Statistical Theory of Wall Turbulence

A steady fully developed turbulent shear flow of incompressible fluid between parallel walls is considered. The Fourier transforms of the spatial correlations are introduced with respect to the streamwise and the spanwise directions in particular, and then they are expanded in power series of the wall distances near the wall. From the dynamical equations certain relations are obtained between the expansion coefficients. It is shown that the Reynolds stress begins with the fourth-power of the wall distance at the wall in contrast with the usual assumption of the third-power-law.