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A Study of the Wavenumber Spectra of Short Water Waves in the Ocean

Abstract Spatial measurements of capillary-gravity waves in the ocean were obtained using a scanning slope sensor mounted on a free-drifting buoy intended to minimize the flow disturbance. The data provide direct calculation of the wavenumber spectra of surface curvature in the capillary-gravity wave range. The results indicate that 1) a pronounced peak at the wavenumber k = 9 rad cm−1 is evident in the curvature spectra for wind speeds below 6 m s−1; 2) the slopes of the curvature spectra are 1 and −1 on the two sides of the spectral peak, 3) the spectral density and mean-square roughness properties increase linearly with wind speed; and 4) these observations suggest a spectral function of the form χ(k) = Au*c−2cmkmk−4, which is proportional to u*k−3 in the short gravity wave region and u*k−5 in the capillary wave region, where u* is the wind friction velocity, cm the minimum phase velocity of surface waves, and km the corresponding wavenumber. Capillary-gravity wave wavenumber spectra obtained from the ...