Synchronization of Marangoni waves by temporal modulation of interfacial heat consumption

It is known that a horizontal two-layer liquid film heated from above is subject to a long-wave oscillatory Marangoni instability. The action of a time-periodic modulation of interfacial heat consumption on the temporal dynamics of nonlinear Marangoni waves is investigated. The problem is studied numerically in the framework of long-wave amplitude equations. We focus on the phenomenon of synchronization between instability-induced oscillations and external parameter modulation. It is found that the time-periodic heat consumption modulation can create either a time-periodic regime (synchronization) or a quasiperiodic regime (no synchronization). Diagrams of regimes are constructed.