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Wind-generated gravity-capillary waves: laboratory measurements of temporal growth rates using microwave backscatter

Published online by Cambridge University Press:  29 March 2006

T. R. Larson  and
J. W. Wright
T. R. Larson
Affiliation:
Ocean Sciences Division, Naval Research Laboratory, Washington, D.C. 20375 Present address: Ball Brothers Research Corp., P.O. Box 1062, Boulder, Colorado 80303.
J. W. Wright
Affiliation:
Ocean Sciences Division, Naval Research Laboratory, Washington, D.C. 20375
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Abstract

The growth rates of wind-induced water waves at fixed fetch were measured in a laboratory wave tank using microwave backscatter. The technique strongly filters out all wavenumber component pairs except for a narrow window at the resonant Bragg scattering conditions. For these waves the spectral amplitude was measured as a function of the time after a fixed wind was abruptly started. The radars were aligned to respond to waves travelling in the downwind direction at wavelengths of 0·7-7 cm. Wind speeds ranged from 0·5 to 15 m/s. Fetches of 1·0, 3·0 and 8·4 m were used. In every case, the spectral amplitude initially grew at a single exponential rate β over several orders of magnitude, and then abruptly ceased growing. No dependence of the growth rate on fetch was observed. For all wavelengths and wind speeds the data can be fitted by \[ \beta (k,u_{*},{\rm fetch})=f(k)\,u^n_{*}, \] with n = 1·484 ± 0·027. Here u* is the friction velocity obtained from vertical profiles of mean horizontal velocity. For each wind speed, f(k) had a relative maximum near k = kn ≃ 3·6 cm−1. Rough estimates of β/2ω, where ω is the water wave frequency, and of the wind stress supported by short waves indicate that the observed growth rates are qualitatively very large. These waves are tightly coupled to the wind, and play a significant role in the transfer of momentum from wind to water.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 70 , Issue 3 , 12 August 1975 , pp. 417 - 436
Copyright
© 1975 Cambridge University Press

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References

Duncan, J. R., Keller, W. C. & Wright, J. W. 1974 Fetch and windspeed dependence of Doppler spectra. Radio Sci. 9, 809–819.Google Scholar
Gottifredi, J. C. & Jameson, G. J. 1970 The growth of short waves on liquid surfaces under the action of a wind. Proc. Roy. Soc. A 319, 373–397.Google Scholar
Hasselmann, K. 1968 Weak interaction theory of ocean surface waves. In Basic Developments in Fluid Mechanics, 5.2. Academic.
Hidy, G. M. & Plate, E. J. 1966 Wind action on water standing in a laboratory channel. J. Fluid Mech. 26, 651–687.Google Scholar
Hsu, E. Y. & Yu, H. U. 1970 Laboratory investigation on air-sea interaction. Proc. 8th Symp. on Naval Hydrodyn., paper ARC-179. Office of Naval Research.
Keller, W. C., Larson, T. R. & Wright, J. W. 1974 Mean speeds of wind waves at short fetch. Radio Sci. 9, 1091–1100.Google Scholar
Lai, R. J. & Shemdin, O. H. 1971 Laboratory investigation of air turbulence above simple water waves. J. Geophys. Res. 76, 7334–7350.Google Scholar
Mitsuyasu, H. 1969 On the growth of the spectrum of wind generated waves (II). Rep. Res. Inst. Appl. Mech., Kyushu University, vol. 12, no. 59. Fukuoka, Japan.Google Scholar
Stewart, R. H. 1970 Laboratory studies of the velocity field over deep-water waves. J. Fluid Mech. 42, 733–754.Google Scholar
Sutherland, A. J. 1968 Growth of spectral components in a wind-generated wave train. J. Fluid Mech. 33, 545–560.Google Scholar
Valenzuela, G. R. & Laing, M. B. 1972 Nonlinear energy transfer in gravity-capillary wave spectra, with applications. J. Fluid Mech. 54, 507–520.Google Scholar
Wilson, W. S., Banner, M. L., Flower, R. J., Michael, J. A. & Wilson, D. G. 1973 Wind-induced growth of mechanically generated water waves. J. Fluid Mech. 58, 435–460.Google Scholar
Wright, J. W. 1966 Backscattering from capillary waves with application to sea clutter. I.E.E.E. Trans. Antennas Propagat. AP14, 749–754.Google Scholar
Wright, J. W. 1968 A new model for sea clutter. I.E.E.E. Trans. Antennas Propagat. AP16, 217–223.Google Scholar
Wright, J. W. & Keller, W. C. 1971 Doppler spectra in microwave scattering from wind waves. Phys. Fluids, 14, 466–474.Google Scholar