Abstract
The three-seconds power law for wind waves of simple spectra, already derived byToba (1972 and 1973), may also be derived by introducing surface-wave properties into the form of the rate of energy dissipation in the theory of turbulence. The universal constantB, which was formerly determined empirically as 0.062 is here obtained asB=(2π)−3/2=0.0635. Thus wind waves have the duality of turbulence and wave.
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References
Landau, L.D. and E.M.Lifshitz (1954): Fluid Mechanics. Japanese edition vol. 1, translated by H.Takeuchi, Tokyo-Tosho.
Toba, Y. (1972): Local balance in the air-sea boundary processes, I. On the growth process of wind waves. J. Oceanog. Soc. Japan,28, 109–120.
Toba, Y. (1973): Local balance in the air-sea boundary processes, II. Partition of wind stress to waves and current. J. Oceanog. Soc. Japan,29, 70–75.
Toba, Y. (1973a): Local balance in the air-sea boundary processes, III. On the spectrum of wind waves. J. Oceanog. Soc. Japan,29, 209–220.
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Toba, Y. Duality of turbulence and wave in wind waves. Journal of the Oceanographical Society of Japan 30, 241–242 (1974). https://doi.org/10.1007/BF02111050
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DOI: https://doi.org/10.1007/BF02111050