the solution is obtained by substituting Equations 16 and 24 into Equation 25 

 as follows: 



>(r,e) = 1 



t /-i >> ^ o V inir/2v . . na 



J_(kr) + 2 > e J , (kr) cos — cos 



La n/v v 



v 

 n=l 



(26) 



Equation 26 is the solution for the combined wave reflection and diffraction 

 by a vertical wedge of arbitrary wedge angle and is considered to be extended 

 from the solution by Stoker (1957) who only solved the problem of a thin semi- 

 infinite breakwater. The solution in Equation 26 and the one by Stoker are 

 not only in nonclosed form but also in terms of Bessel functions. It seems 

 that the calculations of the solutions are very difficult without using a mod- 

 ern high-speed computer. This is probably the reason why Stoker arrived at 

 his solution expressed in the same cosine series but did not use it to calcu- 

 late the result. Instead, he further transformed the expression into a very 

 complex integral form for further approximation in calculating the result. 



16. Notably, the solution at the origin point is obtained by simply 

 substituting r = into Equation 26 to arrive at 



+(0,9) = \ (27) 



Therefore, wave response at the origin point depends only on the wedge angle 

 and does not depend on the incident wave angle. 



Two Special Cases 



17. The solutions for two special cases are used to verify Equation 26: 

 one for the case of a thin semi-infinite breakwater and the other for the case 

 of an infinite wall extending from x = -<*> to °° . 



18. The vertical wedge should reduce to a thin semi-infinite breakwater 

 as the wedge angle reduces to deg. Therefore, solution of the combined wave 

 reflection and diffraction by a thin semi-infinite breakwater is obtained by 

 substituting v = 2 (that is, 6 = 2ir) into Equation 26 which then becomes 



11 



