Two-point correlation model and the redistribution of Reynolds stresses

A quasi-isotropic locally homogeneous model for the two-point double-velocity correlation tensor is developed by the application of a plausible set of symmetry restrictions to this tensor. The two-point correlation is related to the single-point correlation by three independent functions, and reduces to the nonisotropic single-point correlation and the isotropic two-point correlation in the limiting cases. It is shown that the model implies that by the use of three independent microscales (and macroscales) it is possible to describe a matrix of 27 elements of microscales (and macroscales) which describe the nonisotropic field. The model is also used to calculate the dissipation rate of the components of the Reynolds stresses. Finally, a formula which expresses the redistribution of the velocity fluctuations due to pressure fluctuations is developed.