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A methodology to quantify the nonlinearity of the Reynolds stress tensor

type de publication      article dans une revue internationale avec comité de lecture
date de publication 2010
auteur(s) Thompson Roney L.; Mompean Gilmar; Thais Laurent
journal (abréviation) Journal of Turbulence (Journal of Turbulence)
volume (numéro) 11 (33)
pages 1 – 26
résumé Turbulent models provide closure equations that relate the Reynolds stress with kinematic tensors. In this study, we present a methodology to quantify the dependence of the Reynolds stress tensor on mean kinematic tensor basis. The methodology is based upon tensor decomposition theorems which allow to extract from the anisotropic Reynolds stress tensor the part that is linear or nonlinear in the strain rate tensor D, and the parts that are in-phase (sharing the same eigenvectors) and out-of-phase with the strain rate. The study was conducted using direct numerical simulation (DNS) data for turbulent plane channel (from Reτ = 180 to Reτ = 1000) and square duct flows (Reτ = 160). The results have shown that the tensorial form of the linear Boussinesq hypothesis is not a good assumption even in the region where production and dissipation are in equilibrium. It is then shown that the set of tensor basis composed by D, D2 and the persistence-of-straining tensor D · (W−ΩD) − (W−ΩD) · D, whereWis the vorticity tensor and ΩD is the rate of rotation of the eigenvectors of D, is able to totally reproduce the anisotropic Reynolds stress. With the proposed methodology, the scalar coefficients of nonlinear algebraic turbulent models can be determined, and the adequacy of the tensorial dependence of the Reynolds stress can be quantified with the aid of scaled correlation coefficients.
mots clés Reynolds stress; DNS; channel flow; square duct flow; tensor decomposition; Boussinesq hypothesis
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