Pulse evolution for Marangoni-Benard convection

Abstract

Marangoni-Benard convection is the process by which oscillatory waves are generated on an interface due to a change in surface tension. This process, which can be mass or temperature driven, is described by a perturbed Korteweg-de Vries (KdV) equation. For a certain parameter range, this perturbed KdV equation has a solitary wave solution with an unique steady-state amplitude for which the excitation and friction terms in the perturbed KdV equation are in balance. The evolution of an initial sech2 pulse to the steady-state solitary wave governed by the perturbed KdV equation of Marangoni-Benard convection is examined. Approximate equations, derived from mass conservation, and momentum evolut..