A number of performance envelope tests were conducted on the numerical 

 scheme to determine the extent to which it came close to the continuum 

 limitation shown in Figure 44. These were all for nonbreaking waves and 

 included the following one- and two-dimensional tests: 



(1) One-dimensional : 



(a) Finite-amplitude, periodic wave propagation on a horizontal 

 bottom; 



(b) Full and partial wave reflections (transmission); 



(c) Wave shoaling on plane beach. 



(2) Two-dimensional : 



(a) Wave diffraction, and 



(b) Comparison with physical model results of harbor resonance. 



An example perspective view of two-dimensional short wave propagation on 

 the computer is shown in Figure 45. A comparison of the numerical results 

 with physical experiments and other theories is presented in Chapter 4. 

 For practical applications, 1-second time steps and 10-meter space steps 

 are estimated to give reasonable results for engineering purposes. 



I 



Figure 45. Numerical propagation of quasi- long waves in two dimensions using | 

 Boussinesq equations (from Abbott, 1979 ). ] 



154 



