f. Diffraction Around an Offshore Breakwater . In recent years there has 

 been increased interest in using offshore breakwaters as shoreline stabiliza- 

 tion structures. Reorientation of the shoreline in response to the waves dif- 

 fracted around the breakwater tips is of interest. The diffraction pattern in 

 the lee of a single breakwater can be approximated by superimposing two semi- 

 infinite breakwater diffraction patterns. One diffraction diagram is centered 

 at each end of the breakwater and a combined diffraction coefficient deter- 

 mined (Harms, 1979; Harms, et al., 1979). The approximate superposition solu- 

 tion is valid about two wavelengths behind the breakwater and beyond. Close 

 to the breakwater and in front of it the solution is not valid. For waves 

 approaching perpendicular to the breakwater, the diff ration pattern for one 

 end is the mirror image of the pattern for the other end. For nonperpendic- 

 ular wave approach, the diffraction pattern for one end is the mirror image 

 for the supplementary angle of the diffraction pattern for the other end, as 

 shown on Figure 2-59. If the incident waves are long crested and monochro- 

 matic, the wave propagating around each breakwater tip will either reinforce 

 or cancel each other depending on their relative phase. To calculate the 

 relative phase angle of the two wave components, crest patterns must be con- 

 structed. Behind the breakwater in the shadow zone the crests can be approxi- 

 mated by circular arcs centered at each breakwater tip. On the wave crest 

 diagram where two crests or two troughs intersect, the two wave components 

 will be in phase; where a wave crest crosses a wave trough, the waves will be 

 180° out of phase (see Fig. 2-59). Lines of constant phase difference could 

 be constructed. These would be lines radiating outward from the breakwater as 

 shown in Figure 2-59. The diffraction coeficient for the composite wave field 

 can be calculated from the diffraction coefficients of the waves coming around 

 each breakwater tip by 



2 2 



K' 



k; + k^2 ^ 2k: ki cos 



where 



K' = combined diffraction coefficient 



K! = diffraction coefficient for the waves coming around the left 

 tip of the breakwater 



Kl = diffraction coefficient for the waves coming around the right 

 tip of the breakwater 



= phase difference between the two component waves at the point 

 of interest 



Application of the approximate method is illustrated here by an example prob- 

 lem. 



*************** EXAMPLE PROBLEM 10*************** 



GIVEN ; A breakwater 200 meters (656 feet) long is built in water 5 meters 

 (16.4 feet) deep. Waves with a period T = 10 seconds and a height H = 3 

 meters (9.8 feet) approach at such an angle that the incoming wave crests 

 make a 30° angle with the breakwater's axis. 



2-105 



