Kinetic staging of multi-mode Rayleigh–Taylor instability via thermodynamic nonequilibrium metrics

Multi-mode Rayleigh–Taylor instability (RTI) exhibits more complex nonlinear interactions and richer multiscale interfacial dynamics than single-mode cases, resulting in fundamentally distinct thermodynamic nonequilibrium (TNE) behaviors beyond conventional hydrodynamic predictions. This study employs a multiphase discrete Boltzmann model with surface tension to examine macroscopic dynamics and TNE features of multi-mode RTI. At the macroscopic level, surface tension enhances mode coupling in the early stage, delays the onset of Kelvin–Helmholtz instability, and suppresses mixing between light and heavy fluids. Notably, within a certain range, increasing the surface tension slightly enhances disturbance amplitudes in the later stages. At the nonequilibrium level, various TNE metrics are analyzed to capture fine-scale interface structures and characterize stage-wise evolution. Among these metrics, the global average TNE strength DTNE and heat flux strength D3,1 demonstrate high sensitivity and robustness in identifying distinct evolutionary stages. The growth rate of TNE strength reveals distinct regime transitions: exponential in the linear stage, linear in the self-similar stage, and oscillatory during the turbulent mixing stage. The effects of the initial perturbation wavenumber on RTI evolution are also examined. Although bubble and spike velocities vary considerably with wavenumber, the TNE strength growth rate follows a consistent trend, underscoring its reliability as a staging indicator. These findings demonstrate that TNE-based kinetic diagnostics provide new physical insights into multi-mode RTI evolution, complementing and extending traditional hydrodynamic analysis.