The problem of coherent perturbations in a turbulent shear layer is revisited for the purpose of developing a mathematical model based on the unsteady RANS equations. The ensemble-averaged flow parameters (velocity, pressure) are split into two parts: mean and coherent. The governing equations for these parts are derived, assuming eddy-viscosity equivalence for the random part of the flow, and solved by iterations to provide a coupled solution of the problem as a whole. Calculations agree well with experimental data in the upstream part of the layer, where the spreading rate grows rapidly and the mean-coherent flow interaction is the most important. In this region, the interaction changes the mean flow velocity distribution in such a manner that the neutral stability curve is shifted upstream relative to its position in the undisturbed layer and the perturbation intensity decreases further downstream. Experiments show that the coherent waves suppress the turbulent Reynolds-stress production downstream of this region, but the model fails to predict the layer spreading correctly due to an inadequate turbulence closure of the mean flow. In the case of a turbulent mixing-layer flow, we proposed a new closure, which takes into account this coherent-random interaction. Results of calculations with the improved closure correlate well with existing experimental data. THE GOVERNING EQUATION
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