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Statistical characteristics of individual waves in laboratory wind waves I. Individual wave spectra and similarity structure

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Abstract

Statistical characteristics of individual waves in laboratory wind waves have been studied by use of a wind-wave tunnel. The individual waves are defined by actual undulations of the water surface at any instant, and are characterized by concentrated shearing stress and strong vorticity at their crests. A conspicuous self-similarity structure is found in the individual wave field. The similarity manifests itself as a simple spectral form, and as the statistical 3/2-power law between nondimensional wave height and wave period, and further as the -1/2-power relationship between nondimensional phase speed and frequency, for waves of the high frequency side. The normalized energy spectrum, specially defined for individual waves, has a form practically equivalent to the traditional spectrum for component waves in the main frequency range from 0.7 to 1.5 in the frequency normalized by the peak frequency, but does not have secondary peaks at harmonics. The phase speed of individual waves also coincides with that of component waves in the main frequency range.

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References

  • Banner, M. L. andO. M. Phillips (1974): On the incipient breaking of small scale waves. J. Fluid Mech.,65, 647–656.

    Google Scholar 

  • Banner, M. L. andW. K. Melville (1976): On the separation of air flow over water waves. J. Fluid Mech.,77, 825–842.

    Google Scholar 

  • Chang, P. C., E. J. Plate andG. M. Hidy (1971): Turbulent air flow over the dominant component of wind-generated water waves. J. Fluid Mech.,47, 183–208.

    Google Scholar 

  • Cox, C. S. (1958): Measurements of slopes of high-frequency wind waves. J. Mar. Res.16, 199–225.

    Google Scholar 

  • Hidy, G. M. andE. J. Plate (1965): Wind action on water standing in a laboratory channel. J. Fluid Mech.,26, 651–687.

    Google Scholar 

  • Kato, H. andK. Tsuruya (1974): On the phase velocity of component waves of wind waves (in Japanese). Proc. 21st Japanese Conf. Coast. Eng., 255–259.

  • Kawai, S. (1981): Visualization of air-flow separation over wind-wave crests under moderate wind. Boundary-Layer Meteorol.,21, 93–104.

    Google Scholar 

  • Kawai, S., K. Okada andY. Toba (1977): Support of the three-seconds power law and thegu*σ−4-spectral form for growing wind waves with field observational data. J. Oceanogr. Soc. Japan,33, 137–150.

    Google Scholar 

  • Kuo, Y.Y., H. Mitsuyasu andA. Masuda (1979): Experimental study on the phase velocity of wind waves. Part 1. Laboratory wind waves. Rep. Res. Inst. Appl. Mech., Kyushu Univ.,27, 1–19.

    Google Scholar 

  • Lake, B., H. Yuen, H. Rungaldier andW. Ferguson (1977): Nonlinear deep-water waves: theory and experiment. Part 2. Evolution of a continuous wave train. J. Fluid Mech.,83, 49–74.

    Google Scholar 

  • Lake, B. andH. Yuen (1978): A new model for nonlinear wind waves. Part 1. Physical model and experimental evidence. J. Fluid Mech.,88, 33–62.

    Google Scholar 

  • Masuda, A., Kuo, Y. Y. andH. Mitsuyasu (1979): On the dispersion relation of random gravity waves. Part 1. Theoretical framework. J. Fluid Mech.,92, 717–730.

    Google Scholar 

  • Mitsuyasu, H., Y. Y. Kuo andA. Masuda (1979): On the dispersion relation of random gravity waves. Part 2. An experiment. J. Fluid Mech.,92, 731–749.

    Google Scholar 

  • Mollo-christensen andA. Ramamonjiarisoa (1978): Modelling the presence of wave groups in a random wave field. J. Geoph. Res.,83, 4117–4122.

    Google Scholar 

  • Neumann, G. (1952): On wind generated ocean waves with special reference to the problem of wave forecasting. Dept. Met. and Oceanogr., New York Univ. Prepared for Office of Naval Res., 136 pp.

