Thermally Driven Flow in a Rotating Spherical Shell: Axisymmetric States

Abstract

Numerical models are utilized to study a spherical analogue of the rotating annulus experiments modeling atmospheric motion. Motivation for this work is partially provided by NASA's proposal to conduct such an experiment on Spacelab (the Atmospheric General Circulation Experiment). A liquid is contained between two rigid, co-rotating, concentric hemispheres, with thermal gradients imposed upon both spheres. Temperature are lower on the inner sphere than on the outer sphere, and decrease towards the pole. A constant radial body force (inward) is assumed. Utilizing the Navier-Stokes equations assuming symmetry about the polar axis, finite-difference numerical models obtain steady-state solutions to the equations. The differences in solutions for case of varying rotation rates and latitudinal thermal gradients are discussed and explained. Hydrostatic and nonhydrostatic solutions are compared for cylindrical and spherical cases. For the spherical shell, it is found that the differences between hydrostatic and nonhydrostatic solutions are small, and the differences are confined mostly to regions near the pole and equator. It is suggested that nonhydrostatic effects upon the axisymmetric state will not affect the baroclinic stability of the flow.