Abstract
A numerical study is made of the early-stage behavior of spin-up flows of a highly compressible fluid in a rapidly-rotating cylinder. The focus is placed on describing the temporally small-scale motions within and near the Ekman layers. Numerical solutions are acquired to the full, time-dependent, compressible Navier-Stokes equations. The numerical results are processed to render physically meaningful interpretations of the small-time behavior in and around the Ekman layer. Vector plots on the meridional plane are constructed to illustrate the prominence of the compressible Rayleigh effect in the nonlinear regime. The emergence of the corner jet is portrayed. Extensive diagnostic studies are performed to disclose the dominant dynamic effects. Time-histories of the major physical variables are plotted. The time needed for the formation of the Ekman layer is seen to shorten in the nonlinear regime. The oscillatory behavior is clearly depicted, and it is demonstrated that, as the nonlinearity strengthens, the oscillatory frequency increases and the more irregular oscillation patterns emerge.
