Entering Figure 2-63 with cot B = 5, and using the curve for Ho/ho - 

 0.01, a value o£ " X2 ~ 0-41 is found. Assuming that since the beach 



is impermeable, Xi = 0.8 and 



X = X, X2 = 0.8(0.41) = 0.33 . 



The steepest incident wave which will be nearly perfectly reflected from 

 the given revetment is, from Figure 2-62, 



0.005 . 



It is interesting to note the effectiveness of flat beaches in dissipat- 

 ing wave energy by considering the above wave on a beach having a slope 

 of 0.02 (1:50). From Equation 2-87 (noting that 3 « sin B « tan B = 0.02), 



I— = 0.000014. 

 \ ol max 

 Hence 



X = X, Xj = 0.8(0.0014) = 0.0011, 



or the height of the reflected wave is about 0.1 percent of the incident 

 wave height . 



As indicated by the dependence of reflection coefficient on incident 

 wave steepness, a beach will selectively dissipate wave energy, dissipat- 

 ing the energy of relatively short steep waves and reflecting the energy 

 of the longer, flatter waves. 



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



2.6 BREAKING WAVES 



2.61 DEEP WATER 



The maximum height of a wave travelling in deep water is limited by 

 a maximum wave steepness for which the wave form can remain stable. Waves 

 reaching the limiting steepness will begin to break and in so doing, will 

 dissipate a part of their energy. Based on theoretical considerations, 

 Michell (1893) found the limiting steepness to be given by, 



Ho 1 



— = 0.142 =* - . (2-88) 



which occurs when the crest angle as shown in Figure 2-64 is 120 . This 

 limiting steepness occurs when the water particle velocity at the wave 

 crest just equals the wave celerity; a further increase in steepness would 



2-120 



