UBC Theses and Dissertations
Field observations of frequency domain statistics and nonlinear effects in wind-generated ocean waves Garrett, John Frederick
The objectives of this study were to show how far the statistical assumptions usually made when dealing with the theory of continuum nonlinear interactions were relevant to the case of fetch limited wind generated wave fields, and to observe some consequence of the nonlinearity as a check on the other results. The usual assumption, that the first order wave field is composed of Gaussian random wave components stationary in space and time, is shown to require that the real and imaginary parts of the complex Fourier coefficients of the observed surface elevation at a fixed point are normally distributed with zero mean, and that the real and imaginary parts of the complex coefficient for a given frequency band are independent. Coefficients from different frequency bands must also be independent. Four wave fields were observed and described in terms of their power spectra and frequency-wavenumber spectra. Although their directional spectra were found to be strongly influenced by the particular arrangement of fetch at the observing site, their power spectra agreed well with both theory and other observations, at least after correction for the observed currents. This agreement is important from the point of view of establishing the relevance of the results of this work to other field situations. Observations of the frequency domain statistics for these four wave fields indicated that the assumptions of stationarity and of normal distributions for the Fourier coefficients were correct to good accuracy. Two methods were tried for observing direct evidence of nonlinear effects in the wave field. One of these, the attempt to detect products of second order interactions in the frequency-wavenumber spectra, failed because of the poor resolution of the array of sensors. The other, the bispectrum, succeeded, with reasonable agreement being achieved between the observed bispectra and bispectra predicted from the power spectra using the results of perturbation of theory.
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