The flow caused by the differential rotation of a right circular cylindrical depression in one of two rapidly rotating parallel planes

Abstract

The flow induced by the differential rotation of a cylindrical depression of radius a in one of two parallel rigid planes rapidly rotating about their common normal at speed Q is studied. A Taylor column bounded by the usual Stewartson layers arises, but the shear-layer structure is rather different from any previously studied. The Ei-layers (E = v/ωa2) smooth the discontinuity in the geostrophic flow, but the way in which this is accomplished is related to the possible singu-larities of the E1/3-layer solutions. The fact that the 1/4-layer is partially free and partially attached to a vertical boundary accounts for the new joining conditions for the 1/4-layer. The drag on a right circular cylindrical bump in uniform flow is given in addition to some general comments on the applicability of these joining conditions to the motion of an axisymmetric object of quite general shape.