Field Data Support of Three-seconds Power Law and guσ^-4-spectral Form for Growing Wind Waves

Abstract

Observational data on air-sea boundary processes at the Shirahama Oceanographic Tower Station, Kyoto University, obtained in November, 1969, was analyzed and presented as an example representing the structure of growing wind-wave field. The condition was an ideal onshore wind, and the data contained continuous records of the wind speed at four heights, the wind direction, the air and water temperatures, the tides, and the growing wind waves, for more than six hours. The main results are as follows. Firstly, in both of the wind speed and the sea surface wind stress, rather conspicuous variations of about six-minute period were appreciable. Secondly, the three-seconds power law and its lemma expressed by H=BT^3/2 and σ=2 π BT^-1/2, respectively, are very well supported by the data, where H(=gH/u²) and T(=gT/u) are the dimensionless significant wave height and period, respectively, σ the wave steepness, u the friction velocity of air, g the acceleration of gravity, and B=0.062 is a universal constant. Thirdly, the spectral form for the high-frequency side of the spectral maximum is well expressed by the form of ∅(σ) =α_sguσ^-4, where σ is the angular frequency and ∅(σ) the spectral density. The value of α_s is determined as 0.062±0.010 from the observational data. There is a conspicuous discrepancy between the spectral shape of wind waves obtained in wind-wave tunnels and those in the sea, the former con taining well-defined higher harmonics of the spectral peak, and consequently there is an apparent difference in the values of α_s also. However, it is shown that the discrepancy of α_s may be eliminated by evaluating properly the energy level of the spectral form containing higher harmonics.