Microscopte Structures of Wind Waves 
time when the airflow boundary layer becomes turbulent. The rela- 
tive frequencies of occurrence of various slopes generally follow a 
normal distribution. At lower wind velocities, the formation of para- 
sitic waves causes a skewed slope distribution; at high wind velocities, 
the wave breaking causes a peaked slope distribution, The skewed 
slope distribution may produce different back scattering of electro- 
magnetic waves from the leeward and from windward faces of the 
basic wave profile. 
The curvature distribution of the wind-disturbed water sur- 
face observed from different angles is generally skewed with greater 
radius of curvature at steeper viewing angles from the normal to the 
mean water surface. As the wind velocity increases, the average ra- 
dius of curvature decreases; rapidly at low wind velocities when waves 
are effectively excited by wind, and gradually at high wind velocities 
when waves approach saturated staté. The skewness is caused by 
the presence of parasitic capillaries at low wind velocities and by 
nonlinear wave-wave interaction at high wind velocities. The back 
scattering measurement is ideally made at small angles from the 
normal, where the sea surface is nearly isotropic. 
The present measurements of surface curvatures are the 
only set of data of its kind. The mean-square surface slopes are com- 
pared with those determined in the field, and the difference is explai- 
ned as a result of various directional distribution of wave components. 
Equilibrium energy spectra of wind waves was first established for 
the gravity range and later extended to the capillary range. The veri- 
fication of the latter extension and the determination of the spectral 
coefficients for both ranges are discussed on the basis of the experi- 
mental results for mean-square slopes. Good agreement between 
present and oceanic results indicate a possible modeling of the micro- 
structure of the air-sea interface in a laboratory tank. 
ACKNOWLEDGEMENT 
This is a summary report of our work on measurements and 
modeling of microstructures of the air-sea interface. This program 
is under the direction of Mr. M.P.Tulin, who also suggested the 
design of the optical instrument, and of Dr. S.G. Reed, Jr., who also 
reviewed this report. Portions of this report have been published else- 
where. This work was supported by the Office of Naval Research under 
Contracts N° N00014-70-C-0345, NR 220-016 and N° N00014-72-C-0509, 
NR 062-472. 
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