Nonlinear Properties of Laboratory Wind Waves at Energy Containing Frequencies

Part 2. Detailed Structures of Power Spectra and their Evolution with Fetch

Abstract

The fine structure of wind-wave spectra in a wind-wave tunnel is investigated inconnection with the process of nonlinear interaction among spectral components, where eachspectrum is calculated from about one hour of data measured with 8 wave gauges arrangedat a distance of 25 cm. It is found that there are several significant spikes, or primary modes, around the spectral maximum f_o. Among such primary modes, three primary modes includingthe spectral maximum satisfy the resonance condition 2f₀=f₁-F-f₂, where fi and f₂ are frequenciesof the higher and lower frequency modes adjacent to fo, while the frequency widthbetween adjacent modes, f₁-f₀ or f₀-f₂, is nearly equal to 0.1 f₀. In the process of growthof the spectra with fetch, the energy density at the lower frequency f₂ increases accompaniedwith an energy decrease at the higher frequency f₁, and the mode f₂ replaces the mode foas the spectral maximum. This evolutional process is repeated several times in the range ofthe present experimental condition. These results suggest that the discrete primary modesare not due to statistical error, but rather due to some wave-wave interaction.