frequency (about 0.32 Hz), only about 10 percent of the cases are unimodal , 

 about 30 percent are bimodal (diagonal shading) , about 30 percent are trimodal 

 (white shading) , and the remaining 30 percent (blank space above the white - 

 shaded bar) has more than three modes. At the lowest frequency (about 

 0.05 Hz), roughly 70 percent of the cases are unimodal, another 25 percent are 

 bimodal, and the rest are trimodal. 



207. Taken as a whole, the figure indicates that well over half of all 

 single -frequency directional distributions are unimodal. This is deduced from 

 the figure by the ratio of total black- shaded area to total area for all 

 frequencies. Roughly another 20 percent are bimodal (ratio of diagonal -shaded 

 area to total area) and the rest have more than two modes. The large per- 

 centage of multimodal distributions indicates that this is an important 

 feature of natural, shallow-water, wave fields. 



208. The computation that led to Figure 23 only counted the number of 

 modes and not their relative strength (the extent to which energy is dis- 

 tributed among the modes). For instance, a bimodal distribution could have 

 90 percent of its energy in one mode and only 10 percent in the other. In 

 this case, the second mode is of little importance from an energy standpoint 

 because it contains very little energy. However, if each mode in a bimodal 

 distribution has half the energy of the distribution, then both modes are of 

 equal importance, and neither can be neglected. 



209. To examine this effect, a computation was done with the modal 

 fractional energy parameter F^^ defined by Equation 24 and listed with the 

 individual mode parameters in Part V. For each directional distribution 

 (including the unimodal ones), the mode with the maximum energy, i.e., having 

 the maximum fraction P^*^^ of total energy, was isolated and identified as 

 the primary mode. For unimodal cases this was the only mode, and its fraction 

 of total energy was identically one (100 percent). Primary mode energy 

 fractions were then grouped into 10-percent-wide bands and counted; that is, a 

 certain number of distributions had 90 to 100 percent of their energy in the 

 primary mode (maximum P^*^^ in the range 0.9 to 1.0), others had 80 to 



90 percent in the primary mode, yet others had 70 to 80 percent in the primary 

 mode, and so on. The number of cases in each group was divided by the total 

 number (1,046) of cases in the data set and multiplied by 100 percent. The 

 result was the percent of all cases having a given fractional range of energy 

 in the primary mode. For example. Figure 9a shows a bimodal distribution with 



85 



