The spectrum with narrow spreading is attenuated more by the breakwater, but 

 no so much as is a monochromatic wave. The monochromatic wave diffraction 

 coefficient is approximately K' = 0.085 ; hence, the use of the mono- 

 chromatic wave diffraction diagrams will underestimate the diffracted wave 

 height. 



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



Diffraction of directional spectra through breakwater gaps of various 

 widths are presented in Figure 7-62 through 7-65. Each figure is for a 

 different gap-width and shows the diffraction pattern for both wide 

 directional spreading (Sj^^^ = 10) and narrow directional spreading (Sj^^^^ = 

 75). Diagrams are given for the area near the gap (0 to 4 gap-widths behind 

 it) and for a wider area (a distance of 20 gap-widths). Each diagram is 

 divided into two parts. The left side gives the period ratio, while the right 

 side gives the diffraction coefficient. Both the period ratio patterns and 

 diffraction coefficient patterns are symmetrical about the center line of the 

 gap. All the diagrams presented are for normal wave incidence; i.e., the 

 center of the directional spreading pattern is along the center line of the 

 breakwater gap. For waves approaching the gap at an angle, the same approxi- 

 mate method as outlined in Chapter 3 can be followed to obtain diffraction 

 patterns. 



*************** EXAMPLE PROBLEM 15*************** 



GIVEN : A wave spectrum at a 300-meter- (984-foot-) wide harbor entrance has a 

 significant wave height of 3 meters (9.8 feet) and a period of maximum 

 energy density of 10 seconds. The water depth at the harbor entrance and 

 inside the harbor is 10 meters (32.8 feet). The waves were generated a 

 large distance from the harbor, and there are no locally generated wind 

 waves . 



FIND ; The significant wave height and period of maximum energy density at a 

 point 1000 meters (3281 feet) behind the harbor entrance along the center 

 line of the gap and at a point 1000 meters off the center line. 



SOLUTION : Since the waves originate a long distance from the harbor, the 

 amount of directional spreading is probably small; hence, assume Sj^^^^ = 

 75 . Calculate the deepwater wavelength associated with the period of 

 maximum energy density: 



L = 1.56 T^ = 1.56 (100) 

 o p 



L = 156 m (512 ft) 

 o 



Therefore 



d/L^ = 10/156 = 0.0641 



Entering with d/L^ = 0.0641 , yields d/L = 0.1083 . The wavelength at the 

 harbor entrance is, therefore. 



7-94 



