where (H /L ) cr is the critical wave steepness to obtain complete reflection 



and is defined as : 



1/2 



2/3 



sin z p 



(9) 



in which fi is the slope angle in degrees. 



19. Battjes (1975) reexpressed Miche's (1951) equation to obtain K r 

 as a function of the surf similarity parameter. The resulting equation was: 



K r = O.U§ 



(10) 



Battjes compared Equation 10 with data collected by Moraes (1971) and found 

 good agreement with the data for breaking waves and £ < 2.5 . 



20. Ahrens (1987) conducted experiments to determine the stability, 

 transmission, reflection, and energy dissipation characteristics of reef 

 breakwaters. Ahrens defined the reef reflection parameter P as 



z^L Q 



P = 



AJi c 



(11) 



where 



z = height of reef 

 L s and h s = wavelength and depth at toe of reef, respectively 

 A b = cross -sectional area of reef 



Ahrens performed a regression analysis to relate wave reflection to the reef 

 reflection parameter and obtained 



(1.0 + 8.284P" - 951 ) 



(12) 



The coefficient of determination for Equation 12 was 0.8. 

 Summary 



21. Equation 8 (Miche 1951) and Equation 10 (Battjes 1975) include 

 beach slope and deepwater wave steepness to estimate the reflection 

 coefficient. Equation 12 (Ahrens 1987) was developed for reef breakwaters, 

 which differ from the bars and reefs modeled in the present study in that reef 



18 



