Trapped modes in the water-wave problem for a freely floating structure

Bound states in the continuum are waves that, defying conventional wisdom, remain localized even though they coexist with a continuous spectrum of radiating waves that can carry energy away. Their existence was first proposed in quantum mechanics and, being a general wave phenomenon, later identified in electromagnetic, acoustic, and water waves. They have been studied in a wide variety of material systems such as photonic crystals, optical waveguides and fibers, piezoelectric materials, quantum dots, graphene, and topological insulators. This Review describes recent developments in this field with an emphasis on the physical mechanisms that lead to these unusual states across the seemingly very different platforms. We discuss recent experimental realizations, existing applications, and directions for future work.

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“…But this procedure can also be extended to more complex shapes 209,210 and to free-floating instead of fixed obstacles [211][212][213] .…”

Section: Boundary Shape Engineeringmentioning

confidence: 99%

Bound states in the continuum

et al. 2016

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“…When trapped modes around floating structures were discovered by McIver & McIver (2006) a new nomenclature emerged: sloshing-trapped modes were said to occur around fixed structures and motion-trapped modes around floating bodies. Motion-trapping structures which enclosed part of the free surface within axisymmetric shapes of complicated vertical cross-section (McIver & McIver 2007), and later simple rectangular crosssection (Porter & Evans 2008) were found.…”

Section: Introductionmentioning

confidence: 99%

Experimental observation of a near-motion-trapped mode: free motion in heave with negligible radiation

Wolgamot

Taylor

et al. 2015

J. Fluid Mech.

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A simple geometry which exhibits near-motion-trapping is tested experimentally, along with perturbed versions of the structure. The motion of the freely floating structure and the surrounding wave field is tracked and the near-motion-trapped mode is found, characterised by a slowly decaying heave motion with very small linear radiation of energy. It is found that the latter property is a better discriminator of the perturbed geometries as viscous damping masks fine differences in radiation damping as far the motion of the structure is concerned. The magnitude of this viscous damping is reasonably well predicted by a simple Stokes' oscillatory boundary layer analysis.

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“…(The paper contains, in particular, the uniqueness theorem in which rather restrictive assumptions are made about both the structure's geometry and the frequency of motion.) The reason for this is the difficulty of the problem, which motivated attempts to use a model in which only heave motion of a freely floating structure is allowed; see, for example, the papers [4] and [5]. Their topic was the construction of trapped-mode solutions in the framework of this simpler model.…”

Section: §1 Introductionmentioning

confidence: 99%

On the problem of time-harmonic water waves in the presence of a freely floating structure

Kuznetsov

2011

St. Petersburg Math. J.

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Abstract. The two-dimensional problem of time-harmonic water waves in the presence of a freely floating structure (it consists of a finite number of infinitely long surface-piercing cylinders connected above the water surface) is considered. The coupled spectral boundary value problem modeling the small-amplitude motion of this mechanical system involves the spectral parameter, the frequency of oscillations, which appears in the boundary conditions as well as in the equations governing the structure's motion. It is proved that any value of the frequency turns out to be an eigenvalue of the problem for a particular structure obtained with the help of the so-called inverse procedure. §1. IntroductionThis paper deals with coupled boundary value problems describing the irrotational motion of an inviscid, incompressible, heavy fluid (water) in which a structure consisting of a finite number of rigid bodies is floating freely. Water extends to infinity in the horizontal directions as well as downwards and is bounded above by a free surface, thus modeling an infinitely deep open sea. The surface tension is neglected on the free surface and the coupled motion of the structure and water is assumed to be of small amplitude near equilibrium, which allows us to use a linear model. We restrict ourselves to considering structures formed by infinitely long horizontal surface-piercing cylinders that are rigidly connected with each other above the water surface (an infinitely long pontoon is a typical example). This assumption leads to another simplification that consists in studying only the case of two-dimensional motion that is the same in every plane orthogonal to the structure's generators.The time-dependent equations for the two-dimensional mechanical system described above are formulated in Subsection 2.1. A full discussion of the three-dimensional coupled boundary value problem was given by John in his pioneering work [1] (see also the paper [2] by Beale, who presented the equations of motion in a more convenient matrix form). In Subsection 2.2, we turn to the case where the water waves are time-harmonic, as well as the motion of the structure, and the so-called external forces (they, for example, are due to constraints on the structure motion) are absent. We also discuss conditions that must be imposed on the behavior of a time-harmonic solution at infinity. The resulting problem is the coupled spectral problem involving the spectral parameter, the frequency of oscillations, which appears in the boundary conditions as well as in the equations of 2010 Mathematics Subject Classification. Primary 76B15, 76B03, Secondary 35Q35, 35P05.

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Trapped modes in the water-wave problem for a freely floating structure

Cited by 43 publications

References 13 publications

Bound states in the continuum

Bound states in the continuum

Experimental observation of a near-motion-trapped mode: free motion in heave with negligible radiation

On the problem of time-harmonic water waves in the presence of a freely floating structure

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