We test the performances of an incompressible turbulence Reynolds-Averaged Navier-Stokes one-closure equation model in a boundary layer, which requires the determination of the mixing length. A series of direct numerical simulation are performed, with flat and non trivial topographies, to obtain by interpolation a generic formula = (Re , z), Re being the frictional Reynolds number, and z the distance to the wall. Numerical simulations are carried out at high Reynolds numbers with this turbulence model, in order to discuss its ability to properly reproduce the standard profiles observed in neutral boundary layers, and to assess its advantages, its disadvantages and its limits. In an appendix, we achieve the mathematical analysis of the model.