Falttnsen 
direction of the positive x-axis. 
=) L/2 
Figure 1 Coordinate system 
The ship is slender and there is no other bodies in the fluid. The 
fluid has infinite depth. It is incompressible and the flow is irrota- 
tional, so that there exists a velocity potential ¢ which satisfies the 
Laplace equation. 
in the fluid domain. The ship is restrained from performing any os- 
cillatory motions, and so the boundary condition on the wetted surface 
of the ship will be 
= <iDeeron inn . Swed) (Sea.0%8) ave (2) 
Here z= h(x,y) is the mathematical description of the wetted surface 
of the ship. 0 /0@n denotes the derivative in the direction of the 
outwards normal on the surface of the ship. 
The conditions on the free surface, z= {¢ (x,y,t), are, 
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