Short- and long-time behavior of eddy-viscosity models
type: Item
instance of: scholarly article
title: Short- and long-time behavior of eddy-viscosity models
zbMATH Open document ID: 0781.76049
DOI: 10.1007/BF00417927
author: Leslie Smith
author: Victor Yakhot
published in: Theoretical and Computational Fluid Dynamics
publication date: 1994-02-10T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 76F10
zbMATH DE Number: 429334
zbMATH Keywords: Reynolds stress
zbMATH Keywords: effective viscosity
zbMATH Keywords: homogeneously sheared turbulence
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf00417927
OpenAlex ID: W2024228999
description: scientific article; zbMATH DE number 429334