O.OA 



006 h/L 



05 



01 h/L, 



b I Breaking 

 mm 



Figure 52, 



Comparison of cnoidal theory of wave setdown with experiments 

 for regular waves (after Svendsen and Hansen, 1976). 



job but also gives incorrect values (too small) near breaking. These 

 results are from the theory given in equation (116). This poor fit near 

 breaking is greatly improved by modifying the approximation employed 

 (l-n/d) in the bottom velocity u^^ as given by equation (115). The result, 

 consistent with all other cnoidal approximations, is 



2g 



|i-0.35)i -1.9'^' 



(155) 



where both c and n are determined from second-order cnoidal wave theory. 

 Equation (155) (shown as eq. 14 in Fig. 52) gives excellent results right 

 up to the breaker limit. 



Finally, the work of Jonsson and Buhelt (1978) on maximum wave setup 

 has been included here since the motion just outside the breaker line is 

 calculated as a series of solitary waves. Figure 53 compares the results 

 of equation (118) with some experimental results. Maximum setup does indeed 

 vary with deepwater wave steepness to the one-third power. Also, y (calcu- 

 lated values shown as constant across the surf zone and values in parentheses 

 with setdown neglected) increases with beach slope as expected from Battjes' 

 (1974a) analysis (see Table 5). Unfortunately, due to other assumptions 

 involved. Figure 53 cannot alone justify whether y is a constant in the surf 

 zone. 



164 



