of reflection was to alter the breaking wave process somewhat since there is 

 no evident feature in the surf zone profile attributable to reflected waves. 



Equilibrium bar volume 



239. As a bar moves offshore, it increases in volume to approach an 

 equilibrium size. Figure 15 shows bar volume for the main breakpoint bar as a 

 function of time for the CE and CRIEPI experiments, respectively. Some of the 

 cases were not run sufficiently long to attain the equilibrium volume. The 

 approach to equilibrium is typically smooth. If a breakpoint bar formed on a 

 profile where onshore transport (accretion) dominated, equilibrium volume was 

 reached rapidly and was relatively small. Examples are Cases 101, 301, and 

 801 from the CE data, and Case 2-3 from the CRIEPI data. Bar volume changed 

 abruptly if the smaller seaward breakpoint bar merged with the main breakpoint 

 bar. Often, further growth of the main breakpoint bar was hindered by this 

 coalescence of bars, as shown in Case 300 (occurs at 15.0 hr) . Profiles 

 having only one bar showed a more regular development in time toward an 

 apparent equilibrium volume. 



240. Since equilibrium bar volume was not entirely reached in some 

 cases, and in order to obtain an objective method for determining equilibrium 

 bar volume, a simple expression of exponential type was least-square fitted to 

 the data for each case. The chosen expression is often encountered in growth 

 problems where an equilibrium state exists. The same expression was used by 

 Kriebel and Dean (1985a) to characterize dune erosion. The bar volume V is 

 assumed to grow toward the equilibrium volume V according to 



V = V,„ (1 - e-**^) (7) 



where t is time, and a is an empirical temporal rate coefficient. 

 Correlation analysis (25 cases evaluated) involving pertinent wave and beach 

 profile parameters showed that equilibrium bar volume was most closely related 

 to deepwater wave height, sand fall speed (or grain size), and initial beach 

 slope, although the correlation coefficients (see Appendix A) were not high 

 (0.6-0.7). A larger wave height implied a larger bar volume, a greater fall 

 speed (or larger grain size) implied a smaller bar volume, and an initially 

 steeper slope also produced a larger bar volume for a given grain size. Fall 



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