Abstract: Most of the studies relating to the gradually varied flows were based on the analysis of the average magnitude and the evolution of the associated free surface curve. The phenomena of erosion or of friction on the bottom being globalised or being deduced from models defined for uniform permanent flows. In the research presented here, we study the flow above a threshold by privileging an approach based on the analysis of turbulence and the turbulent boundary layer, in a flow where the phenomena related to the acceleration and deceleration cannot be neglected. Our objective is to obtain a formulation allowing to define the evolution of the share stress in the various points of the surface of the threshold.