Oscillatory Convection in Rotating Spherical Shells: Low Prandtl Number and Non-Slip Boundary Conditions

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 σ = 0.1 subject to radial gravity, filling a shell of radius ratio η = 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, and at supercritical 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.