Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-19T08:53:40.333Z Has data issue: false hasContentIssue false
  • English
  • Français

The growth of duration-limited wind waves

Published online by Cambridge University Press:  12 April 2006

Hisashi Mitsuyasu  and
Kunio Rikiishi
Hisashi Mitsuyasu
Affiliation:
Research Institute for Applied Mechanics, Kyushu University, Fukuoka, Japan
Kunio Rikiishi
Affiliation:
Research Institute for Applied Mechanics, Kyushu University, Fukuoka, Japan
Get access Rights & Permissions [Opens in a new window]

Abstract

Laboratory measurements have been made of the one-dimensional spectra of the duration-limited wind waves which are generated when a wind abruptly begins to blow over a water surface, maintaining a constant speed during the succeeding period of time. The duration dependences of the wave energy E and the spectral peak frequency fm determined from the measured spectra are slightly different from those inferred from the fetch dependences of these quantities. The normalized spectra of the duration-limited wind waves are also slightly different from those of fetch-limited wind waves: the concentration of the normalized spectral energy near the spectral peak frequency is smaller, in many cases, for the duration-limited wind waves than for fetch-limited wind waves. The exponential growth rates β of the duration-limited wind-wave spectra are generally larger than those of fetch-limited wind-wave spectra. Furthermore, both for the duration-limited wind waves and for fetch-limited wind waves the exponential growth rate has a behaviour which is different from the empirical formula of Snyder & Cox (1966). A new empirical formula for the growth rate of the wave spectrum is proposed, from which the empirical formula of Snyder & Cox (1966) can be derived as a special case. Agreement between the new empirical formula and the experimental results is satisfactory for fetch-limited wave spectra, but is confined to the qualitative features for the duration-limited wave spectra.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 85 , Issue 4 , 27 April 1978 , pp. 705 - 730
Copyright
© 1978 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Barnett, T. P. 1968 On the generation, dissipation, and prediction of ocean wind waves. J. Geophys. Res. 73, 513–529.Google Scholar
Colonel, J. M. 1966 Laboratory simulation of sea waves. Dept. Civil Engng, Stanford Univ. Tech. Rep. no. 65.Google Scholar
Deleonibus, P. S. & Simpson, L. S. 1972 Case study of duration-limited wave spectra observed at an open ocean tower. J. Geophys. Res. 77, 4555–4569.Google Scholar
Hasselmann, K. 1968 Weak interaction theory of ocean surface waves. In Basic Developments in Fluid Mechanics, 5.2. Academic Press.
Hasselmann, K. et al. 1973 Measurements of wind-wave growth and swell decay during the Joint North Sea Wave Project (JONSWAP). Dtsch. Hydrogr. Z. 12, 1–95.Google Scholar
Hidy, G. M. & Plate, E. J. 1966 Wind action on water standing in a laboratory channel. J. Fluid Mech. 26, 651–687.Google Scholar
Inoue, T. 1966 On the growth of the spectrum of a wind-generated sea according to a modified Miles-Phillips mechanism. Dept Met. Ocean., New York Univ. Rep. TR 66-6.Google Scholar
Iwata, N. & Tanaka, T. 1970 Spectral development of wind waves. Nat. Res. Center Disaster Prevention Japan Rep. no. 4, pp. 1–21 (in Japanese).Google Scholar
Larson, T. R. & Wright, J. W. 1975 Wind-generated gravity-capillary waves: laboratory measurements of temporal growth rates using microwave backscatter. J. Fluid Mech. 70, 417–436.Google Scholar
Liu, P. C. 1971 Normalized and equilibrium spectra of wind waves in Lake Michigan. J. Phys. Ocean. 1, 249–257.Google Scholar
Mitsuyasu, H. 1968 On the growth of the spectrum of wind-generated waves (I). Rep. Res. Inst. Appl. Mech., Kyushu Univ. 16, 459–482.Google Scholar
Mitsuyasu, H. 1969 On the growth of the spectrum of wind-generated waves (II). Rep. Res. Inst. Appl. Mech., Kyushu Univ. 17, 235–248.Google Scholar
Mitsuyasu, H. 1973 The one-dimensional wave spectra at limited fetch. Rep. Res. Inst. Appl. Mech., Kyushu Univ. 20, 37–53.Google Scholar
Mitsuyasu, H. & Honda, T. 1974 The high frequency spectrum of wind-generated waves. J. Ocean. Soc. Japan 30, 185–198.Google Scholar
Mitsuyasu, H. & Rikiishi, K. 1972 On the growth of duration-limited wave spectra. Ann. Conf. Ocean. Soc. Japan.Google Scholar
Mitsuyasu, H. et al. 1973 Laboratory simulation of ocean waves. Bull. Res. Inst. Appl. Mech., Kyushu Univ. no. 39, pp. 183–210 (in Japanese).Google Scholar
Mitsuyasu, H. et al. 1975 Observations of the directional spectrum of ocean waves using a cloverleaf buoy. J. Phys. Ocean. 5, 750–760.Google Scholar
Phillips, O. M. 1958 The equilibrium range in the spectrum of wind-generated ocean waves. J. Fluid Mech. 4, 426–434.Google Scholar
Pierson, W. J. & Moskowitz, L. 1964 A proposed spectral form for fully developed seas based on the similarity theory of S. A. Kitaigorodskii. J. Geophys. Res. 69, 518–5190.Google Scholar
Priestley, M. B. 1965 Evolutionary spectra and non-stationary processes. J. Roy. Statist. Soc. B 27, 204–237.Google Scholar
Priestley, M. B. 1966 Design relation for non-stationary processes. J. Roy. Statist. Soc. B 28, 228–240.Google Scholar
Priestley, M. B. 1967 Power spectral analysis of non-stationary random process. J. Sound Vib. 6, 86–97.Google Scholar
Ramamonjiarisoa, A. 1973 Sur l’évolution des spectres d’énergie des vagues de vent à fetchs courts. Mém. Soc. Roy. Sci. Liège 6, 47–66.Google Scholar
Rikiishi, K. & Mitsuyasu, H. 1976 Notes on the effects of data length and sampling interval upon the spectral estimates for wind waves. Rep. Res. Inst. Appl. Mech., Kyushu Univ. 23, 131–147.Google Scholar
Sell, W. & Hasselmann, K. 1972 Computation of nonlinear energy transfer for JONSWAP and empirical wind wave spectra. Rep. Inst. Geophys., Univ. Hamburg.Google Scholar
Shyder, R. L. 1965 The wind generation of ocean waves. Ph.D. dissertation, University of California, San Diego.
Snyder, R. L. & Cox, C. S. 1966 A field study of the wind generation of ocean waves. J. Mar. Res. 24, 141–178.Google Scholar
Taira, K. 1972 A field study of the development of wind-waves. Part 1. The experiment. J. Ocean. Soc. Japan 28, 187–202.Google Scholar
Tick, L. J. 1959 A non-linear random model of gravity waves I. J. Math. Mech. 8, 643–651.Google Scholar