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Canuto, V.M., and M.S. Dubovikov, 1997: A new approach to turbulence. Int. J. Mod. Phys. A, 12, 3121-3152, doi:10.1142/S0217751X9700164X.
We propose a closed set of dynamic equations to describe turbulence. The equations are the result of systematic and heuristic elements. Specifically, the UV part of the nonlinear interactionsm, represented by a dynamical viscosity, is computed for a stirring force of a partiuclar nature. However, since the results exhibit a general structure, we suggest heuristically to extend them to arbitrary flows. Because of nonrenormalizable divergences, the IR part of the nonlinear interactions has constituted a serious problem. We suggest a heuristic model, the basic ingredient of which is that the transfer of energy among eddies is mostly a local process. We show that possible adjustable parameters are actually fixed by the model itself. Because of the heuristic nature of one part of the model, its overall validity rests largely on the accumulated evidence gathered from checking its predictions against more than seventy turbulence statistics for homogeneous isotropic and anisotropic flows (the Kolmogorov constant is predicted to be Ko = 5/3). The overall performance is good.
Here, we first extend the model to inhomogeneous flows and test the predictions using the newest laboratory and DNS data on turbulent convection at large Ra (Rayleigh number). The model reproduces both types of data quite accurately.
Second, we study the problem of the so-called "sweeping effect" and derive the relation between the ω and k-spectra.
Third, we show that for shear driven flows the present model reproduces well the data at large strain rates while the widely used K — ε does not.
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