The return to isotropy of homogeneous turbulence

The return to isotropy of homogeneous turbulence without mean velocity gradients is attacked by considering changes to be slow relative to turbulence time scales. This single assumption permits the problem to be cast as one of finding the form of three invariant functions. Examination of limiting behavior for large Reynolds number and small anisotropy, as well as small Reynolds number and arbitrary anisotropy, places restrictions on the form of the functions. Realizability conditions (requiring that energies be nonnegative) reduce the problem to two functions subject to further restrictions. A convenient interpolation form is found for the functions, satisfying all the restrictions, and it is shown that predictions based on this are in excellent agreement with all available data.