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  • Open Access

Transition to dilatation-dominated isothermal compressible turbulence

Shadab Alam1, Christoph Federrath2, and Jörg Schumacher1,*

  • *Contact author: joerg.schumacher@tu-ilmenau.de
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Phys. Rev. Research 8, 033011 – Published 6 July, 2026

DOI: https://doi.org/10.1103/xtt8-k51b

Abstract

The kinetic energy dissipation rate is of central importance for small-scale statistics in turbulent flows. Here, we report a transition to the dilatation-dominated regime of three-dimensional isothermal fully compressible, homogeneous, isotropic turbulence by moments of energy dissipation and its components up to order 4 for root-mean-square (rms) Mach numbers 0.1≤Mrms≤10 and for Reynolds numbers 100≤Re≤2400. Our high-resolution numerical simulations show a crossover from incompressible to Mrms-independent, Burgers turbulencelike scaling of energy dissipation rate moments with respect to Reynolds number Re. This confirms the statistical dominance of shocks for rms Mach numbers Mrms≳1.

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Phys. Rev. Research 8, 033011– Published 6 July, 2026
  • Received 10 January 2026
  • Revised 9 April 2026
  • Accepted 4 June 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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