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Advisor(s)
Abstract(s)
We consider trapping of linear water waves by a submerged horizontal cylinder in a three-layer fluid topped by a rigid lid. Trapped modes correspond to time harmonic oscillations with finite energy of the fluid surrounding a submerged structure and can be found as eigenfunctions of a certain spectral boundary-value problem. Our main result is a geometric condition relating the cross sections of the submerged parts of the obstacles and the line integrals along the parts of the interfaces pierced by the obstacles and guaranteeing the existence of trapped modes: This follows from variational techniques applied to a suitable operator formulation of the problem. Several examples of structures (piercing or not the interfaces between the fluid layers) satisfying the condition and supporting trapped modes are given.
Description
Keywords
Spectral problem Three-layer fluid Trapped modes
Citation
CAL, Filipe S.; DIAS, Gonçalo A. S.; PEREIRA, Bruno M. A. M. – Trapped modes in a fluid with three layers topped by a rigid lid. Mathematical Methods in the Applied Sciences. ISSN0170-4214. Vol. 45, N.º 16 (2022), pp. 9928-9944.