The structure of free vertical shear layers in a rotating fluid and the motion produced by a slowly rising body

Abstract

Abstract This paper considers axial motion in a rapidly rotating fluid of small viscosity. It is shown that solutions for the structure of vertical free shear layers must be allowed to be singular at the points where they receive fluid from a rising or spinning axisymmetric body. The possible types of singularities are elucidated by the use of similarity solutions and an hypothesis is introduced to limit their strength. Three particular cases of axially bounded motion are considered in detail; the split disk, the rising disk and the rising sphere. The hypothesis is shown to lead to a unique solution for the Stewartson layers. For the rising body, a Wiener-Hopf problem, which is independent of the body shape, must be solved for the central part of the Stewartson layers.