Microscopte Structures of Wind Waves 
The angular distribution of average radius of curvature, 
shown in figure 13, is normalized with respect to the slope distribu- 
tion and replotted in figure 14. The normalization involves only divi- 
ding the observation angle by the standard deviation of the slope-dis- 
tribution curve. Sucha step, relating the average radius of curvature 
to the relative frequency of occurrence,is helpful for comparing re- 
sults obtained at various wind velocities. The relative frequency 
of occurrence for the converted scale, on the basis of the standard 
deviation, is given by the error function. 
V.4 Skewed angular distribution of surface curvatures 
The angular distribution of average radius of surface curva- 
ture, shown in figure 14, displays three different shapes correspon- 
ding approximately with the occurence of three types of carrier-wave 
patterns discussed in an earlier section. At the lowest wind velocity, 
a very skewed, bell-shaped distribution curve is related to rhombic 
waves, although it is not clear at this stage what is the reason for 
this correlation. 
At medium wind velocities (3 < U,< 9 m/sec), the steep-fa- 
ced parasitic capillaries, riding on the forward face of the carrier 
waves, undoubtedly cause a skewed angular distribution of the avera- 
ge radius of curvature. The observation angle with the minimum ra- 
dius of curvature is about the same as the forward-face slope ‘from 
the horizon) of the carrier wave. This regime with highly skewed 
surface-curvature distributions, however, probably exists only in 
laboratory tanks (Wu 1970) 
At high wind velocity (Uj > 9.5 m/sec), the carrier wave is 
covered rather evenly by ripples. This is the gravity-governing regime. 
The case with the wind velocity of 9.3 m/sec is in the transition re- 
gion between the surface-tension regime at low wind velocities and the 
gravity-governing regime at high wind velocities. The microstructures 
of disturbed water surface for the three highest wind velocities are 
very similar to oceanic conditions; nonlinear interaction between 
short and long waves is believed to be active in this regime. 
The horizontal contraction of the water surface near the crest 
of the long wave was stated by Longuet-Higgins and Stewart (1960) to 
shorten the lengths and to increase the amplitudes of short waves 
(ripples). When these ripples are saturated, further shortening will 
cause their breaking. Phillips (1963) then showed analytically that the 
energy loss by short waves near the crests of long waves is partially 
supplied by the long wave, and, therefore, causes the attenuation of 
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