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record halved. A portion of the resulting y-axis curvature term in 

 the time domain is shown in Figure VI-16. The time series was 

 processed by the FFT and the energy spectra developed. Figure VI-17 

 illustrates the energy spectrum of the curvature term compared to 

 that of the displacement term. The wave frequencies corresponding to 

 peak energy levels of the data set correspond well between the 

 spectra. The curvature spectrum contains greater energy in the high 

 frequency bands than the displacement spectrum. This is expected 

 since the curvature spectrum differs from the displacement spectrum 

 by a factor of the fourth power of the wavenumber. 



Despite the reasonable appearance of the curvature spectra, 

 the directional Fourier coefficient b3 , developed using the water 

 surface curvature along the y-axis, was at least an order of 

 magnitude larger than the other directional coefficients for each 

 case tested. The dominance of this term would create three high 

 energy peaks in the dirctional spectra and invalidate directional 

 estimates. 



The curvature terms were also developed in the time domain 

 before adjacent values in the record were averaged. The results were 

 similar. 



The inability to generate higher order directional Fourier 

 coefficients through the arithmetic creation of the water surface 

 curvature terms is not surprising. The DPG was developed upon the 



