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

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.