Rector (1954), and Swart (1977). Bruun (1954) proposed a power law to relate 

 water depth to distance offshore, which was given support by Dean (1977) on 

 theoretical grounds. The empirical shape parameter in this simple power 

 equation was related to grain size by Moore (1982). 



155. Characteristics of cross-shore sand transport were studied first 

 by Keulegan (1948) and King and Williams (1949) through trap measurements in 

 laboratory wave tanks. By integrating the mass conservation equation between 

 consecutive profiles in time, the net cross-shore transport rate distribution 

 can be obtained, as discussed by van Hijum (1975, 1977); Watanabe, Riho , and 

 Horikawa (1981); Kajima et al. (1983a, b); and Shimizu et al . (1985). 

 Classification of the cross-shore transport rate distributions has been 

 performed by Sawaragi and Deguchi (1981), Kajima et al . (1983a), and Shimizu 

 et al. (1985). 



157. Various formulas for predicting the cross -shore sand transport 

 rate have been expressed in terms of local fluid velocity (Bagnold 1963, 1966; 

 Bailard and Inman 1981); local shear stress (Madsen and Grant 1977, Shibayama 

 and Horikawa 1980a, Watanabe 1982); and local energy dissipation per unit 

 volume (Moore 1982, Kriebel 1982, Kriebel and Dean 1985a). A cross-shore 

 transport equation based on energy dissipation per unit volume under breaking 

 and broken waves was successfully applied in engineering numerical models for 

 predicting beach profile change (Moore 1982, Kriebel 1982, Kriebel and Dean 

 1985a). 



158. Several numerical models for predicting beach profile change have 

 been developed, although few have been used for engineering predictions. Many 

 of the earlier models included mechanisms for bar generation that did not 

 explicitly assume breaking waves as the primary factor (Felder 1978, Nilsson 

 1979). Numerical models of profile change based on breaking waves as the 

 cause of bar formation were developed by Dally (1980), Dally and Dean (1984), 

 Moore (1982), Kriebel (1982), and Kriebel and Dean (1985a). At present, the 

 most successful and widely used numerical model is that developed by Kriebel 

 (1982) and Kriebel and Dean (1985a), and it has been applied to a number of 

 sites along the U.S. coast (Kriebel and Dean 1985b, Kraus et al . 1988). 

 However, this model does not incorporate bar formation and movement, nor does 

 it simulate beach accretion. 



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