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 1.4Hz and wavelengths from 0.6 to 11m. One representative record is analyzed, corresponding to young wind waves with a peak frequency fp= 0.33Hz and a wind speed of 13ms21. 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 fpbut account formost 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 2fpto 4fp, 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� at 4fp. 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= 2fpto 0.11 at f = 4fpand possibly up to 0.2 at f = 5fp, close to the 0.5Ï\u80 value proposed in previous studies