total *- ' -" g t incident "-''-' ^t diffracted 



+ ^^^^^^- (x,0,t)}. (6) 



^t motion "-''-' ^ ' 



The fluctuating component of pressure in the fluid and on the breakwater 

 hull surface may be computed using Bernoulli's equation: 



P(x,y,t) = - P (t-^ (x,y,t). (7) 



By computing pressures on the hull surface and integrating these around 

 the contour, the forces on the breakwater may be computed. The force 

 per unit length acting on the breakwater is then: 



F(t) = P n ds. (8) 



■'c 



o 

 In this case, 



F(t) = force on the breakwater, 



n = unit interior normal vector on the hull surface, 



C = contour of breakwater cross section, 

 o 



The rolling moment is: 



M(t) = P r X n ds, C9) 



■'c 



o 



where, 



r = the vector from the center of gravity to a point on the surface. 



To compute the exciting forces on the breakwater in linear theory, the 

 pressure due to the incident and diffracted waves is integrated over the 

 hull surface. These forces and moments become: 



F, (t) = { - p [(t>^ . . , ^ (s,t) + A ,.^^ ^ j(s,t)] n ds} • 1, 



1^ -^ J "■ t incident '- ' -' ^t diffracted ■" 



""o 



F^(t) = { - p [(J)^ . ., ^ (s,t) + if^ ,.-^ ^ ,(s,t)] n ds} j", 



2'- ^ "^J "-^t incident ^ ' -' ^t diffracted^ ' -^ ■" "' 



o 



F,(t) = { - p [4, (s,t) + A ,.^^ ^ ,(s,t)]rxnds} • k, 



3^ "^ J ■- t incident "- ' ' ^t diffracted 



^o (10) 



Hydrodynamic coefficients are found using the potential resulting 

 from forced oscillation of the breakwater. In this case the pressure 



18 



