Analysis and Interpretation of Frequency-Wavenumber Spectra of Young Wind Waves

The energy level and its directional distribution are key observations for understanding the energy balance in the wind-wave spectrum between wind-wave generation, nonlinear interactions, and dissipation. Here, properties of gravity waves are investigated from a fixed platform in the Black Sea, equipped with a stereo video system that resolves waves with frequency f up to 1.4 Hz and wavelengths from 0.6 to 11 m. One representative record is analyzed, corresponding to young wind waves with a peak frequency f(p) = 0.33 Hz and a wind speed of 13 m s(-1). These measurements allow for a separation of the linear waves from the bound second-order harmonics. These harmonics are negligible for frequencies f up to 3 times f(p) but account for most of the energy at higher frequencies. The full spectrum is well described by a combination of linear components and the second-order spectrum. In the range 2f(p) to 4f(p), the full frequency spectrum decays like f(-5), which means a steeper decay of the linear spectrum. The directional spectrum exhibits a very pronounced bimodal distribution, with two peaks on either side of the wind direction, separated by 150 degrees at 4f(p). This large separation is associated with a significant amount of energy traveling in opposite directions and thus sources of underwater acoustic and seismic noise. The magnitude of these sources can be quantified by the overlap integral I(f), which is found to increase sharply from less than 0.01 at f = 2f(p) to 0.11 at f = 4f(p) and possibly up to 0.2 at f = 5f(p), close to the 0.5 value proposed in previous studies.