Rayleigh–Taylor Instability Across Flow Regimes: A Study in the Knudsen–Mach Parameter Space

The Rayleigh–Taylor instability (RTI) is examined across a broad range of flow regimes defined by the Knudsen number (Kn) and Mach number (M), capturing the transition from continuum to rarefied conditions. To resolve the distinct physical mechanisms that emerge across the Kn–M parameter space, a hierarchy of flow models is employed, with each regime investigated using two independent numerical approaches for validation. In the continuum regime (low Kn), the Navier–Stokes–Fourier (NSF) Equations accurately capture classical advective instability on both the bubble and spike sides. As Kn increases and non-equilibrium effects begin to manifest, the Gas Kinetic Method (GKM) is used to explore the transitional regime. Here, with increasing Kn, a pronounced advective–diffusive asymmetry emerges between the bubble and spike evolution—advective behavior dominates on the bubble side, while enhanced diffusion characterizes the spike side. This asymmetric behavior is confirmed independently using the Unified Gas Kinetic Scheme (UGKS), which is then extended to higher Kn regimes. At large Knudsen numbers, where non-equilibrium effects are dominant, UGKS reveals a fundamentally ballistic diffusive mode of instability evolution, marked by the loss of coherent advective structures. This behavior is further validated using the Direct Simulation Monte Carlo (DSMC) method, reinforcing the transition to a fully kinetic, diffusion-driven regime.

This multi-regime modeling framework provides a comprehensive view of RTI dynamics across continuum, transitional, and kinetic regimes. The results offer new insights into the structure and evolution of RTI under varying Knudsen and Mach numbers, with implications for high-speed aerodynamics, inertial confinement fusion, and astrophysical flows where rarefied gas effects are significant.