Static, wavelike, and chaotic thermal convection in spherical geometries

Abstract

The onset of convection in a Auid 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 (21+1) unstable modes belonging to the Ith 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 I =1 and 1=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 Auid Aow are examined in detail.

GEOFLOW: simulation of convection in a spherical shell under central force field

“…The 1/r 2 case has shown very rich dynamics, in particular the occurrence of motion reversals (Friedrich and Haken, 1986). This motion has astrophysical relevance because it can help to understand quasi-periodic phenomena such the Earth's magnetic field reversal.…”

Resonant interactions in Bénard-Marangoni convection in cylindrical containers

“…Codimension two (CT) points, where two modes become simultaneously unstable are specially interesting because they can lead to a resonant interaction with a characteristic dynamical behaviour. A similar case has been studied in convection in spherical cells (SO(3) symmetry) by Friedrich and Haken [13].…”

Heteroclinic and Periodic Cycles in a Perturbed Convection Model

“…The purpose, of course, is to learn what choices of v are likely to cause magnetic activity. By numerical simulations for the magnetic field of fluids confined in spherical domains, Friedrich and Haken [10], Buses [4] have shown the existence of periodic attractors. In a later work, Armbruster and Chossat [1] conjectured that the dynamical behavior observed for the magnetic field in some experiments could result as a perturbation of convective flows possessing heteroclinic cycles.…”