“…As said previously, in the context of our study, the above dispersion for coincides with (1.1) for since from (3.13 a , b ) and (4.4 a , b ), , so . Figure 13.( a ) The case of arrays of inclined plates studied in Porter (2021) and Porter & Marangos (2022). ( b ) Isofrequencycontour at constant (where ).…”
supporting
confidence: 83%
“…2008, 2010; Carter 2012). Recently, an original anomalous dispersion was proposed by Porter (2021) and Porter & Marangos (2022) with inclined plates piercing the surface, thus forcing the energy flow in one direction only. This example is the only one to our knowledge capable of producing negative refraction for water waves in the subwavelength regime.…”
Section: Introductionmentioning
confidence: 99%
“…Anomalous dispersions, such as that reported by Kosaka et al (1998) in a graphene crystal-like photonic crystal, have been used to produce negative refraction of water waves (Farhat et al 2008(Farhat et al , 2010Carter 2012). Recently, an original anomalous dispersion was proposed by Porter (2021) and Porter & Marangos (2022) with inclined plates piercing the surface, thus forcing the energy flow in one direction only. This example is the only one to our knowledge capable of producing negative refraction for water waves in the subwavelength regime.…”
Section: Introductionmentioning
confidence: 99%
“…We report in this appendix a quick reminder on the strongly dispersive character of rigid plates piercing the free surface (figure 13 a ), introduced by Porter (2021) and Porter & Marangos (2022), which we use as a reference case. To begin with, note that for subwavelength period, this three-dimensional configuration is the exact analogue of the two-dimensional acoustic case, i.e.…”
mentioning
confidence: 99%
“…( a ) The case of arrays of inclined plates studied in Porter (2021) and Porter & Marangos (2022). ( b ) Isofrequencycontour at constant (where ).…”
We study the propagation of water waves in a three-dimensional device alternating open canals and resonant canals with subwavelength resonances. The dispersion of water waves in such a medium is obtained by analysing the full three-dimensional problem and combining Bloch–Floquet analysis with an asymptotic technique. We obtain the closed forms of the dispersions for resonant canals containing one or two resonators, which depend on only two functions associated with symmetric and antisymmetric modes, and on a geometric parameter analogous to the hopping parameter in topological systems. The analysis of the complete band structure reveals frequency ranges alternating between elliptical and hyperbolic dispersions; in particular, the hyperbolic regime gives rise to a negative effective water depth with a consequent negative refraction. Throughout the course of our study, our theoretical results are validated by comparison with numerical calculations of the full three-dimensional problem.
“…As said previously, in the context of our study, the above dispersion for coincides with (1.1) for since from (3.13 a , b ) and (4.4 a , b ), , so . Figure 13.( a ) The case of arrays of inclined plates studied in Porter (2021) and Porter & Marangos (2022). ( b ) Isofrequencycontour at constant (where ).…”
supporting
confidence: 83%
“…2008, 2010; Carter 2012). Recently, an original anomalous dispersion was proposed by Porter (2021) and Porter & Marangos (2022) with inclined plates piercing the surface, thus forcing the energy flow in one direction only. This example is the only one to our knowledge capable of producing negative refraction for water waves in the subwavelength regime.…”
Section: Introductionmentioning
confidence: 99%
“…Anomalous dispersions, such as that reported by Kosaka et al (1998) in a graphene crystal-like photonic crystal, have been used to produce negative refraction of water waves (Farhat et al 2008(Farhat et al , 2010Carter 2012). Recently, an original anomalous dispersion was proposed by Porter (2021) and Porter & Marangos (2022) with inclined plates piercing the surface, thus forcing the energy flow in one direction only. This example is the only one to our knowledge capable of producing negative refraction for water waves in the subwavelength regime.…”
Section: Introductionmentioning
confidence: 99%
“…We report in this appendix a quick reminder on the strongly dispersive character of rigid plates piercing the free surface (figure 13 a ), introduced by Porter (2021) and Porter & Marangos (2022), which we use as a reference case. To begin with, note that for subwavelength period, this three-dimensional configuration is the exact analogue of the two-dimensional acoustic case, i.e.…”
mentioning
confidence: 99%
“…( a ) The case of arrays of inclined plates studied in Porter (2021) and Porter & Marangos (2022). ( b ) Isofrequencycontour at constant (where ).…”
We study the propagation of water waves in a three-dimensional device alternating open canals and resonant canals with subwavelength resonances. The dispersion of water waves in such a medium is obtained by analysing the full three-dimensional problem and combining Bloch–Floquet analysis with an asymptotic technique. We obtain the closed forms of the dispersions for resonant canals containing one or two resonators, which depend on only two functions associated with symmetric and antisymmetric modes, and on a geometric parameter analogous to the hopping parameter in topological systems. The analysis of the complete band structure reveals frequency ranges alternating between elliptical and hyperbolic dispersions; in particular, the hyperbolic regime gives rise to a negative effective water depth with a consequent negative refraction. Throughout the course of our study, our theoretical results are validated by comparison with numerical calculations of the full three-dimensional problem.
In this paper, we study wave scattering and radiation by a surface-piercing vertical truncated metamaterial cylinder composed of a closely spaced array of thin vertical barriers, between which fluid can flow. A theoretical model is developed under full depth-dependent linearised water wave theory, where an effective medium equation and effective boundary conditions are employed, respectively, to describe the fluid motion inside the cylinder and match the flow between the fluid regions in and outside the metamaterial cylinder. A damping mechanism is introduced at the surface of the fluid occupied by the metamaterial cylinder to consider the wave power dissipation in narrow gaps between the thin vertical plates. The wave excitation forces acting on the cylinder and the hydrodynamic coefficients can be calculated straightforwardly in terms of the velocity potential inside the cylinder. An alternative way is by using the velocity potential outside the cylinder, the expression of which has the reduction of the integral and an infinite accumulation that are included in the straightforward expression. The results highlight the patterns of the radiated waves induced by the oscillation of the cylinder and the characteristics of the hydrodynamic coefficients. The metamaterial cylinder when fixed in place and with a damping mechanism included is found to capture more wave power than that of a traditional axisymmetric heaving wave energy converter over a wide range of wave frequencies.
In this paper, we study the interaction of water waves with a surface-piercing truncated cylindrical meta-structure consisting of two overlapping arrays of closely spaced vertical thin plates. The fluid resonance promoted in the narrow vertical channels formed by the cylindrical meta-structure is exploited by a novel design concept of the wave power converter by covering the surface of the cylinder with an array of small cuboid buoys which float in the gaps between the intersecting plate arrays. Each buoy is attached to its own spring and power takeoff damping mechanism, and the vertical displacement of individual buoys is replaced by a continuous two-dimensional function of position which follows from homogenization of the plate/fluid structure of the cylinder. Effective medium equations and boundary conditions are derived under both full depth-dependent theory and shallow-water theory, allowing semi-analytical methods to be developed to investigate the wave scattering and wave energy absorption properties of this cylindrical meta-structure. Results illustrate that the internal resonance of the cylindrical meta-structure can lead to significant wave power capture across a broad range of frequencies.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
