Laminar Compressible Flow Over a Stationary Disk in a Rotating Cylinder

The laminar isothermal compressible flow in a rotating cylinder with a stationary bottom is treated both numerically and by boundary layer matching. The numerical solution of the Navier-Stokes equations is based on a modified Cheng-Allen finite difference scheme. An approximate solution is obtained by matching boundary layers to an interior core. For sufficiently low Ekman numbers, the approximate and numerical solutions are in close agreement. The compressibility is shown to increase the angular velocity in the core and to decrease the meridional circulation. When the aspect ratio of the cylinder is increased, both the angular velocity in the core and the meridional circulation increase.