Linearized Potential Flow Theory for ACVs in a Seaway 



particular solution will then satisfy the homogeneous form of (V. 3) 

 and can be solved in tl 



The Green's Function. 



and can be solved in the same manner as <i> or <f> 



1000 0100 



The potential of a source of maximum unit strength and 

 pulsating with frequency a while moving with uniform velocity V 

 along the x-axis at a depth f below the undisturbed water surface 

 satisfies the conditions stipulated for the Green's function in connec- 

 tion with this problem. This function is given in different forms by 

 various authors, but we shall use the representation derived by 

 Peters and Stoker ( 2 ) . 



G(x, y, z;t , r, , f ) = (x - Z f + (y - r, ) 2 + (z - f ) 2 



f 



I(x - if + (y - 7 ? ) 2 + (z+ r) 2 



■1/2 



+ 



7 oo 

 g / / Pe fv «/ cosp (y-r,) sin0 



o o 



*//■ 



-p(z+f ) + ip(x-£) cos 6 

 g 



if 



i— =-'/ «-— ^ " r w ' / dpd0 + 



gp - ( cr + pV COS0 ) 



-p(z+f) + ip(x-£)cos0 



P e cosp(y-7?) sin 6 



2 dpd0 



gp - (a +pV cos0) 



*// 



De "P(z+r) + ip(x-t) cos0 . 



P^ cosp.(y-T?) siafl 



2 dpd0 



4^2 gp ~ (tr + pVcOS ^ 



where 



7 = 



) if 1 < g/4ffV 



arc cos g/4aV j if g/4 ff V^ 1 



P l' P 2 are the real zeros of the denominator in the integrand 



243 



