Therefore, we can take account of the effect of forward speed in the 

 boundary condition on the hull surface without bothering about the quadratic 

 terms in the free surface condition making the boundary value problem in- 

 tractable. The near field potential for the radiation potential is 

 determined from the two-dimensional boundary value problem with the 

 linearized free surface condition for an oscillating body such as 



a" 1 - — *„ " (129) 



3z g T R 



The well known method of solution for the two-dimensional problem can be 

 applied to the determination of the two-dimensional potential <J) . The 

 solution, however, is not identical to that for an oscillating cylinder of 

 infinite length because of the term involving the forward speed. The 

 results from the boundary condition on the hull surface, 



to* = Ua)(z g -x*)-U*} |^ - U(z g -x^) -^ \jf) (130) 



The last term on the right-hand side may add some complication. The 

 velocity potential in the near field is then expressed by 



<t> N = cf) (2D) + gjU) + z g 2 (x) (131) 



The term yg (x) which appeared in Equation (117) is omitted because of the 

 symmetry of longitudinal oscillations. It is readily shown that there is 

 a relation 



2 

 g.(x) =^- Sl (x) (132) 



because of the free surface condition. The function g, (x) is determined by 

 matching with the inner expansion of the far field potential. Since we 



50 



