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Canuto, V., M.S. Dubovikov, Y. Cheng, and A. Dienstfrey, 1996: Dynamical model for turbulence. III. Numerical results. Phys. Fluids, 8, 599-613, doi:10.1063/1.868844.
We present the numerical solutions of the equations developed in papers I and II. (1) The model predicts the Kolmogorov law and Ko = 5/3, in accord with recent data; (2) in the inertial-conductive regime, the model predicts the Corrsin spectrum for the temperature variance and the Batchelor costant Ba = σt Ko, where σt = 0.72 is the turbulent Prandtl number; (3) the predicted energy spectrum in the dissipation region, the temperature is in agreement with recent laboratory measurements; (4) in the intertial-convective region, the temperature variance spectrum is closer than the spectrum (-11/3) obtained by LES when the velocity field is rapidly stirred at all scales than (-17/3), which holds when the velocity field is frozen in time and has a Gaussian statistics; (5) for freely decaying turbulence, the power law spectra for energy and temperature variance, as well as the velocity and temperature integral scales, agree with the most recent LES data; (6) after a few evolutionary times, the skewness S reaches S = 0.5, in accord with a variety of data; (7) for shear-driven flows, the Reynolds stress spectrum E12(k) has an inertial regime with a power -7/3. in accord with recent data; (8) for two shear-driven flows, plane strain and axisymmetric contraction, turbulent kinetic energy, Reynolds stress tensor, and dissipation rate εij versus time compare very well with DNS data; (9) the slow and rapid parts of the pressure-strain correlation tensor compare with DNS data better than the three most widely used phenomenological models. The rapid parts are also in excellent agreement with the DNS data; (10) for homogenous shear, turbulent kinetic energy and Reynolds stress tensor versus time match quite closely LES data. We recall that the model does not contain any free parameters.
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