Equation (124) is the key result of Battjes' (1978) paper and when in- 

 serted into equation (44) permitted H^ms* to be calculated across the surf 

 zone for sloped or bar-type beach profiles. The closure parameters are K 

 and Y, and it is important to point out that Y is only used as a breaking 

 criteria and not to estimate the wave height decay. The main interest is in 

 the resulting mean water surface changes calculated from the momentum balance 

 as discussed below. 



a. Wave Setdown and Setup . Figure 38 displays example theoretical mean 

 water surface profiles for two beach profiles using the theory of Collins 

 (1972). Less wave setdown is evident for the irregular waves than regular 

 (monochromatic) waves with the same energy content. The wave setup profile 

 is also highly nonlinear in the surf zone and maximum setup is less for 

 irregular waves. 



Similar results are shown in Figures 39 from Battjes (1974a) for a plane 

 beach. Note the horizontal axis is Stillwater depth, d, normalized by deep- 

 water wave height, H , and could be related to horizontal distance offshore. 

 Details of the solution method are omitted here but include shoaling and bot- 

 tom refraction effects. Numerical integration procedures are employed and 

 the results reduced to the regular wave setup as a check (eq. 35) for normal 

 wave incidence. Figure 39(a) shows how wave refraction reduces wave setup, 

 as expected and the mean water surface profile is almost linear near the 



1.6 



1.4 



1.2 



1.0 



.8 



.6 



.4 



.2 







-.2 



-4 





1 1 1 1 



1 1 1 



_ 



"\ 



A- 1/50 



Lo=500 ft. 

 <Ho>=20ft.^ 



- 



^^ 



N. y — Monochromatic 



a rSO" 





-w 



\/\ 1 — 1/25 





- 



- \ 







- 



- 



VVr \^^~~-^ 





- 



- 



1 1 1 1 



I 1 1 



- 



200 400 600 



DISTANCE OFFSHORE, ft. 



800 



Figure 38. Illustration of wave setup on offshore slopes of 1:25 

 and 1:50, broken lines Indicate results for periodic 

 waves having the same energy content (from Collins, 

 1972). 



137 



