Nonlinear Pattern Formation near the Onset of Rayleigh-Bénard Convection

Abstract

It is shown that many of the experimentally observed features of pattern formation in Rayleigh-B\'enard convection near onset can be understood in terms of a two-dimensional relaxational equation. In particular, it is shown that disordered roll patterns follow a complicated dynamics that can require up to a hundred horizontal diffusion times to reach equilibrium.