  A simple analytical solution for turbulent plane Couette flow is obtained
from a subset of the Navier-Stokes equations. This approach analyses the effect
of the unsteady state Lagrangian diffusion of viscous momentum on the smoothed
phase velocity. Three initial velocity profiles at the start of a turbulent
wall cycle are considered. The predictions adequate identify the existence of
three layers usually observed in turbulent flow fields, in particular a
viscosity dominated wall layer and a log-law layer. Experimental measurements
of time-averaged velocity are also well correlated.
  Key words: Couette flow, turbulent, attractors, analytical solution,
Lagrangian partial derivative, time scale, initial conditions
