The Response of Wind-Wave Spectra to Changing Winds. Part I: Increasing Winds

Abstract

Continuous time series of wind profiles and wind waves under growing conditions, recorded at Shirahama Oceanographic Tower Station and discussed by Kawai, Okada and Toba, have been reanalysed for this study of the response of one-dimensional wind-wave frequency spectra to unsteady rising winds. The factor αs, in the equilibrium-range spectral form ?(σ) = αsgu*σ?4 (g is gravity, σ is angular frequency and u* is the friction velocity) shows a remarkable fluctuation. It becomes smaller for increasing wind conditions (i.e., increasing friction velocity) and larger for decreasing wind conditions within a range of (5?9) ? 10?2. The slope of the spectra is very close to σ?4 generally, but it has a tendency to be slightly steeper for decreasing winds. The peak of the spectra is broader for increasing winds, and narrower for decreasing winds, when fluctuations of several-minute duration of u* are considered. The time scale of the adjustment of the equilibrium-range spectra is on the order of ten minutes. This time scale is much faster than the time scale of growth of the total energy of the wind waves, and consequently the peak frequency shifts to higher frequencies for increasing u*, or vice versa. This response suggests that the processes of the adjustment of the wind-wave field involve both upward and downward cascading of the wave energy. Further evidence is presented in the form of ocean wave data recorded in Bass Strait, Australia, where the waves, although much larger, show similar trends.