Post-shock Turbulence Structure and Dynamics in the Multi-fluid Shock-Turbulence Interaction

The variable density effects on the post-shock turbulence structure and dynamics are studied using accurate turbulence-resolving shock-capturing Eulerian simulations, together with a Lagrangian particle tracking algorithm. Detailed grid and statistical convergence tests are conducted to show that the simulations are insensitive to the grid resolution and the sample sizes are large enough for statistical analysis. Results show that the density variations not only affect the turbulence structure immediately after the shock wave but also significantly change the transient development in the post-shock region. The correlation between fluid density and flow topology is observed to be significant as the examination of the joint PDFs of the second and third invariants of the velocity gradient tensor indicates. This is identified to be caused by the different roles that density plays through the interaction with the shock wave, which results in a misalignment between the density gradient and vorticity. The dynamics of the turbulence structure in the post-shock region are further examined by the Lagrangian particle method. The variable density effects are found to be mainly manifested in the pressure Hessian contribution in the Lagrangian dynamical equations.