Singular-Perturbation Problems in Ship Hydrodynamics

Publisher Summary This chapter discusses the study of thin-ship prospered and the theory provided some guidance in the reduction of wave resistance, even if it did not give accurate quantitative predictions. The early and continuing success of thin-ship theory is because of two factors: an explicit solution can be found for the case of a ship in steady, straight-ahead motion and the first approximation is essentially a uniform approximation. In all such problems, the ship is replaced by a centerplane distribution of sources, steady or pulsating, as appropriate. The body boundary condition is transferred to the centerplane, thus providing an expression for the normal velocity component on each side of the centerplane from which an explicit expression for source density can be obtained. The chapter highlights that the thin-ship model provides the best strictly analytical information available about the wave resistance of a ship, largely because an explicit solution is obtainable. Corresponding results for ship-motion problems have not been so useful, at least partly because a better mathematical model has evolved. The thin-ship solution is the first term in a perturbation expansion of the corresponding exact problem. The small parameter may be considered as the ratio beam/length.