Wave Making: A Low-Speed Slender-Body Theory

Abstract

A slender_body theory for the wave making of a ship in steady translational motion is developed by assuming that the length of the waves generated by the ship is of the same order of magnitude as the beam of the ship. The exact boundary value problem is formulated and then linearized by assuming that the wave length is short. &&This linearized problem is solved to two orders of magnitude by the method of matched asymptotic expansions. The first order solution turns out to be a simple variation on the Tuck slender_body theory, while the second order solution turns out to be a diffraction problem accounting for the refraction of the waves away from the body. &&Qualitatively, this solution shows some of the same characteristics which Adachi has observed in his experiments on models with long parallel middle bodies. This solution is in many ways similar to the solution which Faltinsen obtained for the diffraction of head seas by a slender ship. Quantitatively, the wave elevations obtained using this theory agree well with experimental measurements obtained from tests on a pointed body of revolution.