where 



g = the acceleration due to gravity 



H' = the equivalent unrefracted deepwater wave height 



R = the vertical- height of runup on the structure if the breakwater 

 were high enough so that no overtopping occurred 



F = breakwater freeboard = h - d g 



h = the structure crest elevation 



d = the water depth at the toe of the structure. 



Q* and a are empirical overtopping coefficients found in the Shore Protection 

 Manual (SPM) (U.S. Army, Corps of Engineers, Coastal Engineering Research Center, 

 1977, Ch. 7). Sample values of the empirical coefficients for an impermeable 

 riprap structure with a 1 on 1.5 seaward slope are shown in Figure 2. 



A first approximation of the wave runup on rubble-mound breakwaters may be 

 estimated using the equation of Ahrens and McCartney (1975): 



R = t™W; 5 = -NF^ (2) 



(1 + b£) 



^ 



where L Q is deepwater wavelength, and 6 is the slope angle of the seaward 

 face of the breakwater; the empirical coefficients a = 0.692 and b = 0.504 are 

 recommended. Note. — Other methods for estimating runup on various structures 

 may be found in the SPM (U.S. Army, Corps of Engineers, Coastal Engineering 

 Research Center, 1977) and Stoa (1979). 



Equations (1) and (2) were developed using monochromatic wave tests, so 

 they should be used for swell wave conditions where the wave height and period 

 from one wave to the next is approximately constant . The method of Ahrens 

 (1977) for modifying equations (1) and (2) for irregular waves is recommended 

 for irregular waves generated by nearby storms. The irregular wave overtopping 

 prediction procedure is rather complicated, so the computer program BWFL0W2 

 (CERC program number 752X6R1ANC) is recommended for irregular waves. This pro- 

 gram is available in the Corps of Engineers Computer Library at U.S. Army 

 Waterways Experiment Station, Vicksburg, Mississippi. Note that the irregular 

 wave overtopping method tends to be conservative because a Rayleigh wave height 

 distribution is assumed, while the actual distribution may be truncated due to 

 depth or steepness limited breaking. 



1. Enclosed Breakwater Systems . 



If the breakwater system is enclosed on either end by impermeable groins 

 and the breakwater has no gaps, water overtopping the breakwater would cause 

 the water level landward of the breakwater, h^, to rise. Eventually, the 

 zone landward of the breakwater would fill up to a ponding level where the sea- 

 ward flow of water over the breakwater would equal inflow and the net flow, q n , 

 would be zero. Diskin, Vajda, and Amir (1970) tested a number of breakwaters 



10 



