A morphological model for the development of local-scour holes behind structures is developed, based on the 2-D Navier Stokes and convection-diffusion equations. The bed-load (transport) and the concentration at a reference level close to the bed are prescribed using a stochastical approach for the instantaneous bed shear-stress. The standard deviation of the latter is closely related to the turbulence energy in the mixing layer and to the bed turbulence.