Nonlinear Rayleigh-Taylor instability of pendent finite-thickness film subjected to vibration

In this study, the realization of nonlinear saturation states in Rayleigh-Taylor instability subjected to vertical vibration is extended beyond the constraints of the thin film regime through comprehensive linear stability analysis and direct numerical simulations. The linear analysis reveals that increasing fluid layer thickness significantly reduces critical amplitudes for the onset of Faraday instability (FI) at low frequencies, while this effect diminishes at high frequencies due to the associated increase in critical wavenumber. The nonlinear evolution of perturbation amplitude proceeds through three distinct stages: growth, decay, and quasi-steady evolution. The excitation and eventual stabilization of FI are clarified using the local average thickness model, which demonstrates the coupling mechanism between FI mode amplitude and local thickness variations. It is found that the saturated amplitude of the interface decreases with increasing vibration amplitudes. Furthermore, the presence of stable RT modes is shown to effectively suppress FI, ultimately leading the interface to harmonic saturated states.