Thermosolutal convection in a rotating viscoelastic Walters fluid

Abstract

In this paper we study the nonlinear Lyapunov stability of the thermodiffusive equilibrium of a viscoelastic rotating Walters fluid, in a horizontal rotating layer heated and salted from below. We reformulate the nonlinear stability problem, projecting the initial perturbation evolution equations on some suitable subspaces of the space of kinematically admissible functions. In this way we preserve the contribution of the Coriolis term and, jointly, all nonlinear terms vanish. When the viscoelasticy parameter vanishes, that is for the classical rotating Bénard problem, if instability occurs as stationary convection, the linear and nonlinear stability bounds are equal.