An approximate wall turbulence theory

The turbulent flow of a viscous incompressible fluid along a boundless plane on which the no-slip condition is placed is discussed, assuming that the mean friction stress is given and that viscosity does not influence at infinity the mean and large-scale pulsation characteristics of the flow. The mean velocity profile in the entire region of the flow is calculated, without recourse to empirical data, by determining the pulsating motion in the viscous zone and by smoothly coupling the solution with the asymptotic relations away from the wall. The calculations are based on the Navier-Stokes equation for the pulsating and mean motion. The solution is obtained in a monoharmonic approximation.