The Spatial Scaling Laws of Compressible Turbulence

TL;DR

This paper derives the spatial scaling laws for compressible turbulence energy spectra, revealing how they approach the -5/3 power law at different Mach number regimes using dimensional analysis and similarity theory.

Contribution

It formulates the velocity and density-weighted energy spectra scaling laws for compressible turbulence in terms of wavenumber, dissipation rate, and Mach number, applying Barenblatt's incomplete similarity theory.

Findings

Energy spectra approach -5/3 power law at Mach number limits

Scaling laws depend on Mach number regimes

Theoretical framework for compressible turbulence spectra

Abstract

The spatial scaling laws of velocity kinetic energy spectrum for compressible turbulence flow and its density-weighted counterpart have been formulated in terms of wavenumber, dissipation rate and Mach number by using dimensional analysis. We have applied the Barenblatt's incomplete similarity theory to both kinetic and density-weighted energy spectrum and showed that, within the initial subrange, both energy spectrums approach the -5/3 power law of the wavenumber, when the Mach number $M$ tends to be naught, unity and infinity, respectively.