Rotating Rayleigh–Taylor instability in viscous, elastic, and viscoelastic media

This study investigates the linear stability of the Rayleigh–Taylor instability in viscous fluids, elastic solids, and viscoelastic media (Maxwell fluids and Kelvin–Voigt solids) subject to rotation with the axis perpendicular to gravity. By establishing a unified dispersion relation, we theoretically demonstrate that rotation serves as a universal stabilizing mechanism across all considered rheological models, fundamentally altering the instability from a purely growing mode to an oscillatory traveling-wave mode. In viscous fluids, the Coriolis force monotonically suppresses the peak growth rate and shifts the dominant instability toward shorter wavelengths, although the dynamics remain governed by viscous mechanisms. In elastic solids, rotation compresses the unstable wavenumber bandwidth and reduces the cutoff wavenumber; notably, a critical rotation rate is identified beyond which the instability is completely suppressed. In viscoelastic media, the coupling between rotation and material relaxation yields complex behaviors. For Maxwell fluids, stress relaxation exhibits a regime-dependent dual role at fixed wavenumbers but consistently destabilizes the most unstable mode. Conversely, in Kelvin–Voigt solids, viscosity acts as a stabilizing factor under weak rotation but becomes destabilizing under strong rotation by damping the Coriolis-induced oscillations. Furthermore, the comparative analysis reveals that the characteristic modal transitions in both viscoelastic models originate from the competition between elastic restoring forces and viscous dissipation.