Newman and Tuck 



( WALL) 



disturbance potential is of the class described in Part I, and the terms "0(O) " 

 and "f^''^)" have the significance discussed after Eq. (1.1). 



The "wall" potential can itself be further decomposed into 



(WALL) (2D) (WALL) 



^(0) (x,y,z) = 0^0^ (y,z;x) + f^^^ (x) 



(3.7) 



where, for constant x, 0^, ^^^ satisfies the two dimensional Laplace equation 

 with respect to y and z. Both terms f^*^''^'' and f^^^^^ represent interactions 

 between sections of the ship and were determined explicitly in Tuck, 1964, in the 

 form 



(WALL) (WALL) 



(3.8) 



( FS) f ( FS) 



(3.9) 



with 



^( WALL) 

 "(0) 



(X) = 



^ £ ["S"" ^°g 2|x|], 



(3.10) 



(FS) 



4 dx 



"o(^)-(2.sgnx)Y„(|^ 



(3.11) 



The above results are in the form of Eq. (1.2), since "us'(f)" is the flvix through 

 the cross section at ^ due to the steady motion, S(^) being the immersed area 

 of the cross section. 



Now a similar analysis holds for the linear vinsteady potential 4>^ j ^ which 

 can be written as 



(WALL) (FS) . 



0^ j^(x,y,z,t) = 0^1^ (x,y,z,t) + f^^^ (x,t) + OCe^loge) 



with the wall potential further decomposed into 



(3.12) 



( WALL) 



( WALL) 



(x,y,z,t) = 0;,/Cx,y,z,t) + f^j^ (x,t) 



( 2D) 

 ( 1) 



(3.13) 



/ Uf AT T > f* F S "1 



if desired. The interaction terms f( i^ and f( i) are not now simply related 

 to the area curve as in (3.8) and (3.9) but, since the vinsteady flow is produced by 

 linear oscillations of the ship, will be linear fvinctions of the magnitude of these 

 motions. Thus we can write 



146 



