A Benard convection problem with a perturbed lower wall

Abstract

The classical Benard problem of fluid confined between two horizontal boundaries and heated from below is perturbed by making the elevation of the lower wall a small and slowly varying function of the horizontal coordinate. Modified amplitude equations, both linear and nonlinear, are found, and modified critical Rayleigh numbers are calculated. For the type of solution found it appears that the horizontal wavenumber is uniquely determined.