Stability of thermal vibrational flow in an inclined liquid layer against finite-frequency vibrations

Stability of the flow that arises under the action of a gravity force and streamwise finite-frequency vibrations in a nonuniformly heated inclined liquid layer is studied. By the Floquet method, linearized convection equations in the Boussinesq approximation are analyzed. Stability of the flow against planar, spiral, and three-dimensional perturbations is examined. It is shown that, at finite frequencies, there are parametric-instability regions induced by planar perturbations. Depending on their amplitude and frequency, vibrations may either stabilize the unstable ground state or destabilize the liquid flow. The stability boundary for spiral perturbations is independent of vibration amplitude and frequency.