Energy lost from the wave train c^ie to bottom friction is treated by means 

 of a single dissipation calculation at the geometric mean depth for the region 

 of interest 



dm = V^TdJ (6) 



Average energy dissipation rate at dm, per unit crest width and per unit 

 length in the propagation direction, is given by 



Em = 0.235 p fem (2Tr Ctn/T) ^ (7) 



For rough turbulent flow over a strongly agitated bed of quartz sand, the energy 

 dissipation coefficient introduced in equation (7) is 



fern = exp [-5.882 + 14.57 (Dm/Cm) °' ^^'*] (8) 



Here Dm is median sand grain diameter at dm and ^m is horizontal ampli- 

 tude of the near-bed fluid excursion arising at dm without energy dissipation, 

 so that (2TrCm/T) in equation (7) is peak near-bed fluid velocity. According 

 to linear wave theory, 



^ = C9) 



"^ 2 sinh (2Trdm/Lm) 



where Hm = (H^ Kg^jj/Kgj) from equation (5). 



Energy-conserving linear wave shoaling is combined with computed energy 

 dissipation rate into an expression giving a wave height at dj equivalent to 

 measured wave height at d^. This expression is a revised form of equation 

 (2): 



8(Pi ± E^X) 



H? = 1 :^— (10) 



J± P g c . n. 



where X is the wave propagation distance between the two water depths (dj 

 and dj), and the upper [lower] sign is used when dj is greater [less] than 

 dj. The conversion given in equation (10) presumes that computed dissipation 

 rate at dm can be considered representative of the entire propagation path. 



III. APPLICATIONS 



Besides the explicitly ignored factors affecting nearshore wave transfor- 

 mations, it is important in applications to consider the requirements stated 

 above on the use of equation (8) for energy dissipation coefficient. The 

 quartz sand bed must be strongly agitated by wave action and near-bed flow 

 must be rough turbulent. Appropriate situations correspond to nearshore field 

 waves with relatively large height and period. 



The strength of bed agitation may be judged using an approximate expression 

 (Hallermeier, 1981, eq. 10) giving maximum water depth, da, for wave agitation 



