turbulent friction. In partly breaking waves, some of the wave energy 

 is reflected and some dissipated. 



NONBREAKING WAVES 



The approaches in theoretical treatment of breaking and nonbreaking 

 waves and their runup have mostly been along the lines of the small am- 

 plitude wave theory and the long wave theory. 



The breaking criterion for small amplitude wave theory is that the 

 maximum water particle velocity of the wave crest exceeds the phase 

 velocity of the wave, or that the Bernoulli equation of the free surface 

 is not satisfied. In the long wave theory the breaking criterion is 

 defined by the inception of a shock wave. 



Based on the small amplitude wave theory, Miche (l95l) has proposed 

 the following theoretical formula for limiting conditions of nonbreaking 

 waves . 



2 



, , . 2a sm 

 H/L < — — ;; — 

 max TT TT 



where H = wave height 



L - wave length 



a = angle of bottom slope 



for a = i+5°, (f) = 0.112 

 ' L max 



a - 15°, (^) = 0.0079 

 jj max 



a - 5°, (?) = 0.00057 

 L max 



The long wave theory and the application of the m.ethod of charac- 

 teristics is considered a better approach than the small amplitude wave 

 theory. However, this method does not give such a simple relationship 

 for limiting conditions as does the small amplitude wave theory. Except 

 foi- some rather limited attempts at finding an analytical solution, the 

 problem of long wave propagation over a gentle slope is largely un- 

 resolved. The most reliable method consists of applying the method of 

 characteristics for each particular case (Wilson, et al, I96U). 



we shall not go into any detail about different theoretical and 

 experimental results on wave runup for nonbreaking waves, but merely 

 include P'igure C-1 to show a trend of results. 



C-2 



