92 



Fig. 5.4 is a steady deep water wave generated by 10th order Fourier theory with 

 the following parameters: wave height = 10 m, period = 10 seconds, water depth = 

 100 m, zero Eulerian current, and direction of travel 10 degrees from the x-axis. This 

 is a fairly large wave in deep water. The window width is 1 sec, 1/10 the zero crossing 

 period, and the LFI solution is computed to third order (j = 3). The LFI method has 

 captured the location of the water surface and the kinematics at the surface essentially 

 exactly. While linear wave theory might do an adequate job of approximating much 

 of the kinematics of a deep water steady wave like this, it is important to remember 

 that each of the points in Fig. 5.4 was computed from a small segment of the record 

 surrounding that point. In this case, the window width is 1/10 of the zero crossing 

 period, or Is. The local nature of this method extends its applicability to irregular 

 wave records. 



Fig. 5.5 is a steady shallow wave generated by 18th order Fourier theory with the 

 following parameters: wave height = 3 m, period = 10 seconds, water depth = 5 

 m, zero Eulerian current, and direction of travel 10 degrees from the x-axis. This is 

 a fairly extreme wave in shallow water. The window width is 1 sec, 1/10 the zero 

 crossing period, and the LFI solution is computed to third order. As with the deep 

 water wave, the LFI method has captured the location of the water surface and the 

 kinematics at the surface essentially exactly, including the pronounced sharp crest. 



Choice of Order 



In order to determine the order necessary to accurately capture the kinematics 

 of measured waves, it is particularly useful to examine a window near the crest of a 

 wave. The crest is usually the region that requires the highest order solution. This is 

 particularly true for shallow water waves, but higher order wave theory in all depths 

 of water indicates that, as the wave height increases, the crest tends to get sharper, 

 and the trough flatter. Capturing this sharp crest requires a high order solution. 



Deep Water A window near a crest of the deep water steady wave given in Fig 5.4 

 has been computed at orders 1 through 4. The results in that window are given in 

 Fig. 5.6 through 5.13. Figures 5.6, 5.8, 5.10, 5.12 are the non-dimensional errors in 



