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

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.