PART III: CALCULATION AND RESULTS 



20. Results of the combined reflection and diffraction by a wedge of 

 arbitrary wedge angle can be calculated from Equation 26. Since the solution 

 is not only in terms of Bessel functions but also in a nonclosed form, the 

 computer program WEDGE is therefore written to calculate the solution. 



21. In the program the subroutine BESJ for calculating Bessel function 

 of fractional or integer order was used. The subroutine was originally writ- 

 ten by Amos, Daniel, and Weston in 1975 (Morris 1984) and is collected in the 

 Naval Surface Weapons Center Library of Mathematics Subroutines (Morris 1984). 



22. In the calculation the summation of the infinite terms in Equa- 

 tion 26 was carried out to the term which is preceded by eight successive 

 terms of the absolute value of the Bessel function, all equal to or less than 



_0 _Q 



10 . The solution has a truncation error less than 10 , and it is of the 

 order of one. 



23. In this study, results of the combined wave reflection and diffrac- 

 tion for the wedge are calculated for two cases: one for a vertical wedge of 

 0-deg wedge angle and the other for a vertical wedge of 90-deg wedge angle. 



Vertical Wedge of 0-Deg Wedge Angle 



24. When the wedge angle is equal to zero, the wedge is actually a thin 

 semi-infinite breakwater extending from x = to » . Figure 3 shows the 

 thin semi-infinite breakwater along with the polar coordinates. In this case 

 the diffraction results for various incident wave angles in the water region 

 from 6 = it to 2tt and r/X < 10 , where X is the incident wave length, 

 have already been presented by Wiegel (1962) and are shown in the SPM, Vol- 

 ume I (1984). The present results combine reflection and diffraction effects 

 and cover the water region from 6 = to 2ir and r/X < 10 . Therefore, 

 the present results for this particular case can be considered to be a comple- 

 mentary and extended version to the ones in the SPM. 



25. In this study wave response was calculated at 1,460 grid points 

 intersected by r/X = 0.5, (0.5), 10 , which means that the values of r/X are 

 from 0.5 to 10.0 with each value increment being 0.5. Hereafter, all similar 

 expressions are to be interpreted in the same way (e.g., = 0, (tt/36) ,2tt for 



13 



