Some characteristics of the development process of the wind-wave spectrum

Abstract

The development process of wind-waves of which spectral peak distributes from 0.6 cps to 9.3 cps will be discussed on the basis of the wind tunnel experiments and of the field observations performed at Lake Biwa. The characteristics of power and slope spectra are here presented. The development process of these wind-waves is characterized by three stages;i.e. “initial-wavelets”, “transition stage” and “sea-waves”. In the wind tunnel experiments, the transition from the stage of the “initial-wavelets” to the “transition stage” occurs when the wave spectral peak arrives at the line 6.40×10⁻⁴ k ⁻²cm²·sec (wherek is wave number) or when the slope spectral density at the frequencyf _max becomes larger than 6.40×10⁻⁴ sec. In the stage of sea-waves, the component wave of a wave-spectral peak is steepest in the component waves. And the wave spectral peak develops along the line 1.02×10² f ⁻⁶ cm²·sec (wheref is the frequency corresponding to the wave numberk) untill it reaches the line 33.3f ⁻⁴cm²·sec, and thereafter develops along the latter line, which indicates the constant density of slope spectrum. It is suggested that the nonlinearity of wind-waves must become stronger as wind-waves develop. The effective momentum fluxΤ _ws from the air flow to wind-waves in this stage is evaluated to be about 4∼9% of the total stressΤ ₀.