Oscillatory convection in rotating spherical shells: low Prandtl number and non-slip boundary conditions

Abstract

A five-degree model, which reproduces faithfully the sequence of bifurcations and the type of solutions found through numerical simulations of the three-dimensional Boussinesq thermal convection equations in rotating spherical shells with fixed azimuthal symmetry, is derived. A low Prandtl number fluid of s=0. 1 subject to radial gravity, filling a shell of radius ratio ¿=0.35, differentially heated, and with non-slip boundary conditions, is considered. Periodic, quasi-periodic, and temporal chaotic flows are obtained for a moderately small Ekman number, E=10-4,andatsupercritical Rayleigh numbers of order Ra~O(2Rac). The solutions are classified by means of frequency analysis and Poincaré sections. Resonant phase locking on the quasi-periodic branches,as well as a sequence of period doubling bifurcations, are also detected.