Compressible Turbulence: The Cascade and its Locality

TL;DR

This paper proves that in compressible turbulence, kinetic energy transfer predominantly occurs through local interactions, establishing a conservative cascade over an inertial range and challenging the belief of direct energy transfer to shocks.

Contribution

It demonstrates that kinetic energy transfer in compressible turbulence is dominated by local interactions and establishes the existence of a conservative inertial range.

Findings

Local interactions dominate energy transfer.

Existence of an inertial range with constant energy flux.

Decoupling of kinetic and internal energy beyond a transitional range.

Abstract

We prove that inter-scale transfer of kinetic energy in compressible turbulence is dominated by local interactions. In particular, our results preclude direct transfer of kinetic energy from large-scales directly to dissipation scales, such as into shocks, in high Reynolds number turbulence as is commonly believed. Our assumptions on the scaling of structure functions are weak and enjoy compelling empirical support. Under a stronger assumption on pressure dilatation co-spectrum, we show that mean kinetic and internal energy budgets statistically decouple beyond a transitional "conversion" range. Our analysis establishes the existence of an ensuing inertial range over which mean SGS kinetic energy flux becomes constant, independent of scale. Over this inertial range, mean kinetic energy cascades locally and in a conservative fashion, despite not being an invariant.