Nonlinear Evolution of the Skewed Varicose Instability in Thermal Convection

Abstract

Rayleigh-Bénard convection in a horizontal layer of incompressible fluid has become a standard illustration for the generation of spatio-temporal structures. The first and simplest pattern which arises, when the increase of the thermal gradient destabilizes the basic homogeneous state, consists of straight convective rolls. The stability of this pattern depends on the Rayleigh number Ra, the Prandtl number Pr and on the wavenumber of the rolls. In this parameter space the domain of stability with respect to various types of perturbations was investigated in a series of papers by Busse and coworkers [1]. In particular, it has turned out [2] that in case of an infinite layer with stress-free boundaries the rolls in a fluid with sufficiently low Prandtl number, Pr ≤ 0.543, are unstable with respect to skewed varicose perturbations already at the very onset of convection.