A finite difference model based on potential flow theory is proposed for estimating the equilibrium scour hole underneath offshore pipelines. The model solves the Laplace equation for velocity potential in a curvilinear coordinate system to cope with the irregular and free boundaries involved in this problem. A local method is used to determine the free boundary formed by the eroded seabed via the equilibrium of all forces acting on a sediment particle on a slope bed. The major features of the present model are: 1) that it takes into account the nonlinear interactions between the flow, pipe and the changing bed topography in calculating the equilibrium scour hole, 2) that the shear stress on sediment particles is represented in terms of a characteristic near-bed velocity, creating a dynamic link between the flow and the sediment movement, and 3) that the model predicts the equilibrium scour hole without using any sediment transport formula, which usually contains many empirical parameters or constants. The maximum scour depth and the upstream part of the scour hole predicted by the model compare well with the experimental data published in the literature.
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