Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-20T05:40:58.576Z Has data issue: false hasContentIssue false
  • English
  • Français

Experimental study of the influence of wind on Benjamin–Feir sideband instability

Published online by Cambridge University Press:  21 April 2006

Larry F. Bliven ,
Norden E. Huang  and
Steven R. Long
Larry F. Bliven
Affiliation:
Oceanic Hydrodynamics, Inc., Salisbury, MD 21801 Present address: NASA Goddard Space Flight Center, Wallops Flight Facility, Wallops Island, VA 23337.
Norden E. Huang
Affiliation:
NASA Goddard Space Flight Center, Greenbelt, MD 20771
Steven R. Long
Affiliation:
NASA Goddard Space Flight Center, Wallops Flight Facility, Wallops Island, VA 23337
Get access Rights & Permissions [Opens in a new window]

Abstract

A laboratory investigation of the influence of wind on the evolution of mechanically generated regular (m.g.r.) waves is reported. Surface elevation measurements were made at four fetches for steep (0.1 < $\overline{ak}$ < 0.2, 2 Hz) m.g.r. waves, moderate (15 < u* < 25 cm s−1, 3–6 Hz) wind waves, and combinations of the m.g.r. and wind waves. The m.g.r. wave spectra exhibit Benjamin—Feir sidebands that grow exponentially with fetch and whose growth rate increases as the initial wave steepness increases. As fetch increases for the wind cases, total energy increases and the frequency of the spectral maximum downshifts, but no spectral lines representing Benjamin—Feir sidebands were detected even though the wave steepness and fetch were similar to the m.g.r. waves whose spectra displayed sidebands. As wind speed increased over the m.g.r. waves, sideband magnitude, sideband growth rate and low-frequency perturbation components associated with the instability mechanism were reduced.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 162 , January 1986 , pp. 237 - 260
Copyright
© 1986 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

