An analytical study is made of linearized internal wave dispersion relation in a density-stratified deep ocean with aN(z) profile which contains turning points. Principal emphasis is placed on obtaining theΩ-k relationship for all frequencies. Taking advantage of the largeness of the nondimensional wavenumber (kS?1), the mathematical tool to attack the governing Sturm-Liouville equation is a combination of the two-variable expansion (valid far away from the turning point) and the limit-process expansion (valid in the neighborhood of the turning point). The matching conditions for these two expansion schemes provide the desiredΩ-k relationship. A numerical example of this method demonstrates satisfactory agreement with the results obtained by the strict analytical solution and the multi-layered matrix numerical model.
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