Flow of a stratified fluid in a cylinder with a rotating lid

Abstract

A numerical study is made for the flow of a density-stratified fluid in a vertical cylinder with a rotating top lid. Under the Boussinesq-fluid assumption, the governing Navier-Stokes equations are numerically solved. For large rotational Reynolds number Re and the cylinder aspect ratio A similar to O(1), details of flow and temperature fields are displayed. The effect of the Prandtl number on global flow patterns is scrutinized for both gravitationally unstable and gravitationally stable configurations. Of particular interest is the behavior of the vortex breakdown stagnation bubble under the influence of buoyancy. Plots are presented for the azimuthal vorticity fields, in line with the simple axisymmetric inviscid kinematic consideration. An explicit comparison is made for the individual terms appearing in the azimuthal vorticity equation. For both gravitationally unstable and gravitationally stable configurations, the argument based on the behavior of azimuthal vorticity is seen to produce predictions consistent with the numerical results. (C) 1999 Elsevier Science Inc. All rights reserved.