Turbulent convection in the zero Reynolds number limit

Abstract

We discuss thermal convection in the infinite Prandtl number limit. This is relevant for convection in planetary interiors, where inertia of momentum is neglegible, i.e., the Reynolds number of the flow is zero. By means of a numerical two-dimensional model of Rayleigh-Bénard convection, we investigate the evolution of a flow at the Rayleigh number (Ra=108) and demonstrate that even in this zero Reynolds number limit convection exhibits key features of turbulent flow, commonly addressed to high Reynolds number convection. Special attention is given to the phenomenon of reversals in the orientation of the underlying large-scale circulation of the flow. Our case study indicates that flow reversals are an intrinsic feature of turbulent thermal convection resulting from competing states whose main modes turn out to be solutions of the underlying stationary equations.