Scour is the lowering of the sea or river-bed as a result of non-equilibrium sediment transport conditions and can be divided into several categories (Breusers and Raudkivi, 1991). Local scour, which may occur at the base of a structure because of the affected flow pattern, can severely endanger the stability of this structure. Many varieties of localscour systems downstream from hydraulic structures exist, each with its own particular geometry and hence local scour mechanism. Local scour is superimposed on general and constriction scour.
The prediction of local-scour holes that develop downstream from hydraulic structures plays an important role in their design. Excessive local scour can progressively undermine the foundation of a structure. Because complete protection against scour is too expensive generally, the maximum scour depth and the upstream slope of the scour hole have to be predicted to minimize the risk of failure.
In 1961 a systematical research with respect to scour holes started at Delft Hydraulics within the scope of the Dutch Delta works. After the catastrophic flood disaster in 1953 the Delta plan was made to protect the Rhine-Meuse-Scheldt delta for future disasters. Dams with large scale sluices were planned in some estuaries. The severe scour expected necessitated a better understanding of the scour process. To find detailed information about the physical processes playing a role in scour many experiments were carried out, in which various parameters of the f l ow and the scoured material were varied. From the results of experiments in flumes with all difficulties of scale effects and limitations in instrumentation some empirical relations were obtained, which describe the erosion process as function of time and place (Prins, 1963 and Breusers, 1966, 1967).
In these empirical relations a not well defined turbulence coefficient was introduced. Up to now this coefficient was related to the geometry upstream of the scour hole, which relation was based on trial and error. Based on theoretical grounds an analytical relation for the depth-averaged turbulence intensity is derived. This relation, which implies a modification of the turbulence coefficient in the Breusers scour formula, is verified using approximately 300 experiments.
The modified scour formula yields results that compare reasonably well to measured and computed developments of a scour hole in case of a uniform flow upstream of the scour hole corresponding with a large protected bed area. The computations were based on the two-dimensional Navier-Stokes and convection-diffusion equations (Hoffmans, 1992) . The present paper aims at extension of the domain of application of the scour formula to non-uniform flow conditions upstream.