Compressible Turbulence: The Cascade and its Locality

Hussein Aluie
Phys. Rev. Lett. 106, 174502 – Published 28 April 2011

Abstract

We prove that interscale 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 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 cospectrum, 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 subgrid scale 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.

  • Received 2 January 2011

DOI:https://doi.org/10.1103/PhysRevLett.106.174502

© 2011 American Physical Society

Authors & Affiliations

Hussein Aluie

  • Applied Mathematics and Plasma Physics (T-5) & Center for Non-linear Studies, Los Alamos National Laboratory, MS-B258 Los Alamos, New Mexico 87545, USA

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Issue

Vol. 106, Iss. 17 — 29 April 2011

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