RTX

Ekman Layer

Abstract:

The Ekman layer is the layer of fluid near a fluid boundary (can be a rigid boundary or an interface between two fluids) that is affected by a viscous drag due to the no-slip boundary condition, the Coriolis effect (in a rotating frame), and the pressure gradient force. It is common for the Ekman boundary layer to form in both fluids at an interface, such as the region of air above the ocean and in the ocean below the air, as well in a fluid at a rigid bottom boundary, such as at the bottom of a rotating tank. In this layer, an opposing flow forms due to the viscous drag forces at the boundary. The resulting flow is then forced sideways due to the nature of the Coriolis effect and formed into a spiral, lovingly called the Ekman spiral. It may be noted that this resulting flow is in the horizontal plane only, however the this horizontal flow can be divergent, resulting in vertical transport in incompressible fluids (and compressible to a lesser degree).

Ekman transport is thought to be the mechanism for a majority of atmospheric and oceanic mixing due the the vertical velocity associated with Ekman pumping. In the oceanic coastal areas, nutrients and even fish are pulled up from deeper and brought closer to the surface. The consistent atmospheric flows, such as the trade winds near the equator, cause a net oceanic transport toward or away from the equator serving to mix temperature toward the polar directions. Ocean gyres are attributed to Ekman transport as well, through the Coriolis effect.

On much smaller scales, the convergence of tea leaves in the bottom of a stirred teacup is one of the best visualizations of Ekman pumping. The flow of tea in the cup has vorticity and drags at the bottom of the cup, causing a converging horizontal flow in the Ekman layer. The converging flow in the horizontal direction must be accompanied with an upward vertical flow to maintain incompressibility but the tea leaves stay at the bottom do their density relative to the water. See the visualization examples or try it yourself if you have not seen it!