Conservative cascade of kinetic energy in compressible turbulence

Abstract

The physical nature of compressible turbulence is of fundamental importance in a variety of astrophysical settings. We investigate the question: "At what scales does the mechanism of pressure-dilatation operate?" and present the first direct evidence that mean kinetic energy cascades conservatively beyond a transitional "conversion" scale range despite not being an invariant of the dynamics. We use high-resolution 10243 subsonic and transonic simulations. The key quantity we measure is the pressure-dilatation cospectrum, E PD(k), where we show that it decays at a rate faster than k -1 in wavenumber in at least the subsonic and transonic regimes. 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. However, we observe that small-scale dynamics remains highly compressible locally in space and that the statistical decoupling in the energy budgets is unrelated to the existence of a subsonic scale range. Our results suggest that an extension of Kolmogorov's inertial-range theory to compressible turbulence is possible. © 2012. The American Astronomical Society. All rights reserved..