Viscous shear layers in an oscillating rotating fluid

Abstract

When a fluid rotating as if rigid with angular velocity Q is subject to a small disturbance of frequency to ω 2Ω the inviscid governing equations are hyperbolic in the spatial variables. Any irregularity in the boundary conditions is then transmitted through the fluid along the characteristics. An asymptotic solution for v->0, where v is the kinematic viscosity, involves the formulation of a singular inviscid solution and the introduction of viscous shear layers along the singular characteristics. The validity of this limit is examined and the structure of the shear layers discussed by considering a problem in which the full viscous equations are tractable-the extension of Stewartson’s (1957) split-disk configuration to oscillatory disturbances.