APPENDIX C 

 LINEAR HYDRODYNAMIC COEFFICIENTS 



The linear theoretical model used in solving the floating break- 

 water problem has been discussed extensively by Frank (1967) . He de- 

 veloped the approach to solving the boundary value problem which has 

 come to be known as the "Frank close-fit method". The reader is re- 

 ferred to the original reference for a complete presentation of the 

 method . 



In this approach, the classical linear boundary value problem 

 requires that Laplace's equation be satisfied throughout the fluid do- 

 main: 



V^$(x,y,t) =0 for y < 0. (C-1) 



Tlie free-surface boundary condition is applied on the undisturbed free 

 surface; 



$ (x,0,t) + g$ =0 for y = 0. (C-2) 



tt y 



The body-surface boundary condition requires that no fluid flow through 

 the body surface: 



V<|)(x,y,t) • n 



= V.(s) • nCs). (C-3) 



C 



o 



The bottom boundary condition for infinite depth is of the form: 



Jil *y(x.y,t) = 0. (C-4) 



In addition there is a radiation condition specifying that the waves 

 travel away from the body. 



Because the problem is assumed to be linear, the velocity potential 

 may be decomposed and several boundary value problems considered. If 

 this is done the total potential becomes: 



$=$+$+$+$+$ (C-5) 



Here, 



0, = potential representing pure sway motion in calm water, 

 $- = potential representing pure heave motion in calm water, 

 $, = potential representing pure roll motion in calm water. 



104 



