An algebraic model for nonisotropic turbulent dissipation rate in Reynolds stress closures

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Abstract
A method to account for effects of an anisotropic dissipation rate in second‐order moment closures of turbulent flows is presented. The modeled transport equations for the Reynolds stresses and the scalar dissipation rate are supplemented by nonlinear algebraic relations, in which the anisotropies of the dissipation rate tensor are expressed in the anisotropies of the Reynolds stress tensor. Symmetry and other constraints reduce the number of undetermined coefficients to one. It is shown that the model correctly describes the initial behavior of a suddenly distorted turbulence provided that the model parameter assumes a value of (3)/(4) . The model is compared with full numerical simulations of three basic types of strained homogeneous turbulence, and is shown to give good agreement with these data. The present approach of isolating the effects of anisotropic dissipation rate in second‐order moment closures is a step toward improved modeling of the energy redistribution terms in the Reynolds stress transport equations, and could also be used for improved modeling of the scalar dissipation rate equation.

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