Competing Mechanisms at Vibrated Interfaces of Density-Contrast Fluids

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, their concurrent action remains poorly understood, as neither instability alone captures the resulting dynamics. Here, we reveal a previously unseen multi-modal instability emerging from their coexistence. Using linear Floquet stability analysis, we show how vibrations govern transitions between the RT and Faraday instabilities, leading to competition rather than resonant enhancement. 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. Critically, we show that growing RT modes nonlinearly suppress Faraday responses, establishing a bidirectional competition that hinders their sustained coexistence.