Linearized Potential Flow Theory for ACVs in a Seaway 



o(0) v* Ql 



00 



g %100 = ° 



2 2 



0(d a ) V <l> , ft - 2i<r V<I> , rt - a * - e* = 



v/ 1010 1010 1010 8V 1010 



XX X z 



2 2 



0(fla) V 4> - 2i(T Vtf> - a $ - ed> = 



VH ; 0110 *0110 0110 gT 0110 



XX X z 



° m yE *noo -fi*noo = 2v(v *iooo- v* ioo + 



0100 M000 ; 



V 



d 2 



1000 dz v ^0100 

 x xx 



g4> 0100 ' + ^0 



(V 2 4> 



1000 



100 ^z 

 x 



1000 



(V.3) 



It will be noted that the first four equations are homogeneous, 

 whereas the equation for the interference potential is an inhombge- 

 neous one. 



If we denote by ^ the time -independent part of the oscilla- 

 tory potential <£> (i. e. without the factor e 1<T ) , the first four of 

 the above equations reduce to the form 



2 2 



xx x s • z 



(V.4) 



In the case of the steady potentials a is, of course, set equal to zero. 



(iii) On the IFS (z = 0) the condition (4-7) is 



2 

 * - 2V$ + V 4> - g<|> + 2V4>. V(<f> - V4>) + 



tt xt XX ° Z t X 



i p s a 2 



+ (<t> - V* + — — ) — ^— (<f> - 2V$ + V * - gcf> ) + 



g t x P ' dz v tt xt xx B z 



215 



