ture , and other conditions cannot be held perfectly fixed. Also, wave 

 breaking and turbulence formed at the bottom and injected from the surface by 

 wave breaking introduce randomness in the microscale sand motion, with 

 resultant small continuous adjustments of the profile. Nevertheless, at a 

 macroscale level, it has been demonstrated that an equilibrium profile can be 

 approached, in which no significant systematic net sand transport occurs, 

 although small perturbations still remain. Numerous laboratory studies (e.g.. 

 Rector 1954, Nayak 1970, Swart 1975) as well as the data used in this study 

 support the equilibrium beach profile concept, since profile changes diminish 

 with time and the beach profile approaches a stable shape. 



196. From a theoretical viewpoint, it is of minor importance if the 

 equilibrium profile is never realized in the field due to variable waves and 

 water level, and complex three-dimensional hydrodynamic processes, as long as 

 the concept is verified by experiment. Of course, from a practical point of 

 view, it is of great significance if a natural beach of a certain representa- 

 tive grain size has a preferred shape under a given wave climate. 



197. As an indicator of the approach of the beach to an equilibrium 

 shape, cumulative change along the profile was calculated. Cumulative change 

 was defined as the sum of the absolute differences in bottom elevation between 

 initial profile and profile at a specific time (see also Shimizu et al . 1985). 

 This quantity is plotted in Figure 5 for selected CE and CRIEPI cases. 



198. The cumulative profile change will ideally approach a constant 

 value under constant applied waves as the beach profile attains the equilibri- 

 um shape. The decrease in slope of the curves in Figure 5 is a measure of the 

 rate at which equilibrium is approached. Some transport activity will always 

 exist because of unsteadiness in experiment conditions, fluid turbulence, and 

 random character of sand motion, and thus profile change will fluctuate about 

 the equilibrium shape. Some cases exhibited cumulative change which had not 

 completely leveled off at the end of the run, but the rate of change was still 

 an order of magnitude smaller than the initial rate. Decreasing rates of 

 accumulated profile change indicate an increasingly stable shape since less 

 material was redistributed along the profile at later times. 



199. A greater difference between initial profile and equilibrium 

 profile for a specific wave climate and grain size implies that a greater 



60 



