The two layers of armor units reduce the reflection coefficient to less than 

 30 percent of the smooth slope reflection coefficient. 



5. Wave Reflection from Bathymetric Variation . 



Any change in bathymetery such as a shoal or offshore bar results in some 

 reflection of an incident wave. Reflection from complex bathymetric changes 

 can be determined mathematically (Long, 1973) or by physical models (Whalin, 

 1972). Estimates of wave reflection from simple bathymetric changes can be 

 calculated using linear wave theory. Two examples for normally incident waves 

 are presented here. The first example is for a smooth step and the second for 

 a series of sinusoidal offshore bars. Nonlinear effects and wave energy dis- 

 sipation are neglected so reflection coefficient estimates will be high. 



Wave reflection coefficients for smooth sloped steps have been determined 

 by Rosseau (1952; also see Webb, 1965) for several shapes. Linear wave theory 

 was used. The water depth decreases from d to d over a length i. 

 Reflection coefficients for the cases of i/(d + d ) =6 and 12 are given as a 

 function of d /d for various values of d /(gT ) in Figure 2-67 (a and b) . 

 These graphs indicate that for a given i/(d + d ), wave reflection increases 

 as the step size d /d increases and as the wave period increases. Maximum 

 reflection occurs as T approaches infinity independent of Jc, as the upper 

 curves in Figure 2-67 (a and b) show. Wave reflection decreases for a given 

 wave condition and step size as i/(d + d ) becomes larger; i.e., a flatter 

 step. 

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



GIVEN ; A wave with a period T = 10 seconds and a height H = 1 meter in a 

 water depth d^ = 6 meters (19.7 feet) travels over a smooth step in the 

 hydrography into a reduced depth d2 = 2 meters (6.56 feet). The step is 50 

 meters (164 feet) long. 



FIND : The height of the reflected wave. 

 SOLUTION: Calculate 



50 



= 6.25 



d^ + d2 6+2 

 Therefore, Figure 2-67, a, is used. Enter the figure with 



"' 6 



and 



^1 



gT2 9.8(10^) 



= 0.0061 



2-122 



