The four equations for P^, equations 4-31 to 4-34, and the four equations 

 for P^g, equations 4-35 to 4-38, are given in Tables 4-7 and 4-8, respectively, 

 in the SPM, and they are reproduced in Appendix A. 



Appendix A derives the eight equations and identifies the assumptions used. 

 These derivations involve only simple algebra and the assumptions are standard. 

 However, the exact formulation of the assumptions does affect the value of 

 coefficients in the equations. 



2. Wave Height (App. B) . 



The energy flux factor, Poo> depends sensitively on wave height. In one 

 equation, it is an H^ dependence; in another one, H^; and in two equat_ions, 

 h5/2_ xn all, the height enters P£g primarily as the energy density, E, 

 which depends on H^ . Since, in nature, height varies from one wave to the 

 next, the average energy density of a group of waves will not be determined 

 from the average height, but rather from a height which produces the average 

 value of H^ . This is the root -mean-square (rms) height, ^x-ms' 



The height commonly used in coastal engineering work is neither the average 

 height nor the Hy^g, but the significant height, Hg . Appendix B explains 

 the relations between Hp;7,g and Hg , and how the energy flux factor is cali- 

 brated for use with Hg . 



3. The Data (App. C] . 



To obtain an equation to predict Q from P^g , it is necessary to have 

 sufficient data for wave conditions to compute Pj^g and to measure values of 

 Q at the time the wave conditions are measured. Appendix C identifies the 

 sources of data which led to the relation between Q and P£g shown in Figure 

 4-37 and equation 4-40 of the SPM. 



III. WAVE SPEED AND BREAKER ANGLE 



This report primarily provides documentation for the energy fliox method as 

 given in Section 4.532 of the SPM. It does not critically evaluate the method. 

 However, this section does examine the effect of assumptions about wave speed 

 and breaker angle on the computed values of Q to enable the user to form a 

 judgment of the overall accuracy. 



The energy flux is proportional to group velocity. The group velocity for 

 linear waves in shallow water is equal to wave speed. For energy flux entering 

 the surf zone, the appropriate wave speed is the speed of the breaker. Breaker 

 characteristics have long been assumed to be described by solitary wave theory. 

 Solitary theory can be used to locate the breaker point using the rule-of-thumb 



d^ = 1.28 H^ (1) 



and to estimate the breaker speed using an equation of the form, 



c; = /w (2) 



