Abstract
A new growth equation for wind waves of simple spectrum is presented upon three basic concepts. The period and the wave height of significant waves in dimensionless forms, which are considered to correspond to the peak frequency and the energy level, respectively, are used as representative quantities of wind waves. One of the three basic concepts is the concept of local balance, and the other two concern the acquisition of wave energy and the dissipation of wave energy, respectively. It is shown from some actual data that the equation, together with two universal constants concerning the acquisition and the dissipation of wave energy (B=6.2×10−2 andK=2.16×10−5, respectively), is applied universally to wide ranges of wind waves from those in a wind-wave tunnel to fully developed sea in the open ocean.
“The three-second power law for wind waves of simple spectrum”, and a few relations as the lemmas, are derived, such that the mean surface transport due to the orbital motion of wind waves is always proportional to the friction velocity in wind, and that the steepness is inversely proportional to the root of the wave age. It is also derived that the portion of wind stress which directly enters the wind waves decreases exponentially with increasing wave age and is 7.5 % of the total wind stress for very young waves.
Also, equations are presented as to the increase of momentum of drift current, and as to the supply of turbulent energy by wind waves into the upper ocean.
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Kunishi, H. (1963): An experimental study on the generation and growth of wind waves. Disaster Prevention Res. Inst., Kyoto Univ., Bull., No. 61, 41 pp.
Kunishi, H. andN. Imasato (1966): On the growth of wind waves by high-speed wind flume. Disaster Prevention Res. Inst., Kyoto Univ., Annals,9, 667–676 (in Japanese).
Longuet-Higgins, M. S. (1952): On the statistical distribution of the heights of sea waves. J. Mar. Res.,11, 245–266.
Longuet-Higgins, M. S. (1969): A nonlinear mechanism for the generation of sea waves. Proc. Roy. Soc. A.311, 371–389.
Mitsuyasu, H., R. Nakayama andT. Komori (1971): Observations of the wind and waves in Hakata Bay. Rep. Res. Inst. Appl. Mech., Kyushu Univ.,19, 37–74.
Phillips, O. M. (1958): The equilibrium range in the spectrum of wind-generated waves. J. Fluid Mech.4, 426–434.
Stewart, R. W. (1961): The wave drag of wind over water. J. Fluid Mech.,10, 189–194.
Sverdrup, H. U. andW. Munk (1947): Wind, sea and swell. Theory of relations for forecasting. U. S. Hydrogr. Office, Wash., Publ. No. 601.
Toba, Y. (1961): Drop production by bursting of air bubbles on the sea surface (III). Study by use of a wind flume. Memoirs, Coll. Sci., Univ. Kyoto, Ser. A,29, 313–344.
Toba, Y. andH. Kunishi (1970): Breaking of wind waves and the sea surface wind stress. J. Oceanog. Soc. Japan,26, 71–80.
Toba, Y., H. Kunishi, K. Nishi, S. Kawai, Y. Shimada andN. Shibata (1971): Study of the air-sea boundary processes at the Shirahama Oceanographic Tower Station. Disaster Prevention Res. Inst., Kyoto Univ., Annals,14B, 519–531 (in Japanese).
Wilson, B. W. (1965): Numerical prediction of ocean waves in the North Atlantic for December, 1959. Deutsche Hydro. Zeit.,18, 114–130.
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Toba, Y. Local balance in the air-sea boundary processes. Journal of the Oceanographical Society of Japan 28, 109–120 (1972). https://doi.org/10.1007/BF02109772
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DOI: https://doi.org/10.1007/BF02109772