SURFACE PERTURBATIONS OF A SHALLOW VISCOUS-FLUID HEATED FROM BELOW AND THE (2+1)-DIMENSIONAL BURGERS-EQUATION

Abstract

The (2 + 1)-dimensional Burgers equation is obtained as the equation of motion governing the surface perturbations of a shallow viscous fluid heated from below, provided the Rayleigh number of the system satisfies the condition R not-equal 30. A solution to this equation is explicitly exhibited and it is argued that it describes the nonlinear evolution of a nearly one-dimensional kink.