On the spectra of high-frequency wind waves

Displacements of wind waves in the laboratory were measured with a laser displacement gauge, a recent,ly developed, optical, non-intrusive sensor, which avoids the meniscus effect's that severely limit the frequency response of conventional thin- wire gauges. The new gauge is a digital device, which has a maximum frequency response of 2.5 kHz. Its spatial resolution, which depends on the field of view, is t,ypically 0.016 cm for a 4 cm field of view. The wind-wave displacements were measured at several fetches for three wind speeds. Wave-variance spectra derived from these measurements indicate the presence of a quasi-equilibrium spectrum in the capillary-wave regime. The quasi-equilibrium spectrum follows an $f^{-\frac{7}{3}}$ power law that has been predicted on dimensional grounds. The spect'ral density increases with increasing wind speed from 4 to 10 m/s but is independent of the fetch from 3 to 5 m. In addition, the capillary-wave spectrum is practically unchanged when a, relatively long but. low-amplitude mechanical wave is superposed onto the wind- generat'cd waves.