Relative n <=; 

 Depth ^'^ 



(Linear Wave Theory) 



Depth Averaged) 



Linear Wave Theory 

 Quasi, 2-D Theory 



0.2 0.4 0.6 0.8 1.0 L2 L4 

 Depth Factor 



Figure 44. Comparison of horizontal and vertical maximum 

 velocity profiles between quasi, 2-D, and 

 linear wave theories for d/L = 0.22. 



The practical limitations for engineering purposes of the Boussinesq 

 theory are still open to question and require further research. This is 

 because for variable bathymetry, the precise form of the continuum equations 

 involved is not known. In addition, accuracy errors in the numerical solu- 

 tion procedures produce additional numerical amplitude and frequency disper- 

 sion effects. Numerical integration procedures are very important in use 

 of the Boussinesq theory. 



2. Numerical Solution . 



The finite-difference method has been the only numerical integration 

 method employed to date to solve the Boussinesq equations. Early ntmierical 

 efforts to study one-dimensional wave shoaling and transformations over 



152 



