as determined by Abbott, et al. (1978), is presented in Figure 43. In 

 shallow water, the wave celerity approaches the group velocity or speed of 

 energy propagation. Hence celerity is a good indicator of usefulness of 

 the theory. An error of 2 percent is indicated for a wide range at the 

 breaking limit. 



The expected application limit shown is for d/L =0.2 (d/Lp = 0.17). 

 This is in the intermediate wave theory range and near the engineer's limit 

 of d/Lo =0.25 for deepwater waves. Even near this limit, the assumption 

 of a uniform velocity profile is still reasonable as shown in Figure 44, 

 The Ujjj^^ profile based on classical linear wave theory for d/L = 0.22 is 

 shown for comparison. The vertical Wj^^^^ profile is very close to a linear 

 variation with depth. The exponential decay of the horizontal velocity com- 

 ponent is roughly analogous, in some respects, to the fully developed log- 

 arithmic boundary layer profile of open channel flows which are routinely 

 modeled as depth-averaged flow. 



Figure 43. Range of . application of the mass and Boussinesq equation system, 

 (from Abbott, et al, 1978). 



151 



