one direction. The area under this spike is equal to the volume under the 

 frequency- direction spectrum. To add interest, this spectrum has the same 

 H^o , peak frequency, and peak direction of Figure 2a. 



71. If the energy is distributed in direction but not in frequency, a 

 shape like Figure 2c results. In this instance, the waves come from several 

 directions, but all wave trains have a frequency falling in the frequency band 

 centered at about 0.17 Hz. Waves with the highest amplitudes (and highest 

 energy) are coming from a direction of about 45 deg, so the peak direction in 

 this case is the same as for the two prior cases. The frequency spectrum is 

 simply a spike centered at about 0.17 Hz since all the energy is concentrated 

 near this frequency. The direction spectrum shows the total energy in the 

 frequency-direction spectrum in each direction arc. It shadows the main 

 distribution because the main distribution is only one frequency band wide. 

 The shape shown is one member of a class of functions used by Mitsuyasu et al . 

 (1975) to characterize their data. Here again the frequency-direction 

 spectrum has the same H^^ , peak frequency, and peak direction as the 

 previous two cases . 



72. If real seas were as simple as these three cases, it would be 

 straightforward to determine their character. That this is not the case is 

 demonstrated in Figure 2d, which shows a frequency-direction spectrum of a 

 real sea state obtained in the present measurement program. Here, wave energy 

 is distributed in both frequency and direction. The figure shows two distinct 

 groupings of wave energy. In the foreground is a wave field in the early 

 stages of wind generation. It has a distinct peak at frequency 0.17 Hz and 

 direction 45 deg. Energy drops rapidly toward low frequencies and tails off 

 more gradually at high frequencies; a clear directional spread is evident at 

 all frequencies. Behind this primary distribution is another, lesser concen- 

 tration of energy centered at a frequency of approximately 0.08 Hz and a 

 direction of approximately -30 deg. These low- frequency waves are evidently 

 swell waves from some distant disturbance arriving from a finite range of 

 directions different from the wind sea part of the spectrum. 



73. The integrated frequency spectrum of Figure 2d shows the net 

 frequency distribution for both wind sea and swell. The main, wind sea part 

 looks somewhat similar to the JONSWAP curve shown in Figure 2b, indicating 

 that existing models for frequency spectra are capable of approximating real 

 seas reasonably well. 



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