Vertical sided objects with a flat bottom represent a broad class of marine structures, which include barges, pontoons, floating docks, breakwaters and some offshore platforms. When such structures are towed or operated in shallow water, accurate prediction of wave induced motions is required to design the mooring system and to determine the dynamic under-keel clearance. The hydrodynamic analysis may be difficult when the gap between the structure bottom and the sea floor is small, calling for a large number of panels to be used on the bottom and near the edges, to capture the singular behaviour of the flow in these regions. The paper presents a method for hydrodynamic analysis, which is intended to avoid these difficulties and to provide good accuracy for any small value of the under bottom clearance. Following the method of matched asymptotic expansions, the linear wave-body interaction problem is solved by matching the two “outer” flows with the “inner” flow near the structure edge. The three-dimensional hydrodynamic problem is reduced to an integral equation in two dimensions formulated on the water line (footprint) of the structure, simplifying the numerical implementation and reducing the number of subdivisions elements. Because the singular behaviour of the flow near the edge and under the bottom is effectively extracted from the solution, the method enables to use the same number of subdivisions for any small under-keel clearance, providing improving accuracy as the under-keel clearance shrinks to zero. Numerical results are presented and discussed for typical geometries, which compare well with those obtained by other methods.

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