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A simple turbulent energy model, based on an improved version of Wolfshtein’s model for Newtonian flows, with a variable damping parameter, is used to describe the effect of linear polymers on the velocity profile and the turbulent energy distribution in channel and pipe flows. Measured mean velocity profiles seem to be in good agreement with the model, which predicts as well the observed increase in turbulent energy near the wall in flows with drag reduction.

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A simple turbulent flow model for geophysical flows is presented, which is based on the transport equation for turbulent energy and on algebraic expressions relating the Reynolds stress and turbulent heat flux to the velocity and temperature gradients. The model, which is similar to the 2.5 level closure model of Mellor and Yamada, includes constraints based on the realizability conditions as well as expressions for the length scale which account for the influence of stratification and the Coriolis acceleration. The model is shown to reproduce satisfactorily the main features ofexisting laboratory measurements of stress-induced and convective turbulent entrainment in stratified flows.

A turbulent-energy-dissipation model is proposed for flows with and without drag reduction. The model is based on an eddy diffusivity approximation in the momentum equation, and on transport equations for the turbulent energy and the turbulent energy dissipation. The model describes the mean velocity profile and the turbulent energy distribution as a function of the reduction in the friction coefficient. It also yields a turbulent length scale which is shown to grow with drag reduction. The predictions of the model are in good agreement with the available experimental data.

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