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 $\sigma=0.1$ subject to radial gravity, filling a shell of radius ratio $\eta=0.35$, 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 $Ra\sim O(2Ra_c)$. 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.
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