A LESLangevin model for turbulence
type de publication 
article dans une revue internationale avec comité de lecture 
date de publication 
31032006 
auteur(s) 
Laval JeanPhilippe; Dubrulle Bérengère 
journal (abréviation) 
The European Physical Journal B (Eur. Phys. J. B) 
volume (numéro) 
49 
 
pages 
471 – 481 
résumé 
We propose a new model of turbulence for use in largeeddy simulations (LES). The turbulent force, represented here by the turbulent Lamb vector, is divided in two contributions. The contribution including only subfilter fields is deterministically modeled through a classical eddyviscosity. The other contribution including both filtered and subfilter scales is dynamically computed as solution of a generalized (stochastic) Langevin equation. This equation is derived using Rapid Distortion Theory (RDT) applied to the subfilter scales. The general friction operator therefore includes both advection and stretching by the resolved scale. The stochastic noise is derived as the sum of a contribution from the energy cascade and a contribution from the pressure. The LES model is thus made of an equation for the resolved scales, including the turbulent force, and a generalized Langevin equation integrated on a twicefiner grid. We compare the full model with several approximations. In the first one, the friction operator of the Langevin equation is simply replaced by an empirical constant, of the order of the resolved scale correlation time. In the second approximation, the integration is replaced by a condition of instantaneous adjustment to the stochastic force. In this approximation, our model becomes equivalent to the velocityestimation model of Domaradzki et al. [13]. In the isotropic, homogeneous situations we study, both approximations provide satisfactory results, at a reduced computational cost. The model is finally validated by comparison to DNS and is tested against classical LES models for isotropic homogeneous turbulence, based on eddy viscosity. We show that even in this situation, where no walls are present, our inclusion of backscatter through the Langevin equation results in a better description of the flow. 
mots clés 
turlulence, LES, model 
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