A strain parameter turbulence model and its application to homogeneous and thin shear flows

The present paper examines the basic tenets upon which widely-used two-equation (k-ε) turbulence models are based. It is argued that there exists a weakness at the core of this group of models, namely in the assumed stress/rate-of-strain constitutive equation. These remarks apply to both the 'high-Reynolds-number' parent model and to 'low-Reynolds-number' variants of the formulation. Dimensional considerations and the work of Lee et al. (Proceedings of the Sixth Symposium on Turbulent Shear Flows, 1987; J. Fluid Mech. 216 (1990) 561-583) support the contention that the constitutive relation should take account of the ratio of turbulence to mean strain timescales. In an extension of this approach, following Townsend (J. Fluid Mech. 41 (1970) 13-46) and Maxey (J. Fluid Mech. 124 (1982) 261-282), the concept of effective total strain is introduced. A 'strain parameter', S, is then defined as the subject of a third transport equation and a new turbulence model damping function is made to depend principally upon S. The model is compared with data for homogeneous flow transients, steady fully-developed channel flow, and mixed convection flows.