K 



02 



O Ion /9 ■ 082 s 

 + Ion /3 ■ 072 

 • ton /3 • 054 



08 _ 10 



Figure 47, 



Ratio of wave setup slope to beach slope (K) versus y (after 

 Bowen, Inman, and Simmons, 1968). 



is shown in Figure 48 (after Gourlay, 1978) with the equation 



dn 



dx 



=3.4 tan^ 



(154) 



given as line of best fit to the data. The vertical error bar lines 

 indicate possible variatiofi due to wave periods of the experiments. Results 

 of all experimenters, including that by Gourlay (1978) are also shown. 



Van Dorn (1976) concluded that on relatively steep beach slopes 

 (tan 3 ~ 0.1), with some reflection present, setup slope increased with wave 

 period. Conversely, for tan 3 <^ 0.04 the setup was independent of wave 

 frequency (within experimental error). The reason offered by van Dorn 

 (1976) for this difference is the assumed constant breaker ratio y ii^ the 

 theory. Data are presented to approximately confirm this assiunption on the 

 0.083 slope, but the flatter slopes show a nonlinear variation with abrupt 

 wave height decay near the breaker point and little frequency correlation. 

 Thus, Bowen, Inman, and Simmons (1968) may have reached different conclusions 

 if flatter beach slopes had been tested. 



Gourlay (1978) based on his own data and a thorough reanalysis of Bowen, 

 Inman, and Simmons (1968) and Smith (1974) also concluded that experimental 

 data do not show very good agreement with equation (35) as shown in Figure 

 49. All data here are for relatively steep beaches (tan B > 0.083) and a 

 wide range of wave periods. 



159 



