The general purpose of this research project is to model mathematically the scour-hole downstream of a structure (2-D). The model has to simulate the development of the scour as a function of time. Basically two models are necessary namely a flow model and a morphological model. The latter has to describe the bed- and suspended load and the erosion of the bed. In the present study the behaviour of the turbulence in the relaxation zone of a local scour hole (figure 1) is discussed. The purpose of this note is to find a function (prescription) for the eddy viscosity in the relaxation zone, which will be used in the flow model DUCT, where the eddy viscosity is prescribed (Hoffmans, 1988b). The function for the eddy viscosity is based on the transport equations for the kinetic energy and its dissipation, in which the diffusion and gain (production) terms are neglected. Computations by means of the k-eps-model for the flow in a number of configurations (Hoffmans, 1988a), were used for calibration. CONCLUSIONS In the relaxation zone the diffusion and the dissipation do have a damping influence on the behaviour of the turbulence parameters, while the turbulence increases by the production of the Reynolds stresses. In the derivation of the analytical solutions of the damping functions the production and the diffusion are neglected in the transport equations for the kinetic energy and its dissipation. The agreement between the results of the perturbated functions is rather good.