Role of Dominant Wave in Spectrum of Wind-Generated Waves 
the wave spectrum has those significant "humps" at harmonics of the 
frequency of the dominant wave wm. I have pointed out in a previous 
paper (Plate (1971)) that these humps indicate not so much a general 
behaviour of the spectrum, but could be the energy densities associa- 
ted with the higher harmonics of the dominant waves, that is with the 
fact that the dominant wave is not a true sinusoid. 
For an illustration of this point, figure 5 is reproduced, It 
shows the average shape of the highest 20 out of 100 waves observed 
on the surface of a laboratory channel by Chang (Chang et.al. (1971)). 
One notices that this curve is skewed and decidedly non-sinusoidal, 
The skewness can be attributed to the pressure pattern that must 
exist for this case. As the streamline pattern shown in figure 5 indi- 
cates, the air flow separates from the air crest and reattaches at so- 
me distance upslope of the next wave. The result must be a non-sym- 
metric pressure distribution with pressure at the wave backs and suc- 
tion at the wave fronts. Separation is also responsable for a stream- 
line pattern above the dominant wave which is remarkably unaffected 
by the waves : all vertical velocities induced by the wave motion are 
smoothed out because the streamline formed by the wave and the upper 
limit of the separation bubble is pretty much a straight line. In the 
laboratory one therefore finds under these conditions that the air flow 
at some short distance above the water waves resembles that obser- 
ved in the turbulent boundary layer along a rough surface. 
The spectral shape associated with the wave of Chang et, al. 
can be inferred from the Fourier components of the wave of figure 5. 
The spectral density must be proportional to the square of the ampli - 
tude of the phase-shifted harmonic component at any frequency nWy , 
withn=1, 2, 3, ..., divided by the bandwidth as where FP is the 
period of the wave. These are plotted in figure 6 against n, It is seen 
that the envelope to the Fourier component energies is remarkably 
close toa - 5 power law. As spectral analysis is not capable of pro- 
viding filters that are so sharp as to prevent any side lobe leakage, 
it is not unlikely that the similarity spectrum is basically the smeared 
out energy spectrum of the dominant wave, in particular since domi- 
nant waves do not move as a periodic wave train but in groups which 
are phase-shifted with respect to each other. Such a behaviour ex- 
plains the peaky structure of the spectrum. But it also may explain 
the difference in the peaks of the similarity spectra of the waves of 
Mitsuyasu (1969) and Hidy and Plate (1965) which are so evident in 
figure 3. If the spectrum is essentially that of a pure sinusoid, then 
the energy density at the peak is the energy of the sinusoid spread 
over the chosen bandwidth (the resolution bandwidth of spectral analy- 
sis). A very narrow resolution bandwidth leads to a very large density 
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