FIGURE 9. Flow visualization of the 

 initial stage of the generation of wind 

 waves by use of polystyrene particles 

 which had a 2-mm diameter and the specific 

 gravity of about 0.99, and which were 

 placed just beneath the water surface 

 prior to the start of the wind. The wind 

 blows from the left to the right. The 

 wind speed in the tunnel section was 

 8.6 m/s, and the fetch was 2.85 m. The 

 time measured from the start of the wind 

 is shown in seconds. In 2.58 s, initial 

 wavelets may be recognized by streaks of 

 light in the water, and some particles 

 have already begun to disperse into the 

 water. In 4.78 s, waves are already ir- 

 regular wind waves and more particles are 

 dispersed. In 13.5 s, particles are dis- 

 persed down to more than 10 cm, corre- 

 sponding approximately to a half of the 

 representative wave length. [Cited from 

 Toba et al. (1975) .) 



2.58 



478 



found that the phase speed was virtually independent 

 of the frequency, and had the same value as that 

 of the waves of the spectral maximum, at respective 

 fetches. These experimental results are interpreted 

 as indicating that the assumption of wind waves as 

 expansible to component free waves with weak non- 

 linearity is not necessarily appropriate for young 

 growing wind waves. 



On the other hand, since individual waves as 

 instantaneous surface undulations have a specific 

 shearing stress distribution, and a specific interval 

 flow pattern, they may carry some factors as a phys- 

 ical element. We have examined, in a wind-wave 

 tunnel of 15-cm width, energy density distributions 

 for individual waves, as well as their phase speeds, 

 and compared them with those obtained by usual com- 

 ponent wave model for the same experimental data 

 [Tokuda and Toba (1978)].* 



First, a normalized energy spectrum for individual 

 waves has been newly defined and calculated from the 

 statistical distribution of two kinds of the individ- 

 ual waves: zero-crossing, trough-to-trough and all 

 trough-to-trough on our wave records, as illustrated 

 in Figure 10. The definition of the normalized 

 individual-wave spectral density, 9v;, is 



Sn^^n) 



6iAf/(Af/fp)E 



(1) 



where 



, m.T. H. 2 



1,2, 



, ,n + 1 



and where m^ is the number of individual waves of 



rom f 

 0.02 s, n = 100, 



the period class, T^, (frequency from f to f + Af ) , 



Af = l/{2nAt) , where we used At 

 and Af - 0.25 Hz, and also 



♦Tokuda, M. , and Y. Toba (1978): Component waves 

 and individual waves as physical model of wind waves. 

 To be published. 



n+1 

 ^ = iil . 



>-Af 



and where fp is the frequency of the energy maximum. 



Figure 10 shows the comparison. The A-spectrtim 

 is the normalized spectra by the traditional com- 

 ponent wave model in which the secondary peak is 

 seen at the normalized frequency of 2. The B-spectrum 

 is for individual waves of zero-crossing, trough-to- 

 trough, and the C-spectrum for all trough-to-trough 

 on our wave records. In the main frequency range 

 from 0.7 to 1.5, which is the value normalized by 

 the peak frequency, the spectra are virtually 

 equivalent with one another. The second peak at 

 frequency of 2 in the A-spectriom completely dis- 

 appears in the individual-wave spectra. The slope 

 of these straight lines is f~^ for the high frequency 

 side, and f" for the low frequency side. The C- 

 spectrum is considered to give a better represen- 

 tation of the high frequency side which is exactly 

 on the f~^ line, and the B-spectrum represents the 

 low frequency side better, which is more similar to 

 the traditional A-spectrum. We may infer that much 

 energy of the higher frequency part of traditional 

 component waves, which is clearly shown as the 

 energy at higher harmonics of the spectra, is a 

 manifestation of the distorted shape of individual 

 waves of the main frequency range, as was already 

 suggested by Toba (1973) . 



Figure 11 shows the normalized phase speed of 

 individual waves determined by two adjacent wave 

 gauges. It is inversely proportional to the square 

 root of the frequency, in contrast to the phase 

 speed of linear waves which is inversely proportional 

 to the frequency. In addition, the phase speed of 

 the individual waves is much larger than that of 

 linear waves as shown later. In the case of the 

 phase speed of component waves of one-dimensional 



