258. Examination of peak directions and directional spreads of spectra 

 at the frequency-by- frequency level gives results which tend to verify the 

 characteristic properties found in the bulk parameter analysis. High- 

 frequency waves tend to arrive from a broad range of directions, and low- 

 frequency waves tend to be aligned with the shore-normal direction. Direc- 

 tional spreads at the frequency level tend to have a broader range than that 

 found for bulk spread parameter (20 to 60 deg) . Spreads as small as 10 deg 

 and as large as 90 deg are not uncommon. However, peaks in the spread 

 distributions are more tightly constrained. Low- frequency waves have spreads 

 commonly in the 20- to 30-deg range; high-frequency waves are spread commonly 

 in the 40- to 50-deg range. Waves at intermediate frequencies have spreads at 

 intermediate levels, more like the distribution of the parameter characteriz- 

 ing bulk spread. When the data set is restricted to unimodal distributions, 

 the only change in results is that spreads for high-frequency waves tend to 

 become more like those for intermediate frequencies. This means that the 

 spread properties at each frequency are rather like the bulk properties. The 

 occurrence of unidirectional waves (spreads of less than about 10 deg) are 

 extremely rare at any frequency. 



259. Finally, a computation has been done to define the fundamental 

 shapes that constitute directional distributions. It was assumed that 

 multimodal distributions can be constructed from properly scaled, unimodal 

 shapes. Low-energy, potentially noisy data were eliminated. About half of 

 all observed distributions remained after application of these constraints. 

 Fundamental shapes were then found from composite means of individual dis- 

 tributions, and classified by spread and asymmetry parameters. 



260. The result is a set of well-defined (generally having low standard 

 deviations) empirical functions which illustrate and characterize the way wave 

 energy is distributed in direction. The range of spread parameter is 10 to 



62 deg, covering the full range of spreads found in the bulk characterization. 

 It was found that only one -fourth to one -half of the distributions could be 

 considered symmetric (having roughly equally distributed energy on both sides 

 of the peak) . The remaining one-half to three-fourths of the cases were 

 strongly asymmetric. This property may be as important as directional spread 

 in modeling coastal processes and computing system responses to coastal 

 modifications. It was found that the symmetric distributions could be 

 reasonably fitted with a mathematical function proposed by Longuet-Higgins , 



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