An equatorial boundary layer

Abstract

The singularity of the Ekman layer at the equator of a rotating gravitating sphere makes it difficult to satisfy a prescribed stress boundary condition at the surface of a layer of liquid on the sphere. The equations of motion are investigated for a homogeneous ocean with vertical and lateral eddy viscosities. The horizontal Coriolis terms are not neglected. A linear equation for the boundary layer is obtained and a solution of the equation for the boundary-layer part of the velocity field is found in closed form. This is valid in a parameter range which includes the previous solutions of Stewartson and Gill as limiting cases.