PART II: BOUNDARY VALUE PROBLEM 



Mathematical Formulation 



4. In this study our primary interest is the wave reflection and 

 diffraction by a vertical wedge of arbitrary wedge angle in a constant water 

 depth h * subject to the excitation of monochromatic incident waves of infi- 

 nitesimal amplitude coming from infinity. Let (r,0,z) be cylindrical coordi- 

 nates, with z = representing the undisturbed water free surface and upward 

 direction representing the positive z-axis. The tip of the wedge is chosen to 

 be the origin of the coordinates and two rigid walls of the wedge to coincide 

 with 9=0 and 6=6 , respectively, as illustrated in Figure 1. Carte- 

 sian coordinates (x,y,z), corresponding to the cylindrical coordinates, are 

 also occasionally used and shown in the same figure. Therefore, the wedge 



Figure 1. A vertical wedge of 

 arbitrary wedge angle 



* For convenience, symbols and abbreviations are listed in the notation 

 (Appendix B) . 



