Incompressible Homogeneous Anisotropic Turbulence: Buoyancy Force and Mean Stratification

  • Pierre Sagaut
  • Claude Cambon


This chapter deals with buoyancy effects and mean stratification. Under Boussinesq approximation, the fluctuating velocity field remains divergence-free, but a new buoyancy can fluctuate, as an active scalar. The case of stable stratification shows how gravity waves coexist with a vortex (toroidal) mode of motion. Experiments are presented, as well as models ranging from Reynolds Stress Models (e.g. Two-Component-Limit) to Rapid Distortion Theory and EDQNM incorporationg it. Then recent very promising results on unstable stratification are discussed, with applications ranging from geophysics to inertial fusion. Unprecedented quantitative comparisons between anisotropic EDQNM and very high resolution DNS are reported. The scale-by-scale return to isotropy is investigated, and it is shown that the re-isotropization at scales smaller than an Ozmidov scale is only obtained at very high Reynolds number, far beyond those reached by DNS, and only obtained by anisotropic EDQNM. The case of Unstably Stratified Homogeneous Turbulence is extended to the inhomogeneous case of Rayleigh-Taylor turbulence and suggests a system approach to turbulence, with an elaborate nonlinear model of fluctuating to fluctuating interactions, towards high Reynolds numbers.


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Authors and Affiliations

  1. 1.Laboratoire de Mécanique, Modélisation et Procédés Propres, UMR CNRS 7340, Ecole Centrale de MarseilleAix-Marseille UniversitéMarseilleFrance
  2. 2.Laboratoire de Mécanique des Fluides et d’Acoustique, UMR CNRS 5509Ecole Centrale de LyonÉcullyFrance

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