A nonlinear analysis of the stabilizing effect of rotation in the Bénard problem

Abstract

This paper uses a novel ‘generalized energy’ to study the stabilizing effect of rotation in the Bénard problem. The nonlinear stability boundary we find is in very close agreement with the experiments of Rossby (Rossby, H. T. J . Fluid Mech . 36, 309–335 (1969)), who predicts sub-critical instabilities for high Taylor numbers for fluids with Prandtl number greater than or equal to 1, such as water.