FIND ; The approximate diffraction pattern in the lee of the breakwater and 

 the wave height three wavelengths behind the center of the breakwater. 



SOLUTION ; Determine the wavelength in the water depth d = 5 meters. 



^o " f^" " 1-56(10)2 = 156 ^ (512 ft) 

 ^ = -r|r = 0.0321 



O 



Enter Table C-1, Appendix C, with the calculated value of d/L and find 



Y = 0.0739 



Therefore, L = 5/0.0739 = 67.7 meters (222 ft). The breakwater is therefore 

 200/67.7 = 2.95 wavelengths long (say, three wavelengths). The appropriate 

 semi-infinite breakwater diffraction patterns are given in Figure 2-35 and 

 in the mirror image of Figure 2-31. The diffraction patterns are scaled in 

 accordance with the calculated wavelength. 



*************************************** 



From the mirror image of Figure 2-31, the diffraction coefficient three 

 wavelengths behind the center of the breakwater gives Kj^ = 0.6. From Figure 

 2-35, Kt equals 0.15 for the same point. The relative phase angle between 

 the two waves coming around the two ends is 9 = 182" and the combined diffrac- 

 tion coefficient 



K' = ^K^2 + j^2 + 2K£ K|^ cos 



K' = V(0.6)2 + (0.15)2 + 2(0.6)(0.15) cos 182° 



(2-79) 



K' = Vo.36 + 0.0225 + (0.18)(-0.999) 



' = V 0.2026 = 0.450 



K 



Therefore, H = 0.450 (3) = 1.35 meters (4.44 feet). The approximate diffrac- 

 tion pattern can be constructed by determining the diffraction coefficients at 

 various locations behind the breakwater and drawing contour lines of equal 

 diffraction coefficient. The pattern for the example problem is shown in Fig- 

 ure 2-60. The same procedure of superimposing diffraction diagrams could be 

 used for a series of offshore breakwaters using diffraction patterns for wave 

 propagation through a breakwater gap. Equation 2-79 applies to this situation 

 as well. The results of the preceding analysis is approximate. Montefusco 

 (1968) and Goda, Yoshimura, and Ito (1971) have worked out analytical solu- 

 tions, and others (e.g.. Harms, 1979; Harms, et al., 1979) have developed 



2-107 



