Effect of gravity profiles on Rayleigh-Benard convection in spherical shells.

Rayleigh-Benard convection of flows confined by spherical boundaries is analysed by three-dimensional direct numerical simulations in spherical coordinates. The dynamics under different radial gravity profiles have been explored: the different gravity laws can often be absorbed by the introduction of an effective Rayleigh number $Ra_e$, although this is not true for a few particular cases with non-monotonic gravity. Two different fluids have been studied: air (Prandtl number $Pr=0.71$) and water ($Pr=7.1$), and in both cases, onset of convection is at $Ra_e=1800$ for a domain aspect ratio $\eta=0.71$. On the other hand unsteady convection, occurring when the inertial terms overcome the viscous terms, has a clear dependence on $Pr$ and is thus different between the two fluids. In between these two regimes, a series of different quasi-stable states, with a non trivial dependence on the Prandtl number, appear as $Ra$ is increased: this behaviour can induce hysteresis in the system and initial conditions are crucial to determine the final flow configuration.