where 



,1,2 (\ sinh ^ H- 2„ b\ 



and 



V = wave velocity 



B = flume width 



Hj = wave height at Xp = 



H = height after the wave has traveled a distance Xp in water 

 of depth d. 



If the flume width is many times greater than the water depth, equation 

 (4-29) reduces to 



4^3/2^1/2^1/2 

 X2 (sinh ^ + ^) 



(4-30) 



which is the same as that of Eagleson and Dean (1966). According to 

 Keulegan (personal comunication, 1977) the values of a as determined 

 from equation (4-30) should be increased about 25 percent, or 



X2 (smh x* + X*) • 



This increase is deemed necessary because of the energy losses due to 

 the contamination of the water surface by dust and oily molecules. The 

 effects of bottom friction in harbor wave action models, including the 

 suggested 25-percent increase in a, are shown in Figures 4-3 and 4-4. 

 The figures show that (a) effects of bottom friction in the prototype 

 (linear scale of 1:1) are negligible within the area and travel distances 

 reproduced in ordinary wave action models; (b) linear scales less than 

 about 1:100 can seldom be used; (c) energy loss due to bottom friction 

 becomes appreciable as the water depths become small; and (d) wave heights 

 measured in harbor wave action models should be corrected to minimize the 

 scale effects due to bottom friction. The correction coefficients can be 

 calculated from equations (4-28) and (4-31). 



If rubble-mound breakwaters and wave absorbers are modeled geometri- 

 cally similar to their prototype structures, there is relatively more 

 wave reflection from the model structures and relatively less wave trans- 

 mission through the model structures compared with the prototype, unless 



220 



