Rational Approach to Relations between Motions of Differing Scales in Turbulent Flows

An approach developed originally by Coleman and Noll in connection with a rational sequence of approximations to a simple fluid is applied to the problem of predicting the Reynolds stress in a turbulent flow; a rational sequence of approximations is generated in ascending powers of length- and time-scale ratios between the turbulent and mean motions. The same technique is applied to predict the response of motions of one wavenumber to those of another. An estimate is made of the relative importance of terms arising from spatial and temporal inhomogeneity. The spatial terms are found to be of substantially less importance.