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Passive scalar decay laws in isotropic turbulence: Prandtl number effects

type de publication      article dans une revue internationale avec comité de lecture
date de publication 2015
auteur(s) Briard Antoine; Gomez Thomas; Sagaut Pierre; Memari Souzan
journal (abréviation) Journal of Fluid Mechanics (J Fluid Mech)
volume (numéro) 784
  
pages 274 – 303
résumé 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 LT 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.
mots clés isotropic turbulence; turbulent convection; turbulent flows
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