Role of Dominant Wave in Spectrum of Wind-Generated Waves 
It might well be said that this development found its culmina- 
tion in Phillips' (1958) derivation of the - 5 - power law for the high 
frequency end of the spectrum. From reasoning that all component 
waves shorter than some limiting, longest component are at equili- 
brium ina state of breaking, he deduced the equation for the high 
frequency end of the spectrum : 
S beasties w for pie? th xs (1) 
where S (w) is the spectral density, g the acceleration of gravity and 
w» the angular frequency which has a value wm where the maximum 
= ( wm) in the spectral density occurs. How well the - 5 - power law 
equation 1 fits the experimental data is illustrated in figure la (from 
Hess et.al. (1969)). The data are from many different sources and 
range from short fetch laboratory data to long fetch ocean data obtai- 
ned at winds near Hurricane conditions. A separate set of data, by 
Mitsuyasu (1969) is shown in figure 1b. Through both sets, a curve is 
drawn according to equation 1 with 8 = 1.48. afm ss 
Unsatisfactory in equation 1] is the fact that 4 is an empiri- 
cal constant. An analytical model that overcomes this defect by rela- 
ting @ to the energy input into the wave field from the wind was sug- 
gested by Longuet-Higgins (1969). Assuming the rate of energy lost to 
turbulence by wave breaking to be proportional to the wave energy 
contained in the wave field, and equating this to the work done by the 
wind on the waves, he was able to show that if all wave components 
at frequencies above w,_ are in the state of breaking the coefficient 
f can be related to the drag coefficient C for the wind through : 
0,125 
legtleas. 6 pd/ee 
(2) 
where C = Ty /hg hy , Ly, is the water surface stress exerted by the 
wind, p is the density, and Uy is the wind velocity at height h, 
while the subscripts a and w refer to air and water, respectively. A 
drag coefficient of C= 1.5 X 1073 leads toa value of 8 = 1.3 x 10° 
in reasonable agreement with observed values, and since it is empi- 
rically observed that the drag coefficient decreases with fetch, or 
with duration, the theory is even capable of predicting a slight decrea- 
se in @ as has indeed been reported. 
Baz 
