Operationally, the spilling wave assumption means that the wave height of 

 breaking and broken waves is proportional to the local water depth, using a 

 fixed constant of proportionality. With the x-axis directed offshore as 

 shown in Figure 7, offshore transport has a positive sign, and onshore 

 transport has a negative sign. After manipulations, the dissipation D is 

 ultimately expressed in the form 



* (v.1/2 M < n > 



D = const I h 1 '^ q- 1 



in which const is the product of known constant factors. The empirical 

 coefficient k was found to have the value 2.2 x 10~ 6 m 4 /N (Moore 1982) 

 based on the results of profile change found in the large-scale flume 

 experiments of Saville (1957).* From Equations 10 and 11, it is seen that 

 if the depth is greater than the equilibrium depth at a given location, sand 

 will move offshore, i.e., erosion is associated with the higher water levels 

 which would occur during a storm. 



78. It is noted that wave height and wave period do not explicitly 

 enter in the transport rate equation. The water level (the depth h) is seen 

 to be the main external force determining the cross-shore transport rate. 



The wave height is indirectly included in the transport equation since it is 

 used to determine the location of the breaker depth or width of the surf zone 

 over which the model acts. 



79. Beach profile change is put into time-dependent form by inserting 

 the transport rate predictive formula, Equation 10, into the beach material 

 (sand) continuity equation expressed in the form 



I - - d i° « 2 > 



in which t is time. Equation 12 can be numerically solved if the surge 

 hydrograph, initial profile, and offshore wave height and period are given. 

 The hydrograph describes the water level as a function of time and must be 

 either predicted by another numerical model or be specified from measure- 

 ments . 



c Kriebel (1986) recalibrated his revised model using data from 

 Saville (1957) and determined that k should equal 8.7 x 10" 6 m 4 /N. 



40 



