On the Non-Linear Hydrodynamic Forces for Oscillating Bodies in Regular Waves

Abstract

A second-order potential solution for a two dimensional symmetric cylinder in regular waves is sought by regular perturbation theory. In the development of this theory, the assumptions are as follows. (1) A perturbation parameter is taken as the steepness of incident waves of which length is the same order of the beam of the cylinder. (2) The section of the cylinder is Lewis form. (3) The mean position of the cylinder is immovable-that is, the external force with the same magnitude and the opposite direction of drifting force acts on the cylinder. In the resulting potential theory problem, the first-order potential, the second-order radiation potential, and the second-order potential due to body surface interference are solved by Ursell-Tasai's method, and the second-order potential due to free surface interference is solved by Lee's method in consideration of global mass conservation principle. Numerical computations are made for the cases as follows, the circular and rectangular cylinders undergo forced sinusoidal motion in heave, those cylinders in regular waves, and rectangular cylinder floating in regular waves. The results are presented in graphs. Some of the results summarized as follows : (1) The calculation results of the second-order hydrodynamic forces for heaving circular cylinder show good agreement with experimental results by Tasai and Koterayama. (2) The culculation results of drifting force by pressure integral are in agreement with ones by momentum theory. (3) The sinking force and the heel moment of a floating body in regular waves become extremely large at rolling natural period.