The general purpose of this research project is to model mathematically the local scour downstream of a structure (2-D). The model has to simulate the development of the scour as a function of the time. Basically two models are necessary namely a flow model and a morphological model. The latter model has to describe the bed and suspended load and the erosion of the bottom. The choice which model has to be used, depends on the required accuracy and the computer costs. In the present study a mathematical model is described which is based on the two-dimensional unsteady Reynolds equations for the mean flow. The turbulence closure is obtained by use of a two-dimensional model for the transport of the turbulence energy (k) and its dissipation (eps). Experimental data concerning the flow in a number of local scours (Breusers) and in a backward-facing step (Nezu) have been used to verify the model using a standard set of constants. Also a description of the k-model (Jorissen) is given, which is a simplification of the k-eps-model. The results of this model are compared with k-eps calculations. CONCLUSIONS AND RECOMMENDATIONS The k-eps-model predicts the velocities fairly well. The computed turbulence profiles, however, are less satisfactory if compared with measurements. At this moment there are no models which can calculate the above mentioned parameters in a better way. A disadvantage of the k-eps-model is the relatively large computation time needed to solve the complete set of equations, see 2.1. Therefore, the k-eps-model is not a very attractive model for long-term morphological computations and a simpler model will be required. Further research is necessary to determine which model is most suitable to predict the velocity field, the shear stresses and the viscosity profiles in view of costs and reliability. The k-eps-model can serve as a reference to determine this choice.