title: Trapped modes around freely floating bodies in a two-layer fluid channel.
abstract: Unlike the trapping of time-harmonic water waves by fixed obstacles, the oscillation of freely floating structures gives rise to a complex nonlinear spectral problem. Still, through a convenient elimination scheme the system simplifies to a linear spectral problem for a self-adjoint operator in a Hilbert space. Under symmetry assumptions on the geometry of the fluid domain, we present conditions guaranteeing the existence of trapped modes in a two-layer fluid channel. Numerous examples of floating bodies supporting trapped modes are given.
authors.affiliation: CAMGSD/Departamento de Matemática , Instituto Superior Técnico, Universidade de Lisboa , Avenida Rovisco Pais, 1049-001 Lisboa, Portugal.
authors.forename: Filipe S
authors.initials: FS
authors.lastname: Cal
authors.affiliation: CAMGSD/Departamento de Matemática , Instituto Superior Técnico, Universidade de Lisboa , Avenida Rovisco Pais, 1049-001 Lisboa, Portugal.
authors.forename: Gonçalo A S
authors.initials: GA
authors.lastname: Dias
authors.affiliation: CAMGSD/Departamento de Matemática , Instituto Superior Técnico, Universidade de Lisboa , Avenida Rovisco Pais, 1049-001 Lisboa, Portugal.
authors.forename: Juha H
authors.initials: JH
authors.lastname: Videman
keywords: freely floating objects; trapped modes; two-layer fluid