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Spectral modelling for passive scalar dynamics in homogeneous anisotropic turbulence

Published online by Cambridge University Press:  22 June 2016

A. Briard ,
T. Gomez  and
C. Cambon
A. Briard
Affiliation:
$\partial$’Alembert, CNRS UMR 7190, 4 Place Jussieu, 75252 Paris CEDEX 5, France
T. Gomez*
Affiliation:
USTL, LML, 59650 Villeneuve d’Ascq, France Université Lille Nord de France, F-59000 Lille, France
C. Cambon
Affiliation:
Laboratoire de Mécanique des Fluides et d’Acoustique, Ecole Centrale de Lyon, 69134 Écully, France
*
†Email address for correspondence: [email protected]
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Abstract

The present work aims at developing a spectral model for a passive scalar field and its associated scalar flux in homogeneous anisotropic turbulence. This is achieved using the paradigm of eddy-damped quasi-normal Markovian (EDQNM) closure extended to anisotropic flows. In order to assess the validity of this approach, the model is compared to several detailed direct numerical simulations (DNS) and experiments of shear-driven flows and isotropic turbulence with a mean scalar gradient at moderate Reynolds numbers. This anisotropic modelling is then used to investigate the passive scalar dynamics at very high Reynolds numbers. In the framework of homogeneous isotropic turbulence submitted to a mean scalar gradient, decay and growth exponents for the cospectrum and scalar energies are obtained analytically and assessed numerically thanks to EDQNM closure. With the additional presence of a mean shear, the scaling of the scalar flux and passive scalar spectra in the inertial range are investigated and confirm recent theoretical predictions. Finally, it is found that, in shear-driven flows, the small scales of the scalar second-order moments progressively return to isotropy when the Reynolds number increases.

JFM classification

Turbulent Flows: Homogeneous turbulence Turbulent Flows: Turbulence modelling Mixing: Turbulent mixing
Type
Papers
Information
Journal of Fluid Mechanics , Volume 799 , 25 July 2016 , pp. 159 - 199
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Copyright
© 2016 Cambridge University Press 

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