Effects of compressibility and Atwood number on the instability growth of two-dimensional buoyancy-driven shear layers

Direct numerical simulations are used to investigate the impact of compressibility and compositional variable-density (VD) effects on the growth of instability in buoyancy-driven shear layers (BSL), which exhibit features common to both Rayleigh–Taylor (RTI) and Kelvin–Helmholtz (KHI) instabilities. The two-dimensional simulations are performed in a periodic domain with alternating high- and low-density fluid columns under neutral background stratification. This study expands on previous work by Gat et al. [Incompressible variable-density turbulence in an external acceleration field. J Fluid Mech. 2017;827:506–535. doi: 10.1017/jfm.2017.490] conducted in the incompressible regime. The Atwood number, A, and the isothermal Mach number, Ma, are varied to isolate VD and compressibility effects. Two flow regimes are identified. At early times, shear dominates and the evolution resembles KHI with minimal sensitivity to A or Ma. Later, buoyancy becomes dominant and the flow exhibits RTI-like behaviour; increasing A accelerates this transition. Compressibility suppresses the growth of the mixing-layer, reduces bubble and spike penetration, and amplifies the VD-induced mixing asymmetry. Enhanced molecular mixing weakens the baroclinic torque, shifting vorticity production toward dissipative scales and eventually suppressing mixing-layer growth at sufficiently large Ma. The suppressive effect of compressibility strengthens with increasing A, indicating that VD and compressibility are coupled yet competing influences.