Solitary waves in Marangoni-Bénard convecting fluid

Abstract

In this paper the evolution of nonlinear long surface waves in a Marangoni-Benard convecting fluid is considered. The fluid system is bounded below by an isothermic plane and above a free deformable surface, on which a heat flux is fixed. We show that the nonlinear behavior of the long surface wave is governed by the Korteweg-de Vries equation when the Rayleigh number is near its critical value. A head-on collision between two solitary waves traveling from opposite directions is also investigated by use of the Poincare-Lighthill-Kuo method. The results show that the solitary waves emerging from the collision can preserve their original identities to the second order. The phase shifts due to the collision are calculated analytically.