Influence of relaxation time on the two-dimensional Kelvin–Helmholtz instability under dual-mode perturbations

In this paper, a two-component discrete Boltzmann method is used to investigate the influence of the relaxation time on the two-dimensional compressible Kelvin–Helmholtz instability under dual-mode perturbations. The evolution characteristics of density gradient, vorticity, mixing entropy, Knudsen number ( Kn ), and thermodynamic non-equilibrium (TNE) effects are analysed. The results reveal that increasing relaxation time enhances diffusive and dissipative effects, leading to smoother interfaces, weaker vortex structures and suppressed instability growth. The global density gradient and vorticity intensity decrease accordingly. Mixing entropy analysis shows that larger relaxation times promote early mixing through diffusion, while smaller ones enhance late-stage mixing via vortex-induced convection. The Kn and TNE counters exhibit similar spatial and temporal variations, both effectively capturing the interface dynamics and deviations from local equilibrium. Both their magnitudes and the area over which they are spatially distributed increase with relaxation time, reflecting enhanced non-equilibrium effects. Besides, the global Kn and average TNE intensity initially rise, then decline, increase again and finally decrease, increasing with the relaxation time. These are jointly driven by the competitive physical mechanisms of the interface stretching, vortex merging and diffusion mechanisms. The findings provide a theoretical foundation for further exploration of non-equilibrium processes in complex fluid systems.