Nonlinear waves and turbulence in Marangoni convection

Abstract

In the paper we present a numerical study of a new type of nonlinear waves in Marangoni convection. The waves are caused by nonlinear interaction between long-scale deformational instability and short-scale convection. It is shown that, due to a nonlinear coupling with the deformation of the free liquid–gas interface, the primary convection pattern can undergo oscillatory instability generating various kinds of long surface waves which modulate the short-scale convection. The numerical analysis of the system of nonlinear coupled equations describing these waves confirms the predictions of weakly nonlinear analysis and shows the existence of either standing or travelling waves in the proper parametric regions, at low supercriticality. With increasing supercriticality, the waves undergo various transformations leading to the formation of pulsating travelling waves, aharmonic standing waves as well as irregular wavy behavior resembling ‘‘interfacial turbulence.’’ We map regions in the parameter space where various kinds of waves can be observed, and describe some characteristics of irregular wavy behavior.