# A systematic comparison of two-equation RANS turbulence models applied to shock-cloud interactions

## TL;DR

This paper systematically compares six two-equation RANS turbulence models in hydrodynamical simulations, focusing on shock-cloud interactions, and evaluates their performance against high-resolution and ensemble-averaged simulations.

## Contribution

It develops a unified framework for implementing and verifying multiple turbulence models in the Athena code, and applies them to astrophysical shock-cloud interactions.

## Key findings

- Turbulence models increase cloud mixing and spreading.
- Models show variability in predictions of mixing.
- High-resolution inviscid simulations also exhibit increased mixing.

## Abstract

Turbulence models attempt to account for unresolved dynamics and diffusion in hydrodynamical simulations. We develop a common framework for two-equation Reynolds-Averaged Navier-Stokes (RANS) turbulence models, and we implement six models in the Athena code. We verify each implementation with the standard subsonic mixing layer, although the level of agreement depends on the definition of the mixing layer width. We then test the validity of each model into the supersonic regime, showing that compressibility corrections can improve agreement with experiment. For models with buoyancy effects, we also verify our implementation via the growth of the Rayleigh-Taylor instability in a stratified medium. The models are then applied to the ubiquitous astrophysical shock-cloud interaction in three dimensions. We focus on the mixing of shock and cloud material, comparing results from turbulence models to high-resolution simulations (up to 200 cells per cloud radius) and ensemble-averaged simulations. We find that the turbulence models lead to increased spreading and mixing of the cloud, although no two models predict the same result. Increased mixing is also observed in inviscid simulations at resolutions greater than 100 cells per radius, which suggests that the turbulent mixing begins to be resolved.