5. The radiation condition; that is, the energy flux of waves associated with 

 the disturbance of the ship is directed away from the ship at infinity. 

 Equations (5), (6), and (7) are exact boundary conditions. By substitution of 

 Equation (3) into Equations (5) and (6), and by linearization, the free-surface 

 condition is given by 



2 (2 2 



+ (j) +<(})_- — 9 + — — (p H 9 > e =0 (8) 



g oxx oz I 2z g 2 g 2x g 2xx 

 The body condition can be expressed as follows 



(V(})^+V(|)2+U^) • n = U^ • n (9) 



where U = (-U,0,0), steady forward velocity vector 



->- 



U = velocity vector due to oscillation 



n = unit normal vector directed into the fluid domain 

 The solution of Equation (4) with two boundary conditions. Equations (8) and (9), 

 is nonlinear between cj) and (j) . The usual practice for solving this problem is to 

 separate (}) and (}) ; and evaluate these two potential functions independently. By 

 substitution of Equation (3) into Equation (4) and by separation of (j) and (j)„ in 

 Equations (8) and (9), we have two sets of partial differential equations. 



(t> + (f) + (t> =0 (10) 



oxx oyy ozz 



— (j) + (^ =0 (11) 



g oxx oz 



(V(}) +U ) • n = (12) 



o o 



). + <p. +4). =0 (13) 



2xx 2yy 2zz 



