A new unilateral average scheme is proposed in this paper for the purpose of retaining the first-order statistical information of turbulence fluctuations. In this approach, the fluctuations are divided into two groups according to their projections onto the mean flow. A forward (backward) fluctuation has a positive (negative) projection, and the corresponding ensemble average is called forward (backward) drift velocity. The momentum equations of these drift flows are derived within the framework of the Navier-Stokes equations. With the aid of the concept of modified eddy viscosity, these momentum equations join the conventional Reynolds-averaged Navier-Stokes equation constituting rational equations of incompressible turbulent flow. The rational equations contain no empirical coefficients, and their very same form is valid for all flow regions. The merit of the present approach is demonstrated by a numerical example of transition simulation of a flat-plate boundary layer without using the wall functions. Details of the transition, including change in velocity profiles from laminar to turbulent and change in thickness and length of the boundary layer in the transition zone, are in good agreement with existing experimental results.

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