In one case the spectrum has a single dominant peak; in the other case 

 the spectrum has a large peak at one-half the dominant frequency and 

 another major peak at about 1.5 times the dominant frequency. 



A laboratory parallel of this behavior has been observed by Sawaragi 

 and Iwata (1976). A single-peaked spectrum was generated in shallow 

 water of uniform depth. As the waves propagated and broke, an increas- 

 ing fraction of the energy shifted to frequencies which are multiples of 

 the dominant frequency, fp. Eventually, the spectral peak at 2fp was 

 higher than the peak at fp. 



The individual spectral points used in computing mean spectra are 

 plotted for Lake Worth in Appendix B. The distribution of the spectral 

 points about the mean for each band is decidedly unsymmetric in most 

 cases. The distribution usually has a high positive skewness indicating 

 some relatively high values above the mean in the distribution which are 

 not offset by correspondingly low values below the mean. However, the 

 distribution of spectral points about the mean for the band of maximum 

 energy density tends to be more symmetric and more nearly Gaussian. 



Third and fourth moments of the normalized distribution of spectral 

 points in selected bands were computed for all locations considered in 

 this report. The moments are defined analogous to the moments of the 

 distribution function of sea-surface elevations (eq. 6). For all loca- 

 tions, both the third and fourth moments are generally lowest in the 

 vicinity of the spectral peak indicating a relatively symmetric and 

 broad distribution about the mean. 



Typical variations of the third and fourth moments of the normalized 

 distribution of spectral points as a function of frequency are shown in 

 Figures 14 and 15 for mean spectra with peak periods between 7.2 and 7.8 

 seconds at Nags Head. The third and fourth moments in the band of peak 

 energy density actually fall below the values for a normalized Gaussian 

 distribution. Deviations from the normalized Gaussian distribution over 

 all frequency bands are generally less for high-energy spectra than low- 

 energy spectra. It may be concluded that the normalized Gaussian dis- 

 tribution gives a reasonable representation of the scatter of individual 

 spectral energy densities about the peak of each mean spectrum in Appen- 

 dix B, but it is not reliable for representing scatter about lower energy 

 bands away from the peak. 



Seasonal variations in the mean spectrum for each height-period in- 

 terval were studied for Nags Head. Four 3-month seasons were selected 

 using the seasonal summaries in Thompson (1977) as a guide. Mean spectra 

 were con5)uted for winter (December, January, and February) and for summer 

 (June, July, and August). Seasonal differences in the mean spectra did 

 not appear to be significant. The number of cases per height-period 

 interval was considerably reduced when the spectra were grouped by sea- 

 son. Hence, extensive seasonal summarization was not considered in this 

 study. 



36 



