PART VII: MODAL ANALYSIS 



201. The results of the last section were based on bulk properties of 

 frequency- direction spectra. While meaningful, they do not give much informa- 

 tion about the more detailed structure of the spectra. Knowledge of spectral 

 structure is necessary for understanding physical processes associated with 

 wind waves and for incorporating observations into physical and numerical 

 models of those processes, including wave generation, refraction, shoaling, 

 transformation, and nonlinear interactions. An important property of wave 

 directionality is the extent to which there is more than one peak, or mode, in 

 directional distributions of wave energy. Multimodal distributions can arise 

 from any of the processes mentioned, and all of the processes can be active at 

 the present experiment site. In this section, a simple evaluation of the 

 number and relative strengths of modes is conducted as an indication of the 

 necessity for further study. 



202. This type of analysis is different from the bulk analysis of the 

 last section because characteristics at one frequency are considered indepen- 

 dent of characteristics at other frequencies. Any coherence in spectral shape 

 from frequency to frequency is therefore lost. The bulk parameters treated 

 each spectrum as a unit and inherently included shape effects, though in a 

 smoothed, integral fashion. The advantage of frequency-by- frequency analysis 

 is that structural similarities and differences between distributions at 

 different frequencies can be isolated. In this way, it may be possible to 

 define a set of basic modal shapes from which a spectrum or a set of spectra 

 can be constructed. 



203. A simple initial approach is to examine slices through the 

 frequency- direction spectrum along lines of constant frequency and to evaluate 

 the number, strengths, and shapes of the resulting directional modal struc- 

 ture. The simplest result that could be expected from this is that distribu- 

 tions at all frequencies and for all spectra are unimodal, consisting of one 

 primary maximum of energy. However, it can be seen in the high-frequency part 

 of Figure 7 and in the sample distribution of Figure 9 that at least some of 

 the distributions are multimodal. Hence, it is necessary to count them. 



204. Part of the frequency -by -frequency parameter set defined in Part V 

 is the number K of modes found for each frequency in a frequency-direction 

 spectrum. It should be remembered that the mode separation definition used 



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