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