Internal wave dispersion in deep oceans calculated by means of two-variable expansion techniques

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 the-k relationship for all frequencies. Taking advantage of the largeness of the nondimensional wavenumber (kS1), 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 desired-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.