Natural convection between two concentric spheres - Transition toward a multicellular flow

A moderate temperature difference maintained between two concentric spherical surfaces induces, in steady state, unicellular toroidal movements in the enclosed fluid. Beyond a critical temperature difference, the flow becomes unstable and the convective phenomena rearrange into counter-rotating toroidal cells. A two-dimensional axisymmetric numerical model confirms the existence of a unicellular regime and shows that, beyond the critical conditions and for the same set of parameters, two convergent solutions can be obtained. One is unicellular and the other is bicellular; in the latter, the additional cell appears at the top of the layer. The initial conditions determine which one of these two will be established. This transition is investigated as a function of several parameters and the results are compared with the experimental results in the literature.