Competition between diffusive damping and instability growth in a rarefied Rayleigh–Taylor system

The mechanisms underlying the generation and evolution of Rayleigh–Taylor instability (RTI) in rarefied gases are an important issue, particularly in many emerging problems where rarefaction effects become significant. Using a graphics processing unit parallelised direct simulation Monte Carlo approach, we simulate RTI across a wide range of Knudsen numbers (

), and find that instability growth is progressively inhibited as

upper K n K n $Kn$

increases, with complete suppression above a critical value

upper K n almost equals 0.011 K n ≈ 0.011 $Kn \approx 0.011$

. Molecular-scale analysis reveals that rarefaction enhances super-diffusive transport of the molecules, extending the ballistic regime, and favouring the interfacial mixing. This microscale behaviour macroscopically manifests as a rapid decay of the density gradient and the effective Atwood number. To determine whether instability emerges in rarefied conditions, we introduce a stability criterion based on the competition between a diffusive time scale (

tau Subscript upper D τ D $\tau _D$

) and an instability time scale (

tau Subscript upper I τ I $\tau _I$

). The transition to instability occurs only when

tau Subscript upper I Baseline less than tau Subscript upper D τ I < τ D $\tau _I \lt \tau _D$

, a condition that fails for

upper K n greater than or equivalent to 0.011 K n ≳ 0.011 $Kn \gtrsim 0.011$

. The effect of domain height is interpreted through its influence on the Froude number (

upper F r F r $Fr$

). Small domains (large

upper F r F r $Fr$

) hinder the transition from linear to nonlinear growth, while for larger domains, instability suppression is mainly determined by the threshold Knudsen number. The critical threshold

upper K n almost equals 0.011 K n ≈ 0.011 $Kn \approx 0.011$

remains consistent for sufficiently small

upper F r F r $Fr$

. These findings provide a multiscale perspective on flow instability in rarefied gases, and establish a time scale competition framework that quantitatively explains how rarefaction governs the onset of RTI.