Analysis of Ship-Side Wave Profiles 



where 



T^x, y) = 



_U 

 g 



c>x 



2 _ 



d*l J a/u 2 * 2<t> l d*l 



Sx 



$>z\ 



dz 



(33) 



^ = (^ (l^) 2 + (^) 2 <* 



The second order term of the velocity potential <£« is 

 ;iven in accordance with well-known Fourier double integral 



2 4 



f°° c °° 



— / / T^x'.y!) G (x,y, z ; x'.y'.o) dx' dy' 



-CO 



(35; 



where G(x, y, z ; x',y', o) is given in Equation (3) and (4.) 



Once <t>^ is known, y, (x, y) can be calculated by Equa- 

 tion (33) all over the z = plane, then <p ^ is obtained by Equation 

 (3 5). Equation (3 5) means that the velocity potential of second order 

 term is just that of source distribution 7j (x, y) which is distributed 

 over the free surface. 



The second order amplitude function corresponding to % 

 is given as follows after some approximations. 



/oo 

 \ P(0,y') cos(K / sec 2 sin y') 

 / ° 



o A 2 ) 



-Q(0,y') sin(K Q isec 0sin0y')(dy' 



" contd. 



701 



