The half-wave Generalized Lagrangian Mean (GLM) method is applied to deriving the closed equations of incompressible turbulent flow.The set of equations does not contain any correlation terms and empirical coefficients.The eddy-viscosity is determined by the Stokes drift velocity

its length scale and divergence.Without using the wall function and any empirical treatments

the transition process of a plan boundary layer has been successfully simulated by the equations.All the transition details

such as the change of the mean parameters

the transformation of the velocity profiles from laminar to turbulent

the evolution of the thickness of the boundary layer

the length of transition zone

and the curve of friction coefficients

are well consistent with experimental results.