A cascade-transport model for turbulent shear flows

A simple model for local spectral resolution in turbulent shear flows is developed. The original cascade model of Desnyanski and Novikov contains time derivatives, spectral transfer, and viscous dissipation terms for shell-averaged turbulent energy. The model is adapted for shear flows by the addition of a convective derivative, a turbulence production term, and a turbulent transport term. Both production and transport are based on a spectral distribution of the eddy viscosity. When integrated over all scales, the model reduces to the κ equation of κ-ε models, whereas in uniform mean flows it reduces to the original cascade model. Calibration of the model constants is achieved based on experimental results for homogeneous shear flow.