The mechanism of the development of wind-wave spectra

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 ofSmax developing according to viscous mechanism is given bySmax=6.40×10−4kmax−2cm2s andSmax=2.03C(fmax)−2cm2s(Smax is the power density of the wave spectral peak with the frequencyfmax,kmax is the wave number corresponding to the frequencyfmax andC is the phase velocity).