Role of Dominant Wave tn Spectrum of Wind-Generated Waves 
IV. THE EQUILIBRIUM RANGE CONSTANTS B AND £ 1 
One reason for a difference in laboratory and field spectra 
is found in the behaviour of a .We know that a should be less than 
0.5, and a numerical value for a was obtained in section 3 from the 
condition of wave breaking. We note that if S is not constant, then 
a will also vary. Thus, if we take Mitsuyasu's laboratory data, we 
find G = 0.08, about 6 times larger than the field value, and with 
this an a value of 0.148. V6 = 0.36 - very close to the maximum 
theoretical value of 0.5. There exists also the possibility of inferring 
a from the maximum observed wave slope. Observations of dominant 
waves from different sources have been reviewed by Deardorff (1967) 
who finds that the wave slope H1 3/ Lis approximately constant, at 
least for smaller ocean waves, and equal to about 0.08. As the wave 
is approximately sinusoidal with wave number ky = 2 7 /L, where 
Lis the wave length, with frequency w,,, and with wave height H = 
one can infer a value of a@ = 0.25 from the maximum acceleration 
a maxof the sinusoidal wave on deep water : a pax eel Hgk. For la- 
boratory waves, the slope can be steeper. Chang et.al. (1971) report 
a value of H1/5/ L~ 0.1, and thusa~ 0.30. For larger ocean waves, 
the slope appears to decrease further, and consequently the observed 
a decreases.Asaresult, we would expect to find a, value which is 
not quite constant but decreases with increase of wave lenght. This 
is in agreement with the observations of measured £ values. One 
should realize that 8 is likely to be smaller than @, in the laboratory 
because the drop-off of the laboratory spectra near the peak of the 
spectrum is more rapid than the - 5 law of Phillips. In the field, it 
is the other way round, f is larger than 4, . As the values of By 
are not reported from field data, we shall use to approximate (4, 
as we have done above. 
A close inspection of figure la reveals that the - 5 power 
law does not quite connect the peaks of the spectra. At low frequen- 
cies, the experimental spectra have peaks which constantly fall be- 
low, while at high frequencies they lie above the average curve. In 
figure lb, the spectra have slightly different 8 and 8, values, The 
same observation applies to the high frequency end of the spectrum. 
Longuet-Higgins (1969) has given a summary of observed @ values 
which were plotted as a function of the fetch parameter gx/u2 by 
Mitsuyasu (1969) and Liu (1971), from whose paper figure 4 is taken. 
In defining the fetch parameter, x is the distance from the point of 
observation to the nearest upwind shore, or to the storm center, and 
u is the shear velocity u = (tw/Pa ) 1/2 . The curve of Liu (1971) 
through the data may not be a final result, because it is based on da- 
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