Scattering of surface waves by a vertical truncated structured cylinder

Porter, Robert; Zheng, Siming; Liang, Hui

doi:10.1098/rspa.2021.0824

Cited by 9 publications

(7 citation statements)

References 12 publications

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“…Away from resonant conditions, results from homogenisation of plate array structures compare favourably with those derived from the application of direct numerical methods for discrete arrays (e.g. Zheng et al (2020) and Porter, Zheng & Liang (2022), where comparison is made with boundary integral methods). However, low-frequency homogenisation fails when undamped fluid motion in narrow channels is resonant, occurring at the critical frequency ω c indicated above.…”

Section: Introductionmentioning

confidence: 98%

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Water wave propagation through arrays of closely spaced surface-piercing vertical barriers

Huang

Porter

2023

J. Fluid Mech.

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This paper presents and compares two different approaches to solving the problem of wave propagation across a large finite periodic array of surface-piercing vertical barriers. Both approaches are formulated in terms of a pair of integral equations, one exact and based on a spacing $\delta > 0$ between adjacent barriers and the other approximate and based on a continuum model formally developed by using homogenisation methods for small $\delta$ . It is shown that the approximate method is simpler to evaluate than the exact method which requires eigenvalues and eigenmodes related to propagation in an equivalent infinite periodic array of barriers. In both methods, the numerical effort required to solve problems is independent of the size of the array. The comparison between the two methods allows us to draw important conclusions about the validity of homogenisation models of plate array metamaterial devices. The practical interest in this problem stems from the result that for an array of barriers there exists a critical value of radian frequency, $\omega _c$ , dependent on $\delta$ , below which waves propagate through the array and above which it results in wave decay. When $\delta \to 0$ , the critical frequency is given by $\omega _c = \sqrt {g/d}$ , where $d$ is the plate submergence and $g$ is the acceleration due to gravity, which relates to the resonance in narrow channels and is an example of local resonance, studied extensively in metamaterials. The results have implications for proposed schemes to harness energy from ocean waves and other problems related to rainbow trapping and rainbow reflection.

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Section: Introductionmentioning

confidence: 98%

“…Zheng et al. (2020) and Porter, Zheng & Liang (2022), where comparison is made with boundary integral methods). However, low-frequency homogenisation fails when undamped fluid motion in narrow channels is resonant, occurring at the critical frequency indicated above.…”

Section: Introductionmentioning

confidence: 99%

Water wave propagation through arrays of closely spaced surface-piercing vertical barriers

Huang

Porter

2023

J. Fluid Mech.

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“…The paddles are attached to springs and dampers through which wave power is captured. Recently, Porter, Zheng & Liang (2022) considered the scattering of waves by a truncated metamaterial cylinder, which consists of an array of closely spaced thin vertical plates and is fully submerged in the water with its bottom sitting on the seabed.…”

Section: Introductionmentioning

confidence: 99%

Wave scattering and radiation by a surface-piercing vertical truncated metamaterial cylinder

Zheng,

Liang,

Greaves

2024

J. Fluid Mech.

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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.

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“…Recently, Porter et al. published a series of works on plate array metamaterials, for water waves, that exhibit novel wave interactions [16–20]. In [17], Porter considers a closely spaced periodic array of thin plates of Neumann boundary condition, and identical height and tilt angle, and uses the close spacing of the plates to approximate the plate array as an effective medium described simply by a one-dimensional wave equation.…”

Section: Introductionmentioning

confidence: 99%

“…This continuum model stipulates that the plate array acts as a perfectly transmitting negative-refraction metamaterial, capable of perfect waveshifting across the medium as well as being entirely transparent to a plane-wave when the angle of incidence and tilt angle equate. This has been further developed upon by Porter and Zheng to consider cylinders of circular cross section composed of the same plate array medium [18][19][20], being referred to as metamaterial cylinders or metacylinders. In particular, in [18], metacylinders have been used to redirect wave energy for the purposes of focusing and blocking water waves, and the capabilities of energy dissipation within the effective medium have been explored.…”

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confidence: 99%

A tunable electromagnetic metagrating

2022

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We explore electromagnetic (EM) wave incidence upon gratings of reconfigurable metamaterial cylinders, which collectively act as a metagrating, to identify their potential as reconfigurable subwavelength surfaces. The metacylinders are created by a closely spaced, microstructured array of thin plates that, in the limit of small inter-plate spacing, are described by a semi-analytical continuum model. We build upon metacylinder analysis in water waves, translating this to EM for TE polarization (longitudinal magnetic field) for which the metacylinders exhibit anisotropic scattering; this is exploited for the multiple scattering of light by an infinite metagrating of uniform cylinder radius and angle, for which we retrieve the far-field reflection and transmission spectra for plane-wave incidence. These spectra reveal unusual effects including perfect reflection and a negative Goos–Hänchen shift in the transmitted field, as well as perfect symmetry in the far-field scattering coefficients. The metagrating also hosts Rayleigh–Bloch surface waves, whose dispersion is contingent on the uniform cylinder angle, shifting under rotation towards the light-line as the cylinder angle approaches the horizontal. For both plane-wave scattering and the calculation of the array-guided modes, the cylinder angle is the principal variable in determining the wave interaction, and the metagrating is tunable simply through rotation of the constituent metacylinders.

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Scattering of surface waves by a vertical truncated structured cylinder

Cited by 9 publications

References 12 publications

Water wave propagation through arrays of closely spaced surface-piercing vertical barriers

Water wave propagation through arrays of closely spaced surface-piercing vertical barriers

Wave scattering and radiation by a surface-piercing vertical truncated metamaterial cylinder

A tunable electromagnetic metagrating

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