Oceanography Texas A & M University September 2008 Edition

“AMS Glossary”. Retrieved 29.04.2014

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