Subgrid-scale effects in compressible variable-density decaying turbulence

G. S. Sidharth, Graham V. Candler

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Many turbulent flows are characterized by complex scale interactions and vorticity generation caused by compressibility and variable-density effects. In the large-eddy simulation of variable-density flows, these processes manifest themselves as subgrid-scale (SGS) terms that interact with the resolved-scale flow. This paper studies the effect of the variable-density SGS terms and quantifies their relative importance. We consider the SGS terms appearing in the density-weighted Favre-filtered equations and in the unweighted Reynolds-filtered equations. The conventional form of the Reynolds-filtered momentum equation is complicated by a temporal SGS term; therefore, we derive a new form of the Reynolds-filtered governing equations that does not contain this term and has only double-correlation SGS terms. The new form of the filtered equations has terms that represent the SGS mass flux, pressure-gradient acceleration and velocity-dilatation correlation. To evaluate the dynamical significance of the variable-density SGS effects, we carry out direct numerical simulations of compressible decaying turbulence at a turbulent Mach number of 0.3. Two different initial thermodynamic conditions are investigated: homentropic and a thermally inhomogeneous gas with regions of differing densities. The simulated flow fields are explicitly filtered to evaluate the SGS terms. The importance of the variable-density SGS terms is quantified relative to the SGS specific stress, which is the only SGS term active in incompressible constant-density turbulence. It is found that while the variable-density SGS terms in the homentropic case are negligible, they are dynamically significant in the thermally inhomogeneous flows. Investigation of the variable-density SGS terms is therefore important, not only to develop variable-density closures but also to improve the understanding of scale interactions in variable-density flows.

Original languageEnglish (US)
Pages (from-to)428-459
Number of pages32
JournalJournal of Fluid Mechanics
StatePublished - Jul 10 2018

Bibliographical note

Funding Information:
We thank Dr P. Subbareddy and the reviewers for suggestions that improved the paper. This work was sponsored by the Air Force Office of Scientific Research under grant nos FA9550-12-1-0461 and FA9550-17-1-0250, and Department of

Publisher Copyright:
© 2018 Cambridge University Press.


  • compressible turbulence
  • isotropic turbulence
  • turbulent mixing


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