35 



At the limit near the zero crossing, a and u; have the same effect, and the optimization 

 routine can not distinguish them. Widening the window to include more of the 

 surrounding record avoids this difficulty, and is generally successful in this situation 

 as well as in long, flat troughs. 



Another complication can be a record that is exactly symmetric about the crest 

 of a wave. In this case, the equations on either side of the crest are not independent. 

 This situation is unlikely to arise in a field record, and can easily be accommodated 

 by using an asymmetric distribution of points in that window. 



3.4 Theoretical Records 



To avoid complications from measurement error in the initial testing of the method, 

 pressure records generated by Fourier Steady wave theory (Sobey 1989) were used. 

 This approach also has the advantage of providing a solution with the complete kine- 

 matics, to compare with results from the LFI method. Field or laboratory data that 

 includes a full set of measured kinematics are not available. Fourier theory provides 

 a near-exact solution for irrotational steady waves and can be applied at any depth 

 (Rienecker and Fenton 1981; Sobey 1989). The use of analytically generated records 

 also allows the method to be tested under a large range of conditions, by varying 

 water depth, wave period, and wave height. This is useful for establishing criteria for 

 choosing the solution parameters, such as window width, number of nodes in each 

 window, and order of the solution. 



Shallow Water To demonstrate the optimization procedure in a window, figure 3.2 

 summarizes the results from an initial estimate, before the final optimization. This 

 is a window near the crest of a steep, shallow water wave generated by 18th order 

 Fourier theory. The parameters of the wave are: 5m water depth, 3m wave height, 10s 

 period, and zero Eulerian current, with the pressure record measured at the bottom. 

 The parameters of the LFI solution are: sixth order ( J = 6), and window width two 

 seconds (tq = 0.2Tj) , centered 0.5s before the crest. 



The top plot shows the measured dynamic pressure as given by the Fourier theory 



