Wave number spectra of short wind waves: implications from laboratory studies

Directional wavenumber spectra of short wind waves as measured in three different wind-wave tanks at fetches from 5 m to infinity and wind speeds from 2 to 15 ms-1 are analyzed. The data were collected using a refraction-based optical technique that allows the measurement of either the along-wind or cross-wind slope component of the water surface in areas of up to 30 x 40 cm2. The comparison of the directional wavenumber spectra from the different facilities shows that the angular spreading of the waves is most sensitive to the geometry of the facility, especially the width of the water channel. However, all unidirectional wavenumber spectra show two regimes that are also expected to be found in oceanic conditions. The first regime is characterized by a k-3.5 dependence of the wave height spectrum. It ranges from short gravity waves well into the capillary wave range. At a wavenumber of k ≈ 1200 m-1 (wavelength λ ≈ 0.5 cm) a sharp and almost wind speed independent cutoff of the spectral densities occurs. This implies that viscous damping is not the dominant dissipation mechanism for capillary waves. The increase of the spectral densities with friction velocity is found to be dependent on wave number as well as on fetch