Theoretical Investigation of an Eddy-Viscosity-Type Representation of the Reynolds Stress

An eddy-viscosity-type representation of the Reynolds stress is investigated with the aid of a two-scale direct-interaction approximation (TSDIA). The second- and third-order analyses of the TSDIA are applied to the Reynolds stress. Using these results, the nonlinear part of the Reynolds stress and the turbulent-energy dissipation rate equation are discussed in detail. Non-equilibrium effects of turbulence are also incorporated into the nonlinear part in addition to the simple eddy-viscosity one. Further, using the experimental data, we confirm that the K- ε model is improved by the non-equilibrium property.