An Ekman layer is a viscous boundary layer that occurs at a boundary of a large body of rotating fluid: at the bottom of the oceans and atmosphere and at the top of the oceans. This layer is an agent that communicates information regarding velocity (or stress) at the boundary to the fluid outside the layer. The communication is accomplished by means of an Ekman pumping: a vertical flow into (or from) the boundary layer. This vertical flow is determined by integration of the continuity equation, once the horizontal velocity within the layer has been determined by solving the momentum equation.

Ekman layers are encountered

giving us eight physical cases to consider. In the following analysis we will keep track of the position of the Ekman layer relative to the boundary and equator is categorized by the factor s which has values 1 or −1, as follows:

There is yet another categorization of Ekman layers, dealing with the nature of the model employed. We will explore two models of Ekman layer flow and structure – having either constant or variable turbulent kinematic viscosity – and compare the results of these two models.

The equations governing the Ekman layer are presented and solved in § 25.1 and the horizontal Ekman transport is investigated in § 25.2 for both models. Then useful relations between the transport and basal velocity gradient are developed in § 25.3 and Ekman pumping is investigated in § 25.4. Finally, the Ekman-layer theory is applied to the atmosphere and oceans in § 25.5.