Saturated Rayleigh-Taylor instability of an oscillating Couette film flow (Q2770290)

The authors investigate the nonlinear stability of a two-fluid system consisting of a viscous film bounded above by other heavier and thicker film; the both films are placed between two horizontal plates one of which oscillates horizontally about a fixed position. An evolution equation governing the thickness of the viscous film is derived. Numerical simulations of this equation on extended spatial intervals demonstrate nonlinear small-amplitude saturation of Rayleigh-Taylor instability in certain parametric regimes. The authors also give preliminary results of numerical simulations of film evolution in large-amplitude parametric regimes. At some parameter values, film rupture is observed, similar to the case with no base flow. In other regimes the base flow succeeds in preventing rupture.