## Publication Abstracts

### Canuto and Dubovikov 1996

**8**, 587-598, doi:10.1063/1.868843.

Using the formalism developed in paper I, we treat the case of shear-driven flows. First, we derive the dynamic equations for the Reynolds stress. The equations are expressed in both tensorial and scalar forms, that is, as a set of coupled differential equations for the functions that enter the expansion of the Reynolds stress in terms of basic tensors. We specialize the general results to (a) axisymmetric contraction, (b) plane strain, and (c) homogeneous shear, for which there is a wealth of DNS, LES, and laboratory data to test the predictions of our model. Second, for homogeneous shear, in the inertial range, the equation for the Reynolds stress spectral function can be solved analytically, E_{12}(k) = -C*ε^{1/3}*S*k^{-7/3}, which is in excellent agreement with recent data. Since the model has no free parameters, we stress that the model yields a numerical coefficient C, which is also in agreement with the data. Third, we derive the general expressions for the rapid and slow parts of the pressure-strain correlation tensors Π^{r}_{ij} and Π^{s}_{ij}. Within the second-order closure models, the closure of Π^{s}_{ij} (third-order moment) in terms of second-order moments continues to be particularly difficult. The general expression for Π_{ij} are then specialized to the three flows discussed above. When Π^{s}_{ij} is written in the form first suggested by Rotta, we show that the Rotta constant is a nonconstant tensor. Fourth we discuss the dissipation tensor ε_{ij}. In standard turbulence models, one not only assumes that ε_{ij} = (2/3) εδ_{ij} + f(ave(u_{i}u_{j})), where f(x) is a empirical function of the one-point Reynolds stress ave(u_{i}u_{j}), but, in addition, one employs a highly parameterized equation for ε. In the present model, neither of the two assumptions is required nor adjustable parameters are needed since ε_{ij} is computed directly. The model provides the k-dependent R_{ij}(k) as one of the primary quantities.

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#### BibTeX Citation

@article{ca05100g, author={Canuto, V. M. and Dubovikov, M. S.}, title={A dynamical model for turbulence. II. Shear-driven flows}, year={1996}, journal={Phys. Fluids}, volume={8}, pages={587--598}, doi={10.1063/1.868843}, }

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#### RIS Citation

TY - JOUR ID - ca05100g AU - Canuto, V. M. AU - Dubovikov, M. S. PY - 1996 TI - A dynamical model for turbulence. II. Shear-driven flows JA - Phys. Fluids VL - 8 SP - 587 EP - 598 DO - 10.1063/1.868843 ER -

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