ANALYSIS AND MODELING OF ANISOTROPIES IN THE DISSIPATION RATE OF TURBULENCE

The modelling of anisotropies in the dissipation rate of turbulence is considered based on an analysis of the exact transport equation for t he dissipation rate tenser. An algebraic model is systematically deriv ed using integrity bases methods and tensor symmetry properties. The n ew model differs notably from all previously proposed models in that i t depends nonlinearly on the mean velocity gradients. This gives rise to a transport equation for the scalar dissipation rate that is of the same general form as the commonly used model with one major exception . the coefficient of the production term is dependent on the invariant s of both the rotational and irrotational strain rates. The relationsh ip between the new model and other recently proposed models is examine d in detail. Some basic tests and applications of the model are also p rovided alone with a discussion of the implications for turbulence mod elling.