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UBC Theses and Dissertations

Internal waves in a randomly stratified ocean McGorman, Robert Ernest


In this thesis we consider the propagation of internal waves in a rotating stratified unbounded ocean with randomly varying Brunt-Väisälä frequency, N. Keller's method is used to obtain the dispersion relation for the mean wave field correct to second order in Є when N is of the form N² = Nօ² (1+Єμ) where Nօ = constant, 0<Є²<< 1 and μ is a centered stationary random function of either depth or time separately. From the dispersion relation there are derived general formulas for the change in phase speed and growth or attenuation rates due to the random fluctuations μ . These formulas are dependent on the statistics of μ only through the autocovariance function. The phase speed change and growth rate formulas for depth dependent μ , which constitutes a model of the temperature and salinity fine-structure in the ocean, are presented for various special cases including the limiting cases of correlation lengths of μ that are long or short with respect to the wavelength. Observations at station P (50°N, 145° W) indicate that, to a good approximation, the μ are "white noise" and a close examination is made of the theoretical results for this case. With the aid of the station P data it is estimated that, although the phase speed changes are generally small, the amplitude of a wave increases (decreases) significantly in propagating upward (downward) through a depth of a few kilometers. In addition it is found that the mean effect of the depth dependent fluctuations μ is to increase the effective Brunt-Väisälä frequency, or "stiffen" the fluid. This may explain why some recently observed frequency spectra of internal waves do not exhibit a sharp cut-off at Nօ, the deterministic theoretical upper bound for the wave frequency. Finally an attempt is made to asses the range of validity of Keller's method in the context of the present problem.

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