  • Okuda, K. (MS): Internal flow structure of short wind waves. Parts I, II and III. Submitted to J. Oceanogr. Soc. Japan.

  • Okuda, K., S. Kawai, M. Tokuda andY. Toba (1976): Detailed observation of the wind-exerted surface flow by use of flow visualization method. J. Oceanogr. Soc. Japan,32, 51–62.

    Google Scholar 

  • Okuda, K., S. Kawai andY. Toba (1977): Measurement of skin friction distribution along the surface of wind waves. J. Oceanogr. Soc. Japan,33, 190–198.

    Google Scholar 

  • Phillips, O. M. (1958): The equilibrium range in the spectrum of wind-generated waves. J. Fluid Mech.,4, 426–434.

    Google Scholar 

  • Phillips, O. M. andM. L. Banner (1974): Wave breaking in the presence of wind drift and swell. J. Fluid Mech.,66, 625–640.

    Google Scholar 

  • Pierson, W. J., Jr. (1952): A unified mathematical theory for the analysis, propagation and refraction of strom generated ocean surface waves. Parts I and II. Dept. Met. and Oceanogr., New York Univ. Prepared for Beach Erosion Board and Office of Naval Res., 461 pp.

  • Ramamonjiarisoa, A. (1974): Contribution à l'étude de la structure statistique et des mécanismes de génération des vagues de vent. Thèse à L'Université de Provence (Inst. Méch. Stat. de la Turbulence, No. A.O. 10023), 160 pp.

  • Rikiishi, K. (1978): A new method for measuring the directional wave spectrum. Part II. Measurement of the directional spectrum and phase velocity of laboratory wind waves. J. Phys. Oceanogr.,8, 519–529.

    Google Scholar 

  • Sverdrup, H. U. andW. H. Munk (1947): Wind, sea and swell: Theory of relations for forecasting. U.S. Navy Hydrogr. Office, Wash., Pub. No. 601, 44 pp.

  • Toba, Y. (1972): Local balance in the air-sea boundary processes. I. On the growth process of wind waves. J. Oceanogr. Soc. Japan,28, 108–120.

    Google Scholar 

  • Toba, Y. (1973): Local balance in the air-sea boundary processes. III. On the spectrum of wind waves. J. Oceanogr. Soc. Japan,29, 209–220.

    Google Scholar 

  • Toba, Y. (1978): Stochastic form of the growth of wind waves in a single parameter representation with physical implications. J. Phys. Oceanogr.,8, 494–507.

    Google Scholar 

  • Toba, Y. (1979): Study on wind waves as a strongly nonlinear phenomenon. Twelfth Symp. on Naval Hydrodyn., Nat. Acad. of Sci., Wash., D. C., 529–540.

  • Toba, Y., M. Tokuda, K. Okuda andS. Kawai (1975): Forced convection accompanying wind waves. J. Oceanogr. Soc. Japan,31, 192–198.

    Google Scholar 

  • Yefimov, V. V., Yu. P. Solov'yev andG.N. Khristoforov (1972): Observational determination of the phase velocities of spectral components of wind waves. Izv., Atmos. Ocean. Phys.,8, 246–251.

    Google Scholar 

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Author notes

  1. Masayuki Tokuda

    Present address: Institute of Coastal Oceanography, National Research Center for Disaster Prevention, Science and Technology Agency, 254, Hiratsuka, Japan

Authors and Affiliations

  1. Geophysical Institute, Tohoku University, 980, Sendai, Japan

    Masayuki Tokuda & Yoshiaki Toba

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  1. Masayuki Tokuda
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  2. Yoshiaki Toba
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Tokuda, M., Toba, Y. Statistical characteristics of individual waves in laboratory wind waves I. Individual wave spectra and similarity structure. Journal of the Oceanographical Society of Japan 37, 243–258 (1981). https://doi.org/10.1007/BF02070579

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  • DOI: https://doi.org/10.1007/BF02070579

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