Dynamical model for turbulence. III. Numerical results

Abstract

We present the numerical solutions of the equations for turbulence 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 constant Ba=σt Ko, where σt=0.72 is the turbulent Prandtl number; (3) the predicted energy spectrum in the dissipation region is in agreement with recent laboratory measurements; (4) in the inertial-convective region, the temperature variance spectrum is closer to 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 with the three most widely used phenomenological models. The rapid parts are also in excellent agreement with the DNS data; (10) for homogeneous 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.