Static, wavelike, and chaotic thermal convection in spherical geometries

Abstract

The onset of convection in a fluid contained between a hot inner and a cold outer spherical boundary in a radially symmetric gravity field is examined. Due to the spherical symmetry there are usually (2l+1) unstable modes belonging to the lth irreducible representation of the O(3) group. The actual value of l is determined by a properly defined aspect ratio. There are special values of this aspect ratio where two groups of modes simultaneously become unstable. The instability involving the two groups of modes with l=1 and l=2 is considered by investigating the corresponding generalized Ginzburg-Landau equations. By varying the Rayleigh number and the aspect ratio a variety of interesting spatio-temporal behavior is observed. The occurring static, time periodic, and quasiperiodic fluid motions as well as the various types of chaotic fluid flow are examined in detail.