and the free surface condition of Equation (114) 



3 *D ^0 



-5- - = - U ? — - at z = (190) 



dZ W n. 2 



dz 



If the incident wave propagates along the direction of x, £ is constant in 

 the transverse plane. Then the function 



1' = <J>_ + U 5 -^ (191) 



D w dz 



is a plane harmonic function in the lower half space. The boundary 

 condition for it is 



3n* 3n« C w 3n' \3z / K } 



on the hull surface, and 



|^- = at z = (193) 



dz 



If we take only the first order terms, we can write the hull surface 

 boundary condition as 



lil = _:!wlz_ _3_ r!o. 



3n ? 3z 3n' + U C w 3n' V 3z ' 



|^- = - i a) C |V + U c X U-^ (195) 



dn w dn w dn \dz ' 



70 



