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Passive scalar decay laws in isotropic turbulence: Prandtl number effects

Published online by Cambridge University Press:  04 November 2015

A. Briard ,
T. Gomez ,
P. Sagaut  and
S. Memari
A. Briard
Affiliation:
Insitut Jean Le Rond d’Alembert, CNRS UMR 7190, F-75252 Paris CEDEX 5, France
T. Gomez*
Affiliation:
Insitut Jean Le Rond d’Alembert, CNRS UMR 7190, F-75252 Paris CEDEX 5, France Université Lille Nord de France, F-59000 Lille, France USTL, LML, F-59650 Villeneuve d’Ascq, France
P. Sagaut
Affiliation:
Aix-Marseille Université, CNRS, Centrale Marseille, M2P2 UMR 7340, 13451 Marseille, France
S. Memari
Affiliation:
Insitut Jean Le Rond d’Alembert, CNRS UMR 7190, F-75252 Paris CEDEX 5, France
*
†Email address for correspondence: thomas.gomez@univ-lille1.fr
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Abstract

The passive scalar dynamics in a freely decaying turbulent flow is studied. The classical framework of homogeneous isotropic turbulence without forcing is considered. Both low and high Reynolds number regimes are investigated for very small and very large Prandtl numbers. The long time behaviours of integrated quantities such as the scalar variance or the scalar dissipation rate are analysed by considering that the decay follows power laws. This study addresses three major topics. First, the Comte-Bellot and Corrsin (CBC) dimensional analysis for the temporal decay exponents is extended to the case of a passive scalar when the permanence of large eddies is broken. Secondly, using numerical simulations based on an eddy-damped quasi-normal Markovian (EDQNM) model, the time evolution of integrated quantities is accurately determined for a wide range of Reynolds and Prandtl numbers. These simulations show that, whatever the values of the Reynolds and the Prandtl numbers are, the decay follows an algebraic law with an exponent very close to the value predicted by the CBC theory. Finally, the initial position of the scalar integral scale $L_{T}$ has no influence on the asymptotic values of the decay exponents, and an analytical law predicting the relative positions of the kinetic and scalar spectra peaks is derived.

JFM classification

Turbulent Flows: Isotropic turbulence Turbulent Flows: Turbulent convection Turbulent Flows: Turbulent Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 784 , 10 December 2015 , pp. 274 - 303
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Copyright
© 2015 Cambridge University Press 

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