where the index i refers to the cell number counting consecutively from the 

 starting point of the avalanching in the direction of avalanching. The number 

 of cells N that the avalanching will affect is not known a priori and has to 

 be determined iteratively as more cells are incorporated in the calculation 

 until the slope between cells N and N+1 is less than the residual angle 

 after shearing. The avalanching routine limits the growth of the step and 

 prevents the shoreward slope of a bar from becoming too steep. 



Profile Change Model 



422. Changes in the beach profile are calculated at each time-step from 

 the distribution of the cross -shore transport rate and the equation of mass 

 conservation of sand. The equation of mass conservation is written as 



aq ah 



— : (40) 



dx dt 



423. Standard boundary conditions in the model are no sand transport 

 shoreward of the runup limit and seaward of the depth where significant sand 

 movement occurs. The runup height is determined from an empirical expression, 

 Equation 17, derived from the LWT experiment data relating the height of the 

 active profile to the surf similarity parameter and the deepwater wave height. 

 The depth of significant sand movement is determined through the exponential 

 decay of the transport rate with distance seaward from the break point. If 

 the transport rate decreases to a small predetermined value , the calculation 

 stops, and the transport rate is set to zero at the next cell, making that 

 cell the seaward boundary. An expression presented by Hallermeier (1984) for 

 the seaward limit depth was investigated for use in the model. However, this 

 equation failed to predict what were considered to be reasonable closure 

 depths on a wave -by-wave basis, evidently because the formula was developed 

 for extreme annual events. Also, apparently because of the limited range of 

 values from which the equation was derived, the closure depth was found to be 

 too shallow for profiles exposed to the very steep waves that were used in 

 some of the LWT cases . 



173 



