Abstract
Exact solutions for standing internal waves are obtained in a region bounded by horizontal and inclined planes in the linear, ideal stratified fluid approximation at a constant Brent-Vaisala frequency. The solutions are expressed in terms of the Macdonald functions and their derivatives. Nonuiform and uniform asymptotics are also constructed in the case of a small slope of the lower plane. The latter asymptotics are expressed in terms of either the Airy function or the Macdonald function. The exact and asymptotic solutions are numerically compared.
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