HYDRODYNAMICS OF MOORED VESSELS 



by 

 C. J. Garrison 



C. J. GARRISON & ASSOCIATES 

 3088 Hacienda Drive 

 Pebble Beach CA 93953 



1. INTRODUCTION 



The mathematical formulation and solution of the boundary- 

 value problem for the hydrodynamics associated with the motion 

 of a moored vessel in a seaway is rather complex due primarily 

 to the nonlinear free surface boundary condition. Difficulty with 

 the free surface boundary condition has impeded progress on the 

 exact solution for wave/body interaction problems and little pro- 

 gress has been made. Thus, the more fruitful approach has been to 

 pursue linearized solutions as an approximation. The linearized 

 problem is also difficult but computer solutions can be obtained 

 for bodies of practical interest. Moreover, linearization admits 

 the concept of superposition of motions and waves, with which 

 comes the powerful concept of wave excitation spectra and the 

 motion response spectra. Although some rather broad assumptions 

 are made in order to linearize the boundary value problem, linear 

 solutions have been found to give physically realistic results for 

 cases of practical interest. 



In addition to the dynamic response of a moored vessel to 

 wave motion at the frequency of the waves, a second-order effect 

 referred to as slowly-varying drift motion also occurs when the 

 vessel is subject to random waves. This is a phenomena which has 

 received a great deal of attention in recent years and is an area 

 of ongoing research. 



2. LINEARIZED HYDRODYNAMICS OF FLOATING VESSELS 



The theory of the motion of a floating vessel is based on the 

 following assumptions: 



(a) Inviscid fluid and irrotational flow. 



( b) Small amplitude waves and resulting small amplitude 

 response . 



(c) Wave motion and response motion r epresentable by a super- 

 position of regular sinusoids. 



The notion of superposition of both the incident waves and 

 the response of the vessel allows one to view the motion of a . 

 moored vessel in waves as: (a) the wave interaction with the 

 vessel held fixed and ( b) the motion of the vessel oscillating in 

 each of its six degrees of freedom separately in otherwise still 

 water. From consideration of (a) , the wave excitation forces and 

 moments are determined, and from ( b) the reaction forces and 

 moments resulting from the motion of the vessel are determined. 

 The latter are characterized by use of added mass and damping 

 tensors. 



A numerical procedure based on distributed three-dimensional 

 sources has been presented by Garrison (1974) and Faltinsen and 

 Michelsen (1974) for three-dimensional bodies of arbitrary shape. 



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