Alber, I. E. 1978 The effects of randomness on the stability of two-dimensional surface wave trains. Proc. R. Soc. Lond. A 363, 525–546.Google Scholar
Banner, M. L. & Phillips, O. M. 1974 On the incipient breaking of small scale waves. J. Fluid Mech. 65, 647–656.Google Scholar
Benjamin, T. B. & Feir, J. E. 1967 The disintegration of wave trains on deep water. Part 1. Theory. J. Fluid Mech. 27, 417–430.Google Scholar
Crawford, D. P., Saffman, P. G. & Yuen, H. C. 1980 Evolution of a random inhomogeneous field of nonlinear gravity waves. Wave Motion 2, 1–16.Google Scholar
Crawford, D. R., Lake, B. M., Saffman, P. G. & Yuen, H. C. 1981 Stability of weakly nonlinear deep-water waves in two and three dimensions. J. Fluid Mech. 105, 177–191.Google Scholar
Hasselmann, D. E. 1979 The high wave number instabilities of a Stokes wave. J. Fluid Mech. 93, 491–500.Google Scholar
Hatori, M. 1984 Nonlinear properties of laboratory wind waves at energy containing frequencies. J. Ocean. Soc. Japan 40, 1–18.Google Scholar
Hatori, M. & Toba, Y. 1983 Transition of mechanically generated regular waves to wind waves under the action of wind. J. Fluid Mech. 130, 397–409.Google Scholar
Hatori, M., Tokuda, M. & Toba, Y. 1981 Experimental study on strong interactions between regular waves and wind waves- I. J. Ocean. Soc. Japan 37, 111–119.Google Scholar
Huang, N. E. & Long, S. R. 1980 An experimental study of the surface elevation probability distribution and statistics of wind generated waves. J. Fluid Mech. 101, 179–200.Google Scholar
Huang, N. E., Bliven, L. F., Long, S. R. & Dbleonibus, P. S. 1985 A study of the relationship among wind, wave and the drag coefficient. Submitted to J. Geophys. Res.Google Scholar
Hunt, J. N. 1952 Viscous damping of waves over an inclined bed in a channel of finite width. Houitte Blanche, 7, 836–842.Google Scholar
Imai, Y., Hatori, M., Tokuda, M. & Toba, Y. 1981 Experimental study on strong interaction between regular waves and wind waves - II. Tohoku Geophys. J. 28, 87–103.Google Scholar
Jackson, F. C. 1984 Some case studies of ocean wave physical processes utilizing the GSFC airborne radar ocean wave spectrometer. In Remote Sensing of Oceans and Troposphere from Air and Space Platforms, pp. 233–245. NASA Conference Pub. 2303.
Lake, B. M. & Yuen, H. C. 1977 A note on some nonlinear water-wave experiments and the comparison of data with theory. J. Fluid Mech. 83, 75–81.Google Scholar
Lake, B. M. & Yuen, H. C. 1978 A new model for nonlinear wind waves. Part 1. Physical model and experimental evidence. J. Fluid Mech. 88, 33–62.Google Scholar
Lake, B. M., Yuen, H. C., Runglandier, H. & Ferguson, W. E. 1977 Nonlinear deep-water waves: theory and experiment. Part 2. Evolution of a continuous wave train. J. Fluid Mech. 83, 49–74.Google Scholar
Lamb, H. 1932 Hydrodynamics. Cambridge University Press.
Larson, T. R. & Wright, J. T. 1975 Wind-generated gravity-capillary waves: Laboratory measurements of temporal growth rates using microwave backscatter. J. Fluid Mech. 70, 417–436.Google Scholar
Longuet-Higgins, M. S. 1978 The instabilities of gravity waves of finite amplitude in deep water. Proc. R. Soc. Lond. A 360, 471–505.
Longuet-Higgins, M. S. 1980 Modulation of the amplitude of steep wind waves. J. Fluid Mech. 99, 705–713.Google Scholar
Mclean, J. W. 1982a Instabilities of finite-amplitude water waves. J. Fluid Mech. 114, 315–330.Google Scholar
Mclean, J. W. 1982b Instabilities of finite-amplitude gravity waves on water of finite depth. J. Fluid Mech. 114, 331–341.Google Scholar
Mclean, J. W., Ma, Y. C., Martin, D. U., Saffman, P. G. & Yuen, H. C. 1981 Three-dimensional instability of finite amplitude water waves. Phys. Rev. Lett. 46, 817–820.Google Scholar
Melville, W. K. 1982 The instability and breaking of deep-water waves. J. Fluid Mech. 115, 165–185.Google Scholar
Miles, J. W. 1967 Surface-wave damping in closed basins. Proc. R. Soc. Lond. A 297, 459–475.Google Scholar
Mitsuyasu, H. 1966 Interactions between water waves and wind (I). Rep. Res. Inst. Appl. Mech., Kyushu University 14, 67–88.Google Scholar
Mitsuyasu, H. & Honda, T. 1982 Wind-induced growth of water waves. J. Fluid Mech. 123, 425–442.Google Scholar
Mollo-Christensen, E. & Ramamonjiarasoa, A. 1982 Subharmonic transition and group formation in a wind wave field. J. Geophys. Res. 87, 5599–5717.Google Scholar
Phillips, O. M. 1960 On the dynamics of unsteady gravity waves of finite amplitude. Part I. J. Fluid Mech. 9, 193–217.Google Scholar
Phillips, O. M. & Banner, M. L. 1974 Wave breaking in the presence of wind drift and swell. J. Fluid Mech. 66, 625–640.Google Scholar
Plant, W. J. 1982 A relationship between wind stress and wave slope. J. Geophys. Res. 87, 1961–1967.Google Scholar
Regier, L. A. & Davis, R. E. 1977 Observations of the power and directional spectrum of ocean surface waves. J. Mar. Res. 35, 433–452.Google Scholar
Shemdin, O. H. & Hsu, E. Y. 1967 Direct measurement of aerodynamic pressure above a simple progressive gravity wave. J. Fluid Mech. 30, 403–416.Google Scholar
Snyder, R. L., Dobson, F. W., Elliott, J. A. & Long, R. B. 1981 Array measurements of atmospheric pressure fluctuations above gravity waves. J. Fluid Mech. 102, 1–59.Google Scholar
Su, M. Y., Bergin, M., Marler, P. & Myrick, R. 1982 Experiments on nonlinear instabilities and evolution of steep gravity-wave trains. J. Fluid Mech. 124, 45–72.Google Scholar
Su, M. Y. 1982 Three-dimensional deep-water waves. Part 1. Experimental measurements of skew and symmetric wave patterns. J. Fluid Mech. 124, 73–108.Google Scholar
Thompson, T. W., Weissman, D. E. & Gonzalez, F. I. 1983 L-band radar back-scatterdependence upon surface wind stress: a summary of new SEASAT-1 and aircraft observations. J. Geophys. Res. 88, 1727–1735.
Tsimring, L. Sh. 1983 Induced scattering of surface wind waves. Izv. Acad. Nauk 8SSR Atmos. and Ocean Phys. 19, 47–50.Google Scholar
Walsh, E. J., Hancock, D. W., Hines, D. E. & Kenney, J. E. 1982 Development of the fetch-limited directional wave spectrum. In Oceans ′82 Conference Record, pp. 820–825. Marine Tech. Soc., Wash., D.C.
Wu, H. Y., Hsu, E. Y. & Street, R. L. 1977 The energy transfer due to air-input, non-linear wave-wave interactions and white cap dissipation associated with wind-generated waves. Tech. Rep. 207, pp. 1–158. Stanford Univ., Stanford, CA.Google Scholar
Wu, H. Y., Hsu, E. Y. & Street, R. L. 1979 Experimental study of nonlinear wave-wave interaction and white-cap dissipation of wind-generated waves. Dyn. Almas. Oceans 3, 55–78.Google Scholar
Zakharov, Y. E. 1968 Stability of periodic waves of finite amplitude on the surface of a deep fluid. J. Appl. Mech. Tech. Phys. 2, 190–194.Google Scholar