NUMERICAL STUDIES OF BAROCLINIC INSTABILITY IN CYLINDRICAL AND SPHERICAL DOMAINS.

Abstract

Finite difference numerical models based upon the Navier-Stokes equations with the Boussinesq approximation have been utilized to study the dynamics of a rotating liquid with horizontal density gradients. There are two configurations analyzed: a cylindrical annulus of water rotating about a vertical axis (parallel to the body force), and a hemispherical shell of silicone oil with a radial body force, rotating about the polar axis. In both the cylindrical and spherical configurations, the thermal and mechanical forcings (boundary conditions) are symmetric about the axis of rotation. The physical parameters varied are the rotation rate and the amplitude of the horizontal thermal forcing. Two numerical models have been developed for each geometrical configuration: one to calculate axisymmetric flows and another to test the stability of those flows to non-axisymmetric perturbations. The primary purpose of the models is to determine whether axisymmetric or non-axisymmetric flow will be observed in a corresponding laboratory experiment. For the cylindrical annulus, the predictions of axisymmetric and non-axisymmetric flow are in good agreement with laboratory experiments previously performed. In the spherical experiment considered, which has not been performed in the laboratory, there is evidence that if the rotation rate is fixed and the latitudinal thermal forcing is reduced, there exists a transition from non-axisymmetric to axisymmetric flow, but that as the rotation rate is decreased for a fixed latitudinal thermal gradient on the boundaries, the flow does not become axisymmetric. The structures of some of the fastest growing eigenmodes are presented for both cylindrical and spherical cases. Analyses of the energetics indicate that the waves in all cases considered are essentially baroclinic in nature.