Numerical Simulations of Shock-driven Heavy Fluid Layer

Abstract

The present study presents the numerical simulations for a shocked-heavy fluid layer with a stratified N₂/SF₆/N₂ configuration. Simulations were conducted using a third-order modal discontinuous Galerkin method to solve the compressible two-component Euler equations. The results were validated against experimental data, confirming the accuracy of the computational approach. Dynamics of the heavy fluid layer were found to be strongly influenced by the shock Mach numbers M_s = 1.15, 1.25, 1.5. At a lower Mach number Ms = 1.15, the interface deformations remained smooth and relatively symmetric, with limited vorticity generation and weak perturbations. Baroclinic effects at this stage were minimal, and the instability growth remained linear. As the Mach number increased to M_s = 1.25, the interaction became nonlinear, leading to the formation of small-scaled vortex structures driven by moderate baroclinic effects. Interface mixing intensified as rotational motion increased. At the highest Mach number M_s = 1.5, the interface rapidly evolved into chaotic structures, characterized by significant vorticity amplification, vortex roll-up, and the onset of turbulence. The baroclinic vorticity, resulting from the misalignment of pressure and density gradients, dominated the vorticity production mechanism, particularly at higher Mach numbers. Quantitative analysis demonstrated that average vorticity, baroclinic vorticity, and enstrophy grew rapidly with increasing Mach numbers. Enstrophy, which quantifies turbulence intensity, exhibited pronounced growth at M_s = 1.5, marking the transition to turbulent mixing.