Ekman layer

The Ekman layer is the layer in a fluid where there is a force balance between pressure gradient force, Coriolis force and turbulent drag. It was first described by Vagn Walfrid Ekman. Ekman layers occur both in the atmosphere and in the ocean.

There are two types of Ekman layers. The first type occurs at the surface of the ocean and is forced by surface winds, which act as a drag on the surface of the ocean. The second type occurs at the bottom of the atmosphere and ocean, where frictional forces are associated with flow over rough surfaces.

Ekman developed the theory of the Ekman layer after Fridtjof Nansen observed that ice drifts at an angle of 20°-40° to the right of the prevailing wind direction while on an Arctic expedition aboard the Fram. Nansen asked his colleague, Vilhelm Bjerknes to set one of his students upon study of the problem. Bjerknes tapped Ekman, who presented his results in 1902 as his doctoral thesis.

The mathematical formulation of the Ekman layer begins by assuming a neutrally stratified fluid, a balance between the forces of pressure gradient, Coriolis and turbulent drag.

where ${\displaystyle \ u}$ and ${\displaystyle \ v}$ are the velocities in the ${\displaystyle \ x}$ and ${\displaystyle \ y}$ directions, respectively, ${\displaystyle \ f}$ is the local Coriolis parameter, and ${\displaystyle \ K_{m}}$ is the diffusive eddy viscosity, which can be derived using mixing length theory. Note that ${\displaystyle p}$ is a modified pressure: we have incorporated the hydrostatic of the pressure, to take account of gravity.

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