Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-22T07:09:39.925Z Has data issue: false hasContentIssue false
  • English
  • Français

Growth and equilibrium of short gravity waves in a wind-wave tank

Published online by Cambridge University Press:  12 April 2006

W. J. Plant  and
J. W. Wright
W. J. Plant
Affiliation:
Ocean Sciences Division, Naval Research Laboratory, Washington D.C. 20375
J. W. Wright
Affiliation:
Ocean Sciences Division, Naval Research Laboratory, Washington D.C. 20375
Get access Rights & Permissions [Opens in a new window]

Abstract

Temporal and spatial development of short gravity waves in a linear wind-wave tank has been measured for wind speeds up to 15 m/s using microwave Doppler spectrometry. Surface waves of wavelength 4·1 cm, 9·8 cm, 16·5 cm and 36 cm were observed as a function of fetch, wind speed and wind duration. The waves grew exponentially from inception until they were about 10 dB smaller than their maximum height, and the temporal growth and spectral transport (spatial growth) rates were about equal when the wave amplitude was sufficiently small. The amplitude of a short gravity wave of fixed wavelength was found to decrease substantially at winds, fetches or durations greater than those at which the short gravity wave was approximately the dominant wave; such phenomena are sometimes referred to as overshoot. The dominant short gravity wave was observed to reach a maximum amplitude which depended only on wavelength, showing that wave breaking induced by an augmented wind drift cannot be the primary limitation to the wave height. Waves travelling against the wind were observed for wavelengths of 9·8 cm, 16·5 cm and 36 cm and were shown to be generated by the air flow at low wind speeds.

Measured initial growth rates for 16·5 cm and 36 cm waves were greater than expected, suggesting the existence of a growth mechanism in addition to direct transfer from the wind via linear instability of the boundary-layer flow. Initial temporal growth rates and spectral transport rates were compared to yield an experimental determination of the magnitude of the sum of nonlinear interactions and dissipation in short gravity waves. If the steady-state energy input in the neighbourhood of the dominant wave occurs at the measured initial temporal growth rates, then most of the energy input is locally dissipated; relatively little is advected away. Calculated gravitycapillary nonlinear energy transfer rates match those determined from initial growth rates for 9·8 cm waves and the gravity–capillary wave interaction continues to be significant for waves as long as 16·5 cm. For longer waves the gravity–capillary interaction is too small to bring the short gravity wave to a steady state when it is the dominant wave of the wind-wave system.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 82 , Issue 4 , 14 October 1977 , pp. 767 - 793
Copyright
© 1977 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

Banner, M. L. & Phillips, O. M. 1974 On the incipient breaking of small scale waves. J. Fluid Mech. 65, 647–657.Google Scholar
Barrick, D. E. 1972 Remote sensing of sea state by radar. In Remote Sensing of the Troposphere (ed. V. E. Derr), chap. 12, pp. 12–31. Washington: U.S. Govt. Printing Office.CrossRefGoogle Scholar
Beard, C. I. 1963 Coherent and incoherent scattering of microwaves from the ocean. I.R.E. Trans. AP 9, 470–483.Google Scholar
Beard, C. I. 1967 Behaviour of non-Rayleigh statistics of microwave forward scatter from a random water surface. I.E.E.E. Trans. AP 15, 649–657.Google Scholar
Chang, P. L., Plate, E. J. & Hidy, G. M. 1971 Turbulent air flow over the dominant component of wind-generated water waves. J. Fluid Mech. 47, 183–208.Google Scholar
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 Press.Google Scholar
Hasselmann, K. 1971 Determination of ocean wave spectra from Doppler radio returns from the sea surface. Nat. Phys. Sci. 299, 16–17.Google Scholar
Hasselmann, K. Et Al. 1973 Measurements of wind-wave growth and swell decay. Joint North Sea Wave Project (JONSWAP), Dtsches Hydrograph. Inst., Hamburg.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
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
Larson, T. R. & Wright, J. W. 1974 Wind wave studies. Part 2 - the parabolic antenna as a wave probe. N.R.L. Rep. no. 7850, pp. 1–20.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.CrossRefGoogle Scholar
Miles, J. W. 1959a On the generation of surface waves by shear flows. Part 2. J. Fluid Mech. 6, 568–582.Google Scholar
Miles, J. W. 1959b On the generation of surface waves by shear flows. Part 3. Kelvin-Helmholtz instability. J. Fluid Mech. 6, 583–598.Google Scholar
Miles, J. W. 1962 On the generation of surface waves by shear flows. Part 4. J. Fluid Mech. 13, 433–448.Google Scholar
Mitsuyasu, H. & Honda, T. 1975 The high frequency spectrum of wind generated waves. Rep. Res. Inst. Appl. Mech. 12, 327–355.Google Scholar
Phillips, O. M. 1957 On the generation of waves by turbulent wind. J. Fluid Mech. 2, 417–445.Google Scholar
Valenzuela, G. R. 1970 The effective reflection coefficients in forward scatter from a dielectric slightly rough surface. Proc. I.E.E.E. 58, 1279.Google Scholar
Valenzuela, G. R. 1974 The effect of capillarity and resonant interactions on the second order Doppler spectrum of radar sea echo. J. Geophys. Res. 79, 5031–5037.Google Scholar
Valenzuela, G. R. 1976 The growth of gravity-capillary waves in a coupled shear flow. J Fluid Mech. 76, 229–250.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
Valenzuela, G. R. & Wright, J. W. 1976 Growth of waves by modulated wind stress. J. Geophys. Res. 81, 5795–5796.Google Scholar
Wright, J. W. 1966 Backscattering from capillary waves with application to sea clutter. I.E.E.E. Trans. AP 14, 749–754.Google Scholar
Wright, J. W. 1976 The wind drift and wave breaking. J. Phys. Ocean. 6, 402–405.Google Scholar
Wright, J. W. 1977 Detection of ocean waves by microwave radar: the modulation of short gravity capillary waves. Boundary-Layer Met. (to appear).Google Scholar
Wright, J. W. & Keller, W. C. 1971 Doppler spectra in microwave scattering from wind waves. Phys. Fluids 14, 466–474.Google Scholar