Three-dimensional quasiperiodic torsional flows in rotating spherical fluids at very low Prandtl numbers

Abstract

The aim of this study is to determine through numerical simulations the extent and robustness of the three-dimensional torsional dynamics of the thermal convection in rotating spherical fluids at very low Prandtl numbers. It is known that the kinetic energy of the periodic axisymmetric flows propagates latitudinally on the surface of the sphere. Here, it is shown that when the axisymmetry is broken at a secondary Hopf bifurcation, the flow starts to drift in the azimuthal direction giving rise to a quasiperiodic motion that propagates the energy in latitude and longitude. The double direction of propagation gives rise to a meandering path of the kinetic energy, which is still concentrated on the surface, but highly localized. Several new stable states of convection with different symmetries have been identified in a large range of Rayleigh numbers, all of them retaining the torsional motion of the basic velocity field. Particular attention is paid to their dependence on the Rayleigh number and on the values of the frequencies, of the mean zonal flow, and of the kinetic energy of the fluid.