Reynolds stresses and one-dimensional spectra for a vortex model of homogeneous anisotropic turbulence

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Abstract
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.