Mtcroscopte Structures of Wind Waves 
vious paragraph, the microstructure may be considered nearly iso- 
tropic for viewing angles very close to the normal to the mean water 
surface, say, less than the root-mean-square slope. Beyond this 
region, the sizes of specular areas, represented by the average radius 
of curvature, increases rather rapidly with the angle from the normal. 
No data were obtained at very steep angles, where the situation is 
further complicated by possible shadowing effect. 
Judging from the data shown in figure 14, the backscattering 
measurement is ideally made at small angles from the normal, where 
the sea surface is nearly isotropic. A small error of the angular mea- 
surement at large angles would introduce serious change of the results 
because the sea surface in this case is highly nonisotropic. 
V.6 Growth of high-frequency wind waves. 
In order to find the over-all average radius of curvature of 
the disturbed water surface for each wind velocity, the cross product 
of the smooth data shown in figure 13, is found. One curve shows the 
angular distribution of average surface curvature and the other curve 
shows the relative frequency of occurrence of the particular curvature. 
Consequently, the cross product represents the overall average of 
surface curvature obtained at a given wind velocity. 
The overall average radius of surface curvature are shown 
in figure 15. The data indicate a rapid decrease of the radius of sur- 
face curvature with increasing wind-shear velocity is observed at 
low wind velocities and a steady but gradual decrease at high wind 
velocities. Figure 15 shows that the radius of curvature seems to 
reach a saturated value of 1/4 cm, when the wave growth with wind 
ceases, 
VI. SEA-SURFACE SLOPE AND EQUILIBRIUM WAVE SPECTRA 
VI. 1 Equilibrium wind-wave spectra. 
The directional wind-wave spectra W (k) in the equilibrium 
range was proposed by Phillips (1958a, 1966): 
— B -4 
Gravity waves: VW (k)=— f(0)k , ie oe ale 
7 ) 
- ii (7) 
Capillary waves: W (k) =qmi t (18 bbknd -<tdeie Sdkiang > ky 
where k and k are the wave-number vector and scalar, respectively; 
1449 
