Abstract
A nonequilibrium expression of the turbulent viscosity in the Reynolds stress is proposed with the aid of the results from a two-scale direct-interaction approximation. The usual turbulent-viscosity model based on the turbulent kinetic energy K and its dissipation rate ε is extended to include their nonequilibrium effects DK/Dt and Dε/Dt (D/Dt is the Lagrange derivative based on the mean velocity). The validity of the proposed model is confirmed through the test in homogeneous shear turbulence that is in a state of nonequilibrium in time. The relationship with the similar model presented by Taulbee [Phys. Fluids A 4, 2555 (1992)] is also discussed.
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