122 



ing surface. The local nature of the approach allows a nonlinear solution without 

 prohibitive computational costs, using a fairly simple form for the potential function, 

 and allowing the parameters of the potential function to change with time. 



The examples in this Chapter were all computed using Matlab running under 

 the Linux operating system on an Intel 90MHz Pentium processor based PC. The 

 shallow water steady wave (Fig 5.5) took the longest to compute, about 30min, and 

 85x10^ floating point operations (flops). The steady deep water wave (Fig. 5.4) took 

 the least time, lOmin. and 15x10^ flops, the standing wave (Fig. 5.24) took 20min. 

 and 244x10^ flops, the short crested wave (Fig. 5.27) took Umin. and 93x10^ flops, 

 and the laboratory record (Fig. 5.38) took 21min. and 83x10^ flops. 



The examples given in this chapter provide guidance as to the parameters of a 

 solution to be applied to field records. Far from reflecting surfaces, using a potential 

 function representing a single wave is effective. Near a reflecting surface, a potential 

 function representing two nonlinear intersecting waves is capable of capturing the 

 standing or short crested waves that are likely to develop. 



Window widths of 1/10 of the zero crossing period are small enough to maintain 

 the local nature of the solution, and capture the detail of the record, while being 

 large enough to include the local trend of the wave field. On certain segments of the 

 record, the window width must be increased in order to include sufficient curvature 

 in the record to find a solution. The widening of the window is most often needed 

 in long, flat troughs in shallow water, or near zero crossings of the record. In either 

 case, the window rarely needs to be larger than 1/5 of the zero crossing period. 



Low order solutions are quite adequate for deep water waves. For most waves, 

 second order is adequate. For the very steepest waves, slightly higher order may be 

 appropriate, and there is little computational penalty in including the higher order 

 terms. In shallow water, higher order solutions are necessary. Third order is adequate 

 in many cases, but including up to fifth order is recommended for extreme waves. 

 When attempting a high order solution such as this with the two wave method, it 

 may be necessary to use arrays with more than three gauges in order to provide 

 sufficient equations to specify the solution. 



