39 



0.1 





X AiLollg'^ 





o A2ujllg^ 

 + A^u^llg^ 



1 1 1 1 1 







6 



10 



12 



Figure 3.5: Evolution of the solution for a shallow water wave 



pletely independently of the other windows. In this case, the parameters of the LFI 

 solution are: primary window width of 2s (tq = 0.27,), with a sixth order potential 

 function (J = 6), seven samples on the pressure record, and seven water surface nodes 

 (/ = A' = 7), resulting in 21 equations in 16 unknowns in each window. The window 

 width of two seconds is one fifth of the period of the wave, and is a reasonable length 

 of time to extend the locally steady approximation. 



Evolution of the Solution Fig. 3.5 shows the evolution of the solution as the 

 window is moved along the wave. The top figure shows the non-dimensional values of 

 the local fundamental wave number, k, and the local fundamental frequency, ui. The 

 importance of the local nature of the solution is apparent in this figure, as the solution 

 varies substantially from window to window. The wave number and frequency both 

 increase to maximum magnitude near the crest (4 < tu), < 7), and have lower values 

 in the trough region (near tu^ = 3 and tu^ = 9). This pattern suggests that the 

 kinematics in the crest region are similar to those of a much higher frequency lower 



