combine with a steep bottom slope m to form a waveguide which traps wave 

 energy along the shoreline. This trapped energy may increase wave heights and 

 therefore increase erosion along an adjacent section of shoreline. Trapped 

 wave rays are illustrated in Figure 2-69. 



The seaward distance X that the slope must extend to trap waves, and the 

 distance Y that a reflected wave ray will travel before returning to the 

 shoreline are given by Camfield (1982) in dimensionless form as 



Xm 1 



T- - 1 (2-88a) 



dg sin'^a 



Ym 1 



— = — [tt - 2a + sin(2a)] (2-88b) 



dg sin'^a 



where d is the water depth at the toe of the structure, and a is the 

 reflected wave angle in radians (see Fig. 2-69). The bottom slope m is 

 assumed to be uniform, and the waves are assumed to be shallow-water waves 

 (i.e., the wavelength is assumed to exceed 2.0 times the water depth). For 

 convenience, equations (2-88a) and (2-88b) are solved graphically in Figure 

 2-70 with a given in degrees. 



The values of d and m are known for a particular structure or pro- 

 posed structure under investigation. The value of a can be determined from 

 existing wave refraction methods for incident waves as discussed in Section 

 III. Where solutions of equations (2-88a) and (2-88b) show that wave energy 

 will be trapped, a more extensive investigation should be undertaken to deter- 

 mine the effects along the shoreline. 



ie-k-k*itit'k**itie***1t EXAMPLE PROBLEM 17*************** 



GIVEN ; A vertical bulkhead is located along a shoreline in a 2.0-meter (6.5 

 foot) water depth as shown. The bottom slope m is 0.03 and is uniform to 

 a depth of 20 meters (66 feet). Refraction studies show that waves will 

 have an angle of incidence at the wall of 25° (0.436 radian); i.e., they 

 will be reflected at that angle. 



FIND ; Determine if waves may be trapped along the shoreline. 

 SOLUTION ; For the given reflection angle a = 25°, Figure 2-70 gives 



Xm , , 

 d-= ^'^ 



8 



2-126 



