Nonlinear diffusion process in a Bénard system at the critical point for the onset of convection

Abstract

The evolution equation governing surface perturbations of a shallow fluid heated from below at the critical Rayleigh number for the onset of convective motion, and with boundary conditions leading to zero critical wave number, is obtained. A solution for negative or cooling perturbations is explicitly exhibited, which shows that the system presents sharp propagating fronts. © 1993 The American Physical Society.