to estimate a reflection coefficient, x= 0.095. The reflected wave height 

 is, therefore, H = 0.095(1) = 0.095 meter (0.3 foot). 



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



Wave reflection from sinusoidal-shaped bed forms on a flat bottom was ana- 

 lyzed by Eavies (1980) using linear wave theory. His analysis shows that the 

 wave reflection coefficient is periodic in the ratio of wavelength L to bed 

 form length I, and that it is maximum when L = 2£. 



Figure 2-68 gives the reflection coefficient for the case of L = 2il for 

 bedform steepnesses, b/£ = 1/20 and b/ £ = 1/40, where b is the 

 amplitude of the bars. Reflection coefficients are given for various 

 numbers of bars as a function of the ratio of the bar amplitude to water 

 depth. These figures show that for L/ Jl = 2 the reflection coefficient 

 increases as the number of bars increases, as the ratio of bar amplitude to 

 water depth increases, and as bar steepness decreases. Wave reflection 

 coefficients will be smaller than those given in Figure 2-68 if L/ £ is not 

 equal to 2, if the wave is nonlinear, if wave energy dissipation is signifi- 

 cant, or if the bars are not sinusoidal in shape. 



*************** EXAMPLE PROBLEM 16*************** 



GIVEN : Two sinusoidal bars are located in a water depth d = 3 meters (9.8 

 feet) with an amplitude b = 1 meter (3.28 feet) and a length i = 20 meters 

 (65 feet). A normally incident wave with a period T = 8 seconds has a 

 length L = 50 meters (164 feet) and height of 1 meter (3.28 feet). 



FIND : The height of the reflected wave. 



SOLUTION: Calculate 



and 



Enter the upper part of Figure 2-68 with b/d = 0.33 and read x = 0.50. This 

 is an upper bound on the reflection coefficient. The actual reflection 

 coefficient may be smaller due to nonlinear wave effects, energy dissipa- 

 tion, or if the ratio L/£ is not equal to 2. The maximum reflected wave 

 height is, therefore, H^ = 0.50(1) = 0.50 meter (1.64 feet). 



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



6. Refraction of Reflected Waves . 



A substantial increase in reflected wave energy may result where struc- 

 tures are built along a section of coastline with no beach fronting the 

 structure. In cases where the structure is nearly parallel with the bottom 

 contours, and the wave direction and offshore bathymetry near the end of 

 the structure result in wave reflection at a large angle, the structure may 



2-124 



