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A semi-Lagrangian direct-interaction closure of the spectra of isotropic variable-density turbulence

Published online by Cambridge University Press:  31 July 2019

David J. Petty Open the ORCID record for David J. Petty [Opens in a new window]  and
C. Pantano Open the ORCID record for C. Pantano [Opens in a new window]
David J. Petty*
Affiliation:
Department of Aerospace and Mechanical Engineering, University of Southern California, 854 Downey Way, Los Angeles, CA 90089, USA
C. Pantano
Affiliation:
Department of Aerospace and Mechanical Engineering, University of Southern California, 854 Downey Way, Los Angeles, CA 90089, USA
*
†Email address for correspondence: pettyj@usc.edu
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Abstract

A study of variable-density homogeneous stationary isotropic turbulence based on the sparse direct-interaction perturbation (SDIP) and supporting direct numerical simulations (DNS) is presented. The non-solenoidal flow considered here is an example of turbulent mixing of gases with different densities. The spectral statistics of this type of flow are substantially more difficult to understand theoretically than those of the similar solenoidal flows. In the approach described here, the nonlinearly coupled velocity and scalar (which determine the density of the fluid) equations are expanded in terms of a normalised density ratio parameter. A new set of coupled integro-differential SDIP equations are derived and then solved numerically for the first-order correction to the incompressible equations in the variable-density expansion parameter. By adopting a regular expansion approach, one obtains leading-order corrections that are universal and therefore interesting in their own right. The predictions are then compared with DNS of forced variable-density flow with different density contrasts. It is found that the velocity spectrum owing to variable density is indistinguishable from that of constant-density turbulence, as it is supported by a wealth of indirect experimental evidence, but the scalar spectra show significant deviations, and even loss of monotonicity, as a function of the type and strength of the large-scale source of the mixing. Furthermore, the analysis helps clarify what may be the proper approach to interpret the power spectrum of variable-density turbulence.

JFM classification

Mixing: Turbulent mixing Turbulent Flows: Turbulence theory
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 876 , 10 October 2019 , pp. 186 - 236
Copyright
© 2019 Cambridge University Press 

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