Thus the boundary value problem (in which the governing equation is Equa- 

 tion 2, the boundary condition is Equation 5, and the radiation condition is 

 Equation 6) is completely formulated. 



Analytical Solution 



11. Analytical solution to the problem formulated in the preceding 

 section is obtained by following the solution technique by Stoker (1957). To 

 obtain the solution, the water region is divided into three subregions — I, II, 

 and III — by the incident wave ray passing through the tip of the wedge and the 

 reflected wave ray reflected away from the tip of the wedge, as shown in Fig- 

 ure 2. Obviously, the total wave in subregion I is the sum of the incident, 

 reflected, and scattered waves; the total wave in subregion II, where the 

 reflected wave does not exist, is the sum of the incident and scattered waves; 

 and the total wave in subregion III, where the incident and reflected waves 

 have been shaded out, is only the scattered wave. For certain combinations of 



\ 









X 



V 



\ 



* 



a/ 



i 



67 



7 



4/ 



/y 



/ 



/ 



/ 



7777777777777777 ' 



WEDGE 



Figure 2. Three subregions and the wedge 



