399. Wave setup and setdown are incorporated in calculation of the wave 

 height distribution and determined by solving the following differential 

 equation together with Equation 26 (Longuet-Higgins and Stewart 1963) 



dS^^ dr, 



= -pg(h + r?) — (30) 



dx dx 



where 



Sjjx = radiation stress component directed onshore 

 r; = wave setup 

 400. The radiation stress is, using shallow-water approximations, 



S,, = 4g- pgH^ (31) 



Setdown in the first calculation cell is determined from the analytical 

 solution to Equation 30 seaward of the break point, assuming no energy losses, 



n = ^",, ,^, (32) 



4L sinh 



m 



By calculating the wave height distribution across shore at every time-step in 

 the model, a quasi -stationary approach is implied in which it is assumed that 

 the input wave height changes at a time scale significantly longer than the 

 wave period. 



401. Energy dissipation by bottom friction is calculated in the model 

 as done by Dally (1980) using linear wave theory to determine the horizontal 

 component of the wave orbital velocity at the bottom and assuming a shear 

 stress proportional to the horizontal velocity component squared. After the 

 waves break, energy dissipation greatly increases due to the generation of 

 turbulence. In the surf zone, energy dissipation produced by breaking is 

 considerably larger than dissipation due to bottom friction. 



165 



