which gives 



K 100,000 



r* = — — = = 107,530 meters (66.8 miles) 



V 0.93 0.93 



The width of the trapped wave zone from the shoreline to the outer limit 

 is given by 



r* - R* = 107,530 - 100,000 = 7,530 meters (4.68 miles) 

 P 8 



2* d* n 2 2tt d* n 2 



(c) - = 0.068 or T 2 = 



g T2 0.068 g 



t2= 2,(30) (48.65) ^ 

 9.81(0.068) 



T = 117.2 seconds (1.95 minutes) 



for the minimum trapped wave period. 



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



6. Mach-Stem Formation . 



Figure 38 illustrates solutions for trapped waves for angles a, ±45°. 

 Perroud (1957) showed that a-^ = 45° defines a critical angle for wave 

 reflection. When o^ < 45° regular reflection occurs, i.e., the wave 

 reflects in a manner described in Section VI, 1 and 5. When a^ = 45° the 

 end of the wave crest at the shoreline turns perpendicular to the shore- 

 line (see Fig. 39). Regular reflection no longer occurs when 04 > 45°. 



Perroud showed that, for 0^ > 45°, the incident wave produces two 

 components. The first is a reflected wave, lower than the incident wave, 

 and with the angle, a 2 , between the reflected wave ray and the normal 

 to the shoreline defined by a 2 < 04. The second component is a Mach stem 

 which moves along the shoreline in the direction of the longshore compo- 

 nent of the incident wave, growing in size as it progresses along the 

 shoreline. Figure 39 shows the initial growth of a Mach stem along a 

 vertical wall for the critical angle a-^ = 45°. 



Experimental measurements by Perroud (1957) show that the Mach stem 

 has a profile at the shoreline similar to the profile of the incident 

 wave, giving the Mach stem the appearance of a large wave moving along 

 the shoreline. The Mach stem remains attached to the shoreline end of 

 the incident wave crest, so its speed of propagation, C g , along the 

 shoreline is given as 



r C 



C o = -r- (292) 



* sin a. ■ ■* 



where C is the celerity of the incident wave near the shoreline. 



130 



