Competing Mechanisms at Vibrated Interfaces of Density-Stratified Fluids (2505.23578v1)

Abstract: Fluid--fluid interfacial instability and subsequent fluid mixing are ubiquitous in nature and engineering. Two hydrodynamic instabilities have long been thought to govern the interface behavior: the pressure gradient-driven long-wavelength Rayleigh--Taylor (RT) instability and resonance-induced short-wavelength Faraday instability. However, neither instability alone can explain the dynamics when both mechanisms act concurrently. Instead, we identify a previously unseen multi-modal instability emerging from their coexistence. We show how vibrations govern transitions between the RT and Faraday instabilities, with the two competing instead of resonantly enhancing each other. The initial transient growth is captured by the exponential modal growth of the most unstable Floquet exponent, along with its accompanying periodic behavior. Direct numerical simulations validate these findings and track interface breakup into the multiscale and nonlinear regimes, in which the growing RT modes are shown to suppress Faraday responses via a nonlinear mechanism.