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

The directional spectrum of wind-driven surface waves has been measured under conditions of well-defined fetch in Burrard Inlet, which separates the cities of Vancouver and West Vancouver in British Columbia, Canada, and extends seaward to Howe Sound and Strait of Georgia. This investigation was undertaken to check the predictions of two recent theories concerning the mechanism by which the wind acts on the water surface to produce waves. These theories, one due to Phillips and the other to Miles, were first advanced in 1957, and have since been combined into a unified theory by the latter author. The unified theory yields an expression for the directional spectrum of the waves in terms of wind speed and direction, the duration of the wind (or alternatively the fetch available), and the two-dimensional spectrum of the turbulent pressure fluctuations in the wind. The fetch is the distance from the shore to the point of observation. The pressure spectrum has never been measured; it appears, indeed, that even single point pressure measurement is a matter of considerable difficulty. However, it is possible even without knowledge of the pressures, to obtain theoretical estimates of the major features of the directional spectrum. Thus, given the wind speed and direction, and the fetch as a function of azimuth, it is possible to predict the frequency at which the power spectrum should peak; and for this and higher frequencies to predict the range of azimuth over which high spectral values should be observed. Further, when the fetch is small, so that the waves are not fully developed, there is a range of frequencies below that of the spectral peak in which only Phillips’ resonance waves should be present. For these, the theory indicates a bimodal distribution in azimuth, and it also predicts the angle of travel relative to the wind as a function of frequency. The results of the measurements made in the present investigation are in fairly good agreement with the theoretical predictions for the higher frequencies, from the frequency of the peak of the power spectrum up (referred to here as the Miles’ regime; the lower frequencies will be referred to as the Phillips' regime). The asymmetrical fetch results in the prediction that these 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 expectation. In the Phillips’ regime, 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. It is suggested that peculiarities of the experimental site may be responsible for the absence of the second wave train, since the observed effects would be difficult to account for on any basis other than that of Phillips’ theory. In order to demonstrate the physical reality of resonance waves in an absolutely decisive way it would be necessary to measure a spectrum exhibiting the characteristic bimodal form. Further investigations at a more suitable site are planned by the Institute of Oceanography, University of British Columbia, (IOUBC) to determine whether this second wave train is actually present.

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