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A turbulent flow with a given spatial pattern of mean motion invariant with time is treated. No solid boundary is considered. By means of the Fourier analysis of the Navier-Stokes equation, it is possible to obtain an equfl,tion of energy balance in spectral terms. T his involves the following functions: Viscous dissipation, transfer, production, convect.ion, and diffmion. The first two functions are common to the isotropic and homogeneous turbulence without mean motion. Assuming that eddies controlled by inhomogeneity are much larger than those controlled by anisotropy, stationary spectral laws are obtained for small eddies in the viscous and non viscous ranges. The agreement between theory and experiment is shown.
C. M. Tchen (Thu,) studied this question.