536 



0-6 - 



0-6 



0-8 



10 



1-2 



l-A 



1-6 



fN 



FIGURE 11. Phase speed distribution of individual 

 waves (zero-crossing trough-to-trough) , determined 

 by a photographic method, and normalized by values 

 for waves of maximum energy density. Dispersion re- 

 lation for water waves are also entered by the dotted 

 line. [Cited from Tokuda and Toba (1978).] 



is caused by the effect of the wind drift, which is 

 concentrated near the crests. 



Thus, by using appropriate normalization, we 

 may express the energy distribution of physically 

 substantial waves by the energy spectra of individual 

 waves for some local frequency ranges, excluding 

 false energy density. The above mentioned B-spectrum 

 and C-spectrum are two examples of these. Further, 

 we may reinterprete, the traditional energy spectrum 

 for the main frecjuency range as representing the 

 energy distribution of individual waves, rather 

 than the usual interpretation of a linear combination 

 of small amplitudes of freely travelling component 

 waves. In other words, the elementary physical 

 substance of wind waves is rather in the individual 

 waves , which have a specific distribution of local 

 wind stress and flow pattern, and an apparent phase 

 speed inversely proportional to the square root of 

 the frequency. 



Further, Figure 15 shows that, for the individual 

 waves in the main frequency range for each wind and 

 fetch condition, there exists a conspicuous statis- 

 tical relation between normalized wave height and 

 period, for significant waves which Toba (1972) 

 proposed as the 3/2 power law: 



H* 



BT- 



:3/2 



(2) 



1(X) 



E 80 



o 



UJ 



Ld 60 



CL 



to 



UJ 



to AO 

 < 



I 



Q- 



20 



— 1 1 1 r— 



I I I r- 







Fetch 

 87 

 3.80 



2 40 



6 8 



f(Hz) 



10 



12 



where H* = gH/u^ and T* = gT/u* represents the 



FIGURE 13. Original values of the phase speed distri- 

 bution, for eight fetches, before the normalization 

 shown in Figure 12. Peak frequencies for the shortest 

 and the longest fetches are indicated by arrows, other 

 cases being in between of these. The phase speed of 

 linear water waves is indicated by the full line. 

 [Cited from Tokuda and Toba (1978).] 



dimensionless height and period, respectively, 

 normalized by use of the acceleration of gravity 

 g and the friction velocity of the air u*. The 

 figure shows the data for individual waves for 

 various fetches. Except for very short fetches up 

 to about 4 m, the factor of proportionality B is 

 constant of about 0.045. 



It should be noted that although the spectral 

 form of wind waves in wind-wave tunnels is different 

 from that in the sea as discussed, e.g. , by Kawai 

 et al. (1977), nevertheless the above power law 

 holds for both cases, although the constant, B, is 

 sliglitly different [cf, also Toba (1978a)]. Figure 

 16 shows another representation of the same relation: 

 between the wave height and the frequency, normalized 

 for those waves of maximum energy. The slope of 

 the line is -3/2. 



Consistently with this relation and the above- 

 mentioned apparent phase speed, the steepness of the 

 individual waves determined by a photographic method 

 is approximately constant, statistically. It is 



FIGURE 12. Phase speed distri- 

 bution of one-dimensional compo- 

 nent waves , obtained from the 

 cross-spectra of records of adja- 

 cent two wave gauges , and nor- 

 malized by values for waves of 

 maximum energy density. The 

 coherence of the cross-spectra 

 is shown in the upper part. 

 [Cited from Tokuda and Toba 

 (1978).] 



0.6 



0.8 



1.0 



1.2 



1.A 



1.6 



1.8 



2.0 



22 



2.A 



fN 



