Abstract
The mechanism of the development of wind-waves will be proposed on the basis of the observed wave spectra in the wind tunnels and at Lake Biwa (Imasato, 1976). It consists of two aspects: One is that the air flow over the wind-waves transfers momentum concentratively to the steepest component waves and the other is that the upper limit of the growth of a wave spectral density is given by the ultimate value in the slope spectral density. The first aspect means that the wave field has the “momentum transfer filter” on receiving the momentum from the air flow. Wind-waves in the stage of “sea-waves” receive the necessary amount of momentum by the form drag,e.g. according to the Miles' (1960) inviscid mechanism, through a very narrow frequency region around a dominant spectral peak. On the other hand, wind-waves in the stage of “initial-wavelets” receive it according to the Miles' (1962a) viscous model through a fairly broad frequency region around the peak. The upper limit ofS max developing according to viscous mechanism is given byS max =6.40×10−4 k max −2cm2s andS max =2.03C(f max )−2cm2s(S max is the power density of the wave spectral peak with the frequencyf max ,k max is the wave number corresponding to the frequencyf max andC is the phase velocity).
From the second aspect, the upper limit of the growth of wave spectral density is given by 33.3f −4cm2s in the frequency region of late stage of “sea-waves”. Therefore, the spectral peak, which has the largest value in the slope spectral density in the component waves of the wave spectrum, rises high over the line 4.15f −5cm2s. The energy is transported from the spectral peak to the high frequency part and to the forward face of a wave spectrum by nonlinear wave-wave interaction. This nonlinearity is confirmed by the bispectra calculated from the observed wind-wave data. In the stage of “sea-waves”, nonlinear rearrangement of the wave energy comes from a narrow “momentum transfer filter”, and, in the stage of “initial-wavelets”, it comes mainly from small corrugations and small steepness of the wave field.
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Imasato, N. The mechanism of the development of wind-wave spectra. Journal of the Oceanographical Society of Japan 32, 253–266 (1976). https://doi.org/10.1007/BF02107982
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DOI: https://doi.org/10.1007/BF02107982