Marangoni waves in a two-layer film under the action of an inclined temperature gradient

Abstract

The development of the longwave deformational instability of a thermocapillary flow in a two-layer film under the action of an inclined temperature gradient is studied in the framework of the lubrication approximation. The stability boundaries with respect to different oscillatory modes are calculated by means of the linear stability theory. In a contradistinction to the case of a vertical temperature gradient, these boundaries strongly depend on the direction of the wave propagation. Numerical simulations of spatially periodic nonlinear regimes are fulfilled. It is shown that because of the anisotropy of the problem, the most typical kind of patterns is a traveling wave. For small inclination of the temperature gradient, temporally quasiperiodic waves are observed. A number of new three-dimensional traveling wave planforms is revealed.