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⁻²c_mk_mk⁻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, c_m the minimum phase velocity of surface waves, and k_m the corresponding wavenumber. Capillary-gravity wave wavenumber spectra obtained from the ocean and from laboratory studies are compared. It is found that significant differences in many important features of short-wave properties exist in the datasets from these two different environments. A possible reason for the observed differences is attributed to the fluctuation component of the wind field, which is typically a significant fraction of the mean wind speed in the open ocean but much smaller in the laboratory. The steady wind in the laboratory produces a surface boundary condition very different from that in the field. This is reflected in the observation that a spectral gap in the vicinity of the minimum phase velocity (an indication of wave blockage by steady surface drift current) was found in the laboratory measurements but not in the field data. As a consequence, the small-scale structures observed in the laboratory and in the field am significantly different.