Wave Propagation in the Ice-Covered Ocean Wave Guide and Operator Polynomials
Wave propagation in a 2D ocean wave guide covered by a thin ice layer is considered. Various models of ice cover are used (pack ice, solid ice, ice with surface tension, etc.), and the eigenfunctions of the transverse cross—section are analyzed. For each model of ice, an operator polynomial equation for eigenfunctions is derived. It is proved that, for non—critical frequencies, the eigenfunctions form a basis in a suitable Hilbert space. At the critical frequencies, a chain of associated functions might appear. The method is based on some (known) results from the abstract operator theory and some orthogonality relations for eigenfunctions.
KeywordsSelfadjoint Operator Riesz Basis Wave Guide Orthogonality Relation Liouville Problem
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