troughs, it represents a best fit description of a profile passing through 

 such features. 



Figure 7. Definition sketch for the equilibrium beach profile 

 (after Kriebel 1982) 



30. Dean (1977) gave a plausible derivation leading to Equation 1. He 

 showed that if energy dissipation per unit volume of water in the surf zone 

 were assumed to be the dominant factor controlling profile shape, the two- 

 third power law would result. In addition, the general functional dependence 

 of the shape factor A on the dissipation could be predicted. Dean (1977), 

 Hughes (1978), and Moore (1982) have demonstrated that A depends in a 

 rational way on the grain size or fall velocity of the beach material. A 

 grain size of 0.25 mm corresponds to a value of A of approximately 0.13 

 m l/3 (Moore 1982). For larger grain sizes, A increases producing a steeper 

 profile, as observed in nature. Figure 8 shows the dependency of A on the 

 grain size according to Moore (1982). 



31. In the derivation of Dean (1977), the required energy dissipation 

 is calculated from an assumed linear and constant wave height decay with 

 depth, using small amplitude wave theory. This procedure automatically 

 restricts applicability of the method to a surf zone with spilling breakers 

 for which the breaker height and water depth are linearly related. However, 

 if a smoothing mechanism is posited which slowly shifts sand along the 

 profile, it can be assumed that the equilibrium profile will extend to at 

 least the depth corresponding to the depth of the greatest breaking waves 

 during storms. The smoothing mechanism might simply be the back-and-f orth 

 sand movement associated with the wave orbital velocities. 



16 



