# Density Effects on the Post-shock Turbulence Structure and Dynamics

## TL;DR

This study investigates how density variations influence the turbulence structure and dynamics after a Mach 2 shock, revealing significant modifications in flow topology and statistical properties through advanced simulations.

## Contribution

It provides new insights into the role of density in turbulence-shock interactions using turbulence-resolving simulations and detailed statistical analyses.

## Key findings

- Density significantly alters turbulence structure and flow topology.
- Multi-species cases show more symmetrical turbulence PDFs post-shock.
- Pressure Hessian contributions are critically affected by shock and density.

## Abstract

Turbulence structure resulting from multi-fluid or multi-species, variable-density isotropic turbulence interaction with a Mach 2 shock is studied using turbulence-resolving shock-capturing simulations and Eulerian (grid) and Lagrangian (particle) methods. The complex roles density play in the modification of turbulence by the shock wave are identified. Statistical analyses of the velocity gradient tensor (VGT) show that the density variations significantly change the turbulence structure and flow topology. Specifically, a stronger symmetrization of the joint probability density function (PDF) of second and third invariants of the anisotropic velocity gradient tensor, PDF$(Q^\ast, R^\ast)$, as well as the PDF of the vortex stretching contribution to the enstrophy equation, are observed in the multi-species case. Furthermore, subsequent to the interaction with the shock, turbulent statistics also acquire a differential distribution in regions having different densities. This results in a nearly symmetrical PDF$(Q^\ast, R^\ast)$ in heavy fluid regions, while the light fluid regions retain the characteristic tear-drop shape. To understand this behavior and the return to "standard" turbulence structure as the flow evolves away from the shock, Lagrangian dynamics of the VGT and its invariants are studied by considering particle residence times and conditional particle variables in different flow regions. The pressure Hessian contributions to the VGT invariants transport equations are shown to be not only affected by the shock wave, but also by the density in the multi-fluid case, making them critically important to the flow dynamics and turbulence structure.