Numerical study of turbulent diffusion in homogeneous stably stratified turbulence using linear analysis

In this Note, we study numerically turbulent diffusion in the case of homogeneous stably stratified turbulence. This study is based on a linear analysis in spectral space. To express the Lagrangian velocity correlations using Eulerian correlations, we adapt the Corrsin assumption and then we calculate the tensor components of the mean square displacement. We begin by writing the basic linear equations governing the evolution of the spectra of double correlations then we present the Corrsin hypothesis as a model of turbulent diffusion. Subsequently, we describe the numerical method used and analyze the numerical results. Clearly, the Corrsin assumption can give the proper behavior, at large times, of the horizontal diffusion and improves the prediction of vertical diffusion. As an application of the numerical code elaborated, we study the influence of Prandtl number on the vertical diffusion which results in an accentuation of the suppression of vertical diffusion when the Prandtl number (less than 1) diminishes. (C) 2011 Academie des sciences. Publie par Elsevier Masson SAS. Tous droits reserves.