Functional Analysis and Applications Seminar


(organized by the Functional Analysis and Applications Group)


Department of Mathematics, University of Aveiro



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Next talk of the Seminar (11:10, Room Sousa Pinto):


24/05/2018:" Wave interaction with structures in a two-layer fluid "


Filipe S. Cal  (Department of Mathematics, Engineering Superior Institute of Lisbon)


We derive a linear system of equations governing the interaction of water waves with partially or totally submerged freely floating structures in a two-layer fluid. Considering time-harmonic motions, we rewrite the problem as a spectral boundary-value problem consisting of a differential equation coupled with an algebraic system and give a suitable variational formulation for the problem.


We consider trapping of linear water waves by infinite arrays of three-dimensional periodic fixed structures, in particular, along periodic coastlines. We derive a geometric condition ensuring the existence of trapped modes and give several examples of structures (and coastlines) satisfying the condition and supporting edge waves.


We consider the spectral problem that describes the time-harmonic motion of the mechanical system consisting of a three-dimensional rigid body floating freely in a two-layer fluid channel. Unlike the trapping of water waves by fixed obstacles, the interaction of time-harmonic waves with freely floating objects gives rise to a quadratic operator pencil. Under symmetry assumptions on the geometry of the fluid domain and presenting a scheme that reduces the quadratic pencil to a linear spectral problem (linear pencil) for a self-adjoint operator in a Hilbert space, we derive a sufficient condition for the existence of trapped modes.



This Seminar is supported in part by the Portuguese Foundation for Science and Technology (FCT - Fundação para a Ciência e a Tecnologia), through CIDMA - Center for Research and Development in Mathematics and Applications, within project UID/MAT/04106/2013.



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