Hydrodynamics of Large Objects in the Sea Part I-Hydrodynamic Analysis

Abstract

This paper deals with the hydrodynamic forces exerted on a rigid object describing harmonic oscillations under or on a free surface as well as the forces resulting from the interaction of the object held fixed in a train of regular surface waves. The problem is formulated for a body of arbitrary shape in water of finite depth and the development of a numerical scheme for carrying out the calculations is described. An energy balance as well as Haskind's relations are used as a check on the accuracy of the numerical results. Numerical results are presented for a floating sphere, a vertical circular cylinder, and a practical semi-immersed caisson configuration. Nomenclature a = characteristic dimension of body Ct = wave force (or moment) coefficient, Eqs. (36) and (40) Cij - ith component force (or moment) coefficient associated with the ;th component motion d_ = depth of submergence dS - differential surface area / = source strength function G = Green's function g - acceleration of Gravity gi = (i = 1,2,...7) See Eq. (19) h_ - water depth H = wave height i,l,k = cartesian unit vectors L = wavelength Mtj — added mass coef., (added mass /pa3) or (added mom. of I/pa5) Ntj = damping coef., (linear damping/po-a3) or (angular damp