8. Thus only the horizontal part of the velocity potential function <J> 

 is needed to be determined as a solution of Equation 2 in the water region 



> 6 > , with the following boundary conditions at the rigid and imperme- 

 able walls of the wedge: 



It = at 6 = and 6 (5) 



do O 



9. A condition at infinity is also required to ensure a unique solu- 

 tion. The classic approach is to use the Sommerfeld radiation condition at 

 infinity which states that the scattered wave <f) must behave like a cylin- 

 drical outgoing progressing wave at infinity such that ' 



HS ^ (^ + *♦„) = (6) 



The total wave represented by <f> is the linear superposition of an incident 

 wave 4>. , a reflected wave from the the 6 = wall of the wedge <j) , and 

 the scattered wave <j> from the tip of the wedge. 



* = * ± + <J> r + <fr s (7) 



Equation 6 can be satisfied if 



^-ikr 



at r-*>° (8) 



/kr 



10. The incident wave coming from a large distance from the tip of the 

 wedge is assumed to be a plane progressive wave of amplitude a and incident 

 angle a to the x-axis as given by 



* = e ikr C0S (6_a) (9) 



Consequently, the perfectly reflected wave from the y = wall of the wedge 

 is 



= e ikr cos (6-Hx) (1Q) 



