taken as the half length of the ship, L/2. If the fluid velocity is 



normalized by the ship speed U, then the acceleration of gravity is ex- 



2 

 pressed by the dynamic coefficient of gravity Y n = g^/U , or as a function 



2 

 of the Froude number Y n = 1/ (2Fn ) . Instead of a ship moving in still 



water, we assume a uniform flow of velocity U in the direction of x which 



is opposite to the motion of the ship. When a ship hull is introduced at 



a fixed position in the flow, the flow field is specified by a velocity 



potential x + <j). The disturbance potential <f> is harmonic in the space 



occupied by the fluid. Then the Laplace equation 



V 2 cj) = (1) 



is valid outside the hull surface and below the free surface, which is 

 expressed by the equation 



z = C (2) 



The fluid velocities are 



u = 1 + 3<J)/3x, v = 3<)>/3y, w = 3cj)/3z (3) 



The fluid boundary is composed of the wetted hull surface, the sea bottom, 

 and the free surface. Since the fluid is assumed nonviscous, the boundary 

 condition on the hull surface is that the fluid velocity is tangential to 

 the hull surface. It is expressed by 



3n 3n w 



where n is the unit outward normal vector into the hull surface. Since 

 the free surface is expressed by the equation z = £, where £ is a function 

 of x and y, the kinematical condition on it is 



U f + V lf- W=0 (5) 



