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Reynolds stresses and one-dimensional spectra for a vortex model of homogeneous anisotropic turbulence. (English) Zbl 0830.76044
Summary: Homogeneous anisotropic turbulence consisting of a collection of straight vortex structures is considered, each with a cylindrically unidirectional, but otherwise arbitrary, internal vorticity field. The orientations of the structures are given by a distribution $$P$$ of appropriate Euler angles describing the transformation from laboratory to structure-fixed axes. One-dimensional spectra of the velocity components are calculated in terms of $$P$$, and the shell-summed energy spectrum. An exact kinematic relation is found in which volume-averaged Reynolds stresses are proportional to the turbulent kinetic energy of the vortex collection times a tensor moment of $$P$$. A class of large-eddy simulation models for nonhomogeneous turbulence is proposed based on application of the present results to the calculation of subgrid Reynolds stresses. These are illustrated by the development of a simplified model using a rapid-distortion-like approximation.

MSC:
 76F99 Turbulence
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References:
 [1] DOI: 10.1063/1.868318 · Zbl 0827.76037 [2] DOI: 10.1017/S0022112085001136 · Zbl 0587.76080 [3] DOI: 10.1063/1.866513 [4] DOI: 10.1017/S0022112091001957 · Zbl 0721.76036 [5] DOI: 10.1063/1.863957 · Zbl 0536.76034 [6] DOI: 10.1063/1.858798 · Zbl 0793.76046 [7] DOI: 10.1016/S0065-2156(08)70100-5 [8] DOI: 10.1063/1.857955 · Zbl 0825.76334 [9] DOI: 10.1063/1.857730
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