4. The radiation condition: the disturbance vanishes sufficiently fast 

 far ahead of ths ship. 



— 2 2 2 

 2 2 xV2 



(5) 



R - (x + y ) 



5. The bottom condition: the normal velocity at the bottom is zero. 



i 



♦jCx.y.z) - as z *■ - - (6) 



In equation (3), the constant is given as 



ko " & 2 (7) 



U 



and in Equation (4), the unit vector which is oriented normal to the fluid is 

 given by 



(iij, n 2 , n 3 ) - h 



( V n 5 , n 6 ) - r G x a 



(8) 



where r~ ia the position vector of the center of gravity. 



The solution of Equation (2) is given by Brard in an Integral forta as 



K.y.z) - - 7~ // G(P, Q)a(Q)dS(Q) 



4it 



(9) 



where P(x,y,s) is the field point, Q(x ,y ,s ) the source point, S the wetted 

 surface of the body, a the unknown strength of sourcee and sinks distributed on 

 the body surface, and G is the Green function which is given by Uehausen end 

 Laitone as 



