The conservative cascade of kinetic energy in compressible turbulence

TL;DR

This study provides numerical evidence that in compressible turbulence, kinetic energy cascades conservatively beyond a certain scale, allowing for an extension of classical turbulence theory.

Contribution

First direct numerical evidence showing that mean kinetic energy cascades conservatively in compressible turbulence beyond a transitional scale.

Findings

Pressure dilatation decays faster than $k^{-1}$, indicating decoupling of kinetic and internal energy.

Kinetic energy cascade remains conservative beyond a transitional scale.

Results support extending Kolmogorov's inertial-range theory to compressible flows.

Abstract

The physical nature of compressible turbulence is of fundamental importance in a variety of astrophysical settings. We present the first direct evidence that mean kinetic energy cascades conservatively beyond a transitional "conversion" scale-range despite not being an invariant of the compressible flow dynamics. We use high-resolution three-dimensional simulations of compressible hydrodynamic turbulence on $512^3$ and $1024^3$ grids. We probe regimes of forced steady-state isothermal flows and of unforced decaying ideal gas flows. The key quantity we measure is pressure dilatation cospectrum, $E^{PD}(k)$, where we provide the first numerical evidence that it decays at a rate faster than $k^{-1}$ as a function of wavenumber. This is sufficient to imply that mean pressure dilatation acts primarily at large-scales and that kinetic and internal energy budgets statistically decouple beyond a transitional scale-range. Our results suggest that an extension of Kolmogorov's inertial-range theory to compressible turbulence is possible.