where h* is a depth. If h* is set equal to the mean depth, then the breaker 

 speed is that of linear theory 



or using equation (1) 



= 6.42 AC (feet per second) (3) 



If h* is set equal to the depth under the crest of the breaking wave, and 

 the depth is properly corrected for the depression of the trough below mean 

 water level, the result is 



Cj, = 8.02 v4i^ (feet per second) (4) 



If h* is set equal to Hj^ + d-^ without correcting for depression of trough 

 below mean water level, the speed will be 



C^ = 8.57 Ai^ (feet per second) (5) 



Since wave speed enters as a linear multiplier in the equation for energy 

 flux, the estimated energy flux will vary directly as the estimated wave speed. 

 The field data plotted on Figure 4-37, from which the relation between Q and 

 Pj^g is obtained, include estimates of Pj^g using equations (3) and (5). The 

 nine data points from Watts (1953) and Caldwell (1956) have energy flux values 

 computed with equation (3) . The 14 data points from Komar (1969) include 

 energy flux estimates based on both equations (3) and (5) . Equation (4) is 

 used in the derivations for all P„ equations, as shown in Appendix A. 



Since the Pj^.q equations used in the SPM depend on equation (4) for wave 

 speed, it is evident that wave speed has not been treated consistently through- 

 out the analysis. The P^g computed with the equations in the SPM (depending 

 on eq. 4 for wave speed) will be 25 percent too high for the plotted relation 

 between Q and P^^g for the points of Watts (1953) and Caldwell (1956) on 

 Figure 4-37. 



The error between the SPM P ^^ equations and the 14 data points of Komar 

 (1969) is more difficult to evaluate. The depth used by Komar is the 20-minute 

 time average at the wave gage (P.D. Komar, Oregon State University, personal 

 communication, 1978) . This depth was often significantly deeper than the 

 breaker depth, as can be judged from the fact that the average crest angle at 

 the wave gage was about 5 7 percent greater than the average breaker angle in 

 Komar's data (App . IV of Komar, 1969). Thus, the use of the depth at the gage 

 raises the speed above the linear theory estimate of equation (3) toward the 

 value of equation (4). Since it is not easy to evaluate this effect, and since 

 the relation between P^g and Q is heavily dependent on the 14 plotted points 

 of Komar, the error due to using equation (4) for breaker speed in calculating 

 P^g is concluded to be less than 25 percent and may be negligible. 



Moreover, the Komar (1969) data for energy flux probably include an over- 

 estimate of the breaker angle. This is because breaker angle, a, , was 

 computed from the angle at the sensor, a, by 



^b . 

 sm ai) = — sm a 



I I 



