Interactions among multiple three-dimensional bodies in water waves: an exact algebraic method

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This paper deals with three-dimensional water-wave diffraction and radiation by a structure consisting of a number of separate (vertically) non-overlapping members in the context of linearised potential flow. An interaction theory is developed which solves the complete problem, predicting wave exciting forces, hydrodynamic coefficients and second-order drift forces, but is based algebraically on the diffraction characteristics of single members only. This method, which includes also the diffraction interaction of evanescent waves, is in principle exact (within the context of linearised theory) for otherwise arbitrary configurations and spacings. This is confirmed by a number of numerical examples and comparisons involving two or four axisymmetric legs, where full three-dimensional diffraction calculations for the entire structures are also performed using a hybrid element method. To demonstrate the efficacy of the interaction theory, it is applied to an array of 33 (3 by 11) composite cylindrical legs, where experimental data are available. The comparison with measurements shows reasonable agreement. The present method is valid for a large class of arrays of arbitrary individual geometries, number and configuration of bodies with non-intersecting vertical projections. Its application should make it unnecessary to perform full diffraction computations for many multiple-member structures and arrays.