Transverse instability of traveling wave created by longwave Marangoni convection in the liquid layer covered by insoluble surfactant

Abstract

We consider the Marangoni convection in a liquid layer heated from below. The liquid interface is covered by insoluble surfactant that plays an active role in the pattern formation together with inhomogeneity of temperature along the interface and surface deformability. In the vicinity of the onset of Marangoni convection, besides different kinds of stationary patterns (hexagons, rolls, squares), the appearance of wave patterns is possible. We analyze the transverse instability of the single traveling wave (TW) using generalizations of the complex Ginzburg–Landau equation (CGLE).