plotted and then superposed on the study area profiles (see Figure 3). 

 When the depths in the study area at any point are greater than the crit- 

 ical depth, the "critical" waves will break closer inshore and the run-up 

 will exceed the structure height. When the depths in the study area at 

 any point are less than those of the "critical profile", the critical waves 

 will break farther offshore and the run-up will not exceed the structure 

 height. Thus, by overlaying the "critical profile" on each of the study 

 area profiles, the structure design height may be checked. 



COMPUTING THE CRITICAL PROFILE 



A key factor in computing the critical profile is the determination 

 of the wave steepness for use in the run-up calculations. If the storm 

 producing the waves is immediately offshore, the significant wave will have 

 a steepness of approximately 0.20 (see Reference 3, p. 50h) and this steep- 

 ness may be used in computing the run-up. If the storm producing the waves 

 is farther offshore, the steepness of the significant waves must be deter- 

 mined by using wave forecasting methods to determine the wave decay between 

 the generating fetch r.nd the structure site. When the steepness of the 

 significant wave at the structure site has been determined, it must be con- 

 verted into its HVT 2 value. Then, the vertical and horizontal scales of 

 the study area profiles must be plotted on transparent paper and the design 

 SWL established as on the vertical scale (see Figure 4). Smooth slopes 

 of 1/40, 1/30, 1/20, 1/10, and 1/5 are laid out through the intersection of 

 the design SWL with the vertical scale at point 0. 



The deep water wave height (H*) is determined for each slope by enter- 

 ing Figure 1 with the previously determined critical wave steepness and 

 picking off the appropriate value of R/H*. Since R is known, 3.6 feet, H' 

 can be computed. 



2 

 Example: H*/T = 0.20; R = 3.6 feet; slope = 1/30 



From Figure 1, R/H* = 0.175 and H f = 3.6/0.175 = 20.6 feet. 



When H' and the steepness are known, the breaking depth can be de- 

 termined from the solitary wave theory as given by Munk^ 5 ^ and rearranged 

 by Saville^ 1 ). 



d 



b r 2i 1/3 



1.5 [HVT J 



When d. has been computed, it is plotted in the proper place on the 

 1/30 slope (see Figure 4). In the same manner, H' and d fe can be determined 

 for the other slopes (extrapolating the curves of Figure 1 for the 1/40 

 slope) and d^ plotted for each slope. When these critical values of d. are 

 connected, the "critical profile" results. Critical profiles for a maximum 

 wave run-up of 3.6 feet and wave steepnesses of 0.20 and 0.10 are shown in 

 Figure 4. 



