Theoretical study of flow coupling mechanisms in two-layer Rayleigh-Bénard convection

Rayleigh-Bénard convection in a system of two superimposed immiscible fluids, heated from below, is investigated theoretically. In a two-layer system, stationary convection is characterized by two distinct modes of flow coupling, namely, thermal coupling and viscous coupling. We derive two coupled amplitude equations in order to describe the nonlinear interaction of the viscous and the thermal coupling modes, whereby we restrict our analysis to the two-dimensional case. By analyzing the amplitude equations for varying fluid parameters, we make predictions concerning the stability of the involved coupling modes in the weakly nonlinear regime.