Short- and long-time behavior of eddy-viscosity models
The short-time behavior of the turbulent viscosity is inferred from the immediate response of the Reynolds stress deduced by \textit{S. C. Crow} [J. Fluid Mech. 33, 1-20 (1968; Zbl 0197.255)] for the problem of isotropic turbulence subjected to a mean strain at time \(t=0\). The turbulent viscosity \(\nu\) is defined for \(t\to 0\) by the relation \(T_{ij}= -2\nu S_{ij}\), where \(T_{ij}\) is the Reynolds stress and \(S_{ij}\) is the main rate of strain. It follows that the viscosity is \(\nu= O(t)\) for \(t\to 0\). Matching the short- and long-time behaviors, we propose an analytic expression for the effective viscosity valid for all time. Using the proposed viscosity, the \(k-\varepsilon\) model for homogeneously sheared turbulence is reformulated to be valid in both the short- and long-time limits. Comparison of theoretical predictions with the results of physical and numerical experiments is presented.
scientific article; zbMATH DE number 429334
scientific article