where 



qj. = transport rate at wave reformation point 



u = spatial decay coefficient 



Xj. = location of wave reformation point 



x„ = location of minimum transport rate 



qjj = transport rate at second break point 



q^ = minimum transport rate in wave reformation zone 



(determined from Equation 47) 

 Xj3 = location of break point 

 n = exponent determining spatial decay in transport rate 



477. To investigate the possibility of modeling wave reformation and 

 multiple bar formation, one of the CE cases was used for which measurements of 

 a second break point were made (Case 500). Since the wave height in the surf 

 zone approaches the stable wave height F asymptotically as the waves 

 progress onshore (Horikawa and Kuo 1967, Dally 1980), wave reformation will 

 not occur in the model for a beach with monotonically decreasing depth in a 

 surf zone that is exposed to constant wave conditions and water level. As a 

 bar grows in size, the trough becomes more pronounced, but the slope -dependent 

 term in the transport equation (Equation 33) will not allow the trough to 

 become sufficiently deep to initiate wave reformation. 



478. One method of forcing waves to reform in the model is by turning 

 off breaking at a predetermined level somewhat higher than the value of the 

 stable wave height coefficient (see Dolan 1983, Dolan and Dean 1984). A 

 physical argument for a higher value is that an asymptotic decay toward the 

 stable wave height is unrealistic in nature, and wave reformation is initiated 

 through a delicate balance between competing processes close to stable 

 conditions. Consequently, by forcing wave reformation to occur, the phenome- 

 non is included in the model, although the details of the process are simpli- 

 fied. 



479. In this particular simulation, a stable wave height coefficient of 

 r = 0.4 was used in all simulations, whereas breaking was turned off at a 

 value of r = 0.5 to initiate wave reformation. A typical simulation result is 

 displayed in Figure 76. Simulated beach profiles at consecutive times are 



201 



