27. On an idealized 2-D profile, waves provide the mechanism for 

 cross-shore movement of sand, with movement either onshore or offshore 

 depending on wave steepness. If constant wave and water level conditions 

 continue for an extended period of time, an equilibrium shape will be 

 approached. The development of this equilibrium profile has been demon- 

 strated with physical model tests using monochromatic waves (e.g., Saville 

 1957, Swart 1974, and Chesnutt 1978). In general, laboratory experiments 

 have used constant water depths and an initial plane beach profile. Measured 

 changes are greatest at the start of the test, gradually decreasing with 

 time. Since true equilibrium is difficult to obtain in the laboratory, it is 

 generally believed to be seldom reached in nature. 



28. Profile changes resulting from changes in wave characteristics may 

 be thought of as perturbations on a smoother, more idealized profile shape 

 that more or less retains a constant form in equilibrium with the mean water 

 level, mean waves, and beach grain size. As the water level changes, this 

 equilibrium profile shifts accordingly, moving inland and upward with 

 increasing water level. The shape of the profile is maintained by erosion of 

 the beach and deposition offshore. Profiles are more likely to be in 

 equilibrium with long-term effects such as sea level rise but not with short- 

 duration storm surges. 



29. In an empirical study of beaches on the north Danish coast and in 

 California, Bruun (1954) found that the representative, gradually deepening 

 beach profile was well described by a simple equation of the form 



h(x) = Ax 2 / 3 (1) 



where 



h = depth 



x = distance from the shoreline 



A = dimensional factor having units of length to the one third power 



A definition sketch is given in Figure 7. Dean (1977) found the same 

 relationship empirically for 502 profiles along the Atlantic Ocean coast of 

 the United States. Subsequent work (e.g., Hughes 1978, and Moore 1982) has 

 verified the basic validity of Equation 1 for beach profiles in various parts 

 of the world and for profiles generated in laboratory flumes and basins with 

 sand bottoms. Although the two-third power law does not exhibit bars and 



15 



