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The directional spectrum of ocean waves: an experimental investigation of certain predictions of the Miles–Phillips theory of wave generation

Published online by Cambridge University Press:  28 March 2006

A. W. R. Gilchrist
A. W. R. Gilchrist
Affiliation:
Institute of Oceanography, University of British Columbia
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Abstract

The directional spectrum of wind-driven surface waves has been measured under conditions of limited fetch, in order to check the predictions of the Phillips–Miles theory of wave generation (Miles 1960). The expression obtained for the directional spectrum in this theory involves the spectrum of the atmospheric pressure fluctuations, but it is possible to obtain theoretical estimates of the major features of the directional spectrum without knowledge of the pressures. Specifically, it is possible to predict the frequency at which the power spectrum should peak, and, for the higher frequencies, the range of azimuth over which high spectral values should be observed; for the lower frequencies the theory indicates a bimodal distribution in azimuth (Phillips's resonance waves), and gives the angle of travel relative to the wind as a function of frequency.

The results of the measurements are in fairly good agreement with the theoretical predictions for the higher frequencies. The asymmetry of the fetch results in the prediction that the waves will travel at an angle to the wind which varies with frequency, and this was observed. The range of azimuth over which the spectral density is high is also close to the theoretical prediction. For the low frequencies the bimodal distribution was not observed: the waves were found to have a single predominant direction of travel at each frequency. However, this direction conformed closely to that of one of the two wave trains predicted by Phillips, and its variation with frequency was also that given by the theory. There is reason to suppose that the peculiarities of the experimental site may be responsible for the absence of the second wave train, especially as it would be difficult to account for the observed effects on any basis other than that of Phillips's theory.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 25 , Issue 4 , August 1966 , pp. 795 - 816
Copyright
© 1966 Cambridge University Press

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References

Barber, N. F. 1958 Optimum arrays for direction finding. N.Z. J. Sci. 1, 35–51.Google Scholar
Barber, N. F. 1959 A proposed method of surveying the wave state of the open ocean. N.Z. J. Sci. 2, 99–108.Google Scholar
Benjamin, T. B. 1959 Shearing flow over a wavy boundary. J. Fluid Mech. 6, 161–205.Google Scholar
Burling, R. W. 1959 The spectrum of waves at short fetches. Dt. Hydrogr. Z. 12, 45–64, 96–117.Google Scholar
Conte, S. D. & Miles, J. W. 1959 On the numerical integration of the Orr — Sommerfeld equation. J. Soc. Indust. Appl. Math., 7, no. 4.Google Scholar
Hamblin, P. 1965 Cup anemometer wind observations over the sea. M.Sc. dissertation, University of British Columbia.
Kinsman, B. 1960 Surface waves at short fetch and low wind speed. Tech. Rep. no. 19, Chesapeake Bay Institute.Google Scholar
Kinsman, B. 1965 Wind Waves. New Jersey: Prentice-Hall Inc.
Lighthill, M. J. 1962 Physical interpretation of the mathematical theory of wave generation by wind. J. Fluid Mech. 14, 385–398.Google Scholar
Miles, J. W. 1957 On the generation of surface waves by shear flows. J. Fluid Mech. 3, 185–204.Google Scholar
Miles, J. W. 1960 On the generation of surface waves by turbulent shear flows. J. Fluid Mech. 7, 469–478.Google Scholar
Phillips, O. M. 1957 On the generation of waves by turbulent wind. J. Fluid Mech. 2, 417–445.Google Scholar
Phillips, O. M. 1958a Wave generation by turbulent wind over a finite fetch. Proc. 3rd U.S. Congr. Appl. Mech., pp. 785–789.Google Scholar
Phillips, O. M. 1958b The equilibrium range in the spectrum of wind-generated ocean waves. J. Fluid Mech. 4, 426–434.Google Scholar
Phillips, O. M. 1960 On the dynamics of unsteady gravity waves of finite amplitude. J. Fluid Mech. 9, 193–217.Google Scholar
Phillips, O. M. & Katz, E. J. 1961 The low frequency components of the spectrum of wind-generated waves. J. Mar. Res. 19, 57–69.Google Scholar
Ursell, F. 1956 Article in Surveys in Mechanics, pp. 216–249. Cambridge University Press.