Axisymmetric and three-dimensional instabilities in an Ekman boundary layer flow

The instability of Ekman boundary layer flow is studied inside a rotating a nnular cavity with radial throughflow, which is a relevant geometry of the air cooling system in turbines. The flow is computed by direct numerical si mulation using a time-dependent three-dimensional Navier-Stokes solver base d on a pseudo-spectral method. The fluid entering the annulus at the inner section then develops into a rotating geostrophic core flanked above and be low by two nonlinear Ekman boundary layers and exits at the outer section. In this study, the rotation rate of the cavity is fixed at a given high val ue, corresponding to an Ekman number E = 2.24 x 10(-3). When the throughflo w is weak, the motion is steady and the boundary layer flow is well describ ed by Ekman's analytical solution. On increasing the mass flow rate, the fl ow becomes unsteady and perturbations appear in the form of counterrotating pairs of vortices adjacent to upper and lower surfaces of the cavity. Mult iple stable solutions, involving circular and spiral waves with different n umbers of arms, are obtained at fixed mass flow rate. The wavenumber and fr equency of both circular and spiral waves are determined to be characterist ic of the type II viscous Ekman layer instability. (C) 2001 Elsevier Scienc e Inc. All rights reserved.