Transient Stewartson layers of a rotating compressible fluid

Abstract

An analysis of the azimuthal velocity (v) structure in transient Stewartson layers of a rapidly rotating compressible fluid is made. The specific problem formulation is for the case when the rotating sidewall of a cylindrical container is given a small impulsive increase in rotation rate. A two-variable matched asymptotic technique is employed to describe the azimuthal velocity in the Stewartson layer. The Laplace transforms are applied to obtain an approximate analytical solution for v. This solution at large times is consistent with the previously established steady-state behavior. Also, when the fluid compressibility vanishes, this solution recovers the features of incompressible-fluid flows. When the compressibility effect is appreciable, the influence of the local viscosity effect becomes noticeable, and the thicknesses of boundary layers increase. At a given radial location, with the increase of the compressibility effect, the magnitude of v becomes larger. The impact of the compressibility effect is to shorten the transitory time needed to reach the steady state. These results are in qualitative agreement with the assertions of the preceding studies.