Manipulating Scattering Performance of Offshore Structures in Water Waves Using a Wavelength Modulator

Abstract

Through active manipulation of wavelengths, a structure exposed to a water-wave field can achieve a target hydrodynamic performance. Based on the form invariance of the governing equation for shallow water waves, wavelength modulators have been proposed using the space transformation method, which enables wavelength manipulation by distributing an anisotropic medium that incorporates water depth and gravitational acceleration within the modulation space. First, annular wavelength modulators were designed using the space transformation method to reduce or amplify the wavelength of shallow water waves. The control method of wavelength scaling ratios was investigated. In addition to plane waves, the wavelength modulator was applied to manipulate the wavelength of cylindrical waves. Furthermore, the interactions between a vertical cylinder and modulated water waves were studied. Results indicate that the wavelength can be arbitrarily reduced or amplified by adjusting the dimensional parameters of the modulator. Additionally, the modulator is effective for plane waves and cylindrical waves. This wavelength modulator can enable the structure to achieve the desired scattering characteristics at the target wavelength.

References

[1] Berraquero CP, Maurel A, Petitjeans P, Pagneux V. Experimental realization of a water-wave metamaterial shifter. Physical Review E, 2013, 88(5): 051002

[2] Chen H, Yang J, Zi J, Chan CT. Transformation media for linear liquid surface waves. Europhysics Letters, 2009, 85(2): 24004

[3] Cummer SA, Schurig D. One path to acoustic cloaking. New Journal of Physics, 2007, 9(3): 45

[4] Brule S, Javelaud EH, Enoch S, Guenneau S. Experiments on seismic metamaterials: molding surface waves. Physical Review Letters, 2014, 112(13): 133901

[5] Dupont G, Kimmoun O, Molin B, Guenneau S, Enoch S. Numerical and experimental study of an invisibility carpet in a water channel. Physical Review E, 2015, 91(2): 023010

[6] Faltinsen O. Sea Loads on ships and offshore structures, 1993 Cambridge University Press

[7] Farhat M, Enoch S, Guenneau S, Movchan A B. Broadband cylindrical acoustic cloak for linear surface waves in a fluid. Physical Review Letters, 2008, 101: 134501

[8] He G, Zhang Z, Luan Z, Liu S. A nearshore wave energy converter based on wave reflection, 2019 Chinese patent ZL201910191032.7 (in Chinese)

[9] Iida T, Kashiwagi M, He G. Numerical confirmation of cloaking phenomenon array of floating bodies and reduction of wave drift force. International Journal of Offshore and Polar Engineering, 2014, 24(4): 241-246

[10] Iida T, Kashiwagi M. Water wave focusing using coordinate transformation. Journal of energy and power engineering, 2017, 11: 631636

[11] Iida T, Kashiwagi M. Small water channel network for designing wave fields in shallow water. Journal of Fluid Mechanics, 2018, 849: 90-110

[12] Iida T, Zareei A, Alam R. Water wave cloaking using a floating composite plate. Journal of Fluid Mechanics, 2023, 954: A4

[13] Konispoliatis DN, Mavrakos SA. Hydrodynamic efficiency of a wave energy converter in front of an orthogonal breakwater. Journal of Marine Science and Engineering, 2021, 9(1): 94

[14] Leonhardt U. Optical conformal mapping. Science, 2006, 312(5781): 1777-1780

[15] Mei CC, Stiassnie MA, Yue DKP. Theory and applications of ocean surface waves: Part 1: linear aspects, 2005 World Scientific

[16] Neill SP, Hashemi MR. Fundamentals of ocean renewable energy: generating electricity from the sea, 2018 Academic Press

[17] Newman JN. Marine hydrodynamics, 1977 MIT Press

[18] Newman JN. Cloaking a circular cylinder in water waves. European Journal of Mechanics-B/Fluids, 2014, 47: 145-150

[19] Pecher A, Kofoed JP. Handbook of ocean wave energy, 2017 Springer Nature

[20] Pendry JB, Schurig D, Smith DR. Controlling electromagnetic fields. Science, 2006, 312(5781): 1780-1782

[21] Porter R, Newman JN. Cloaking of a vertical cylinder in waves using variable bathymetry. Journal of Fluid Mechanics, 2014, 750: 124-143

[22] Ren J, Jin P, Liu Y, Zang J. Wave attenuation and focusing by a parabolic arc pontoon breakwater. Energy, 2021, 217: 119405

[23] Schurig D, Mock JJ, Justice B, Cummer SA, Pendry JB, Starr AF, Smith DR. Metamaterial electromagnetic cloak at microwave frequencies. Science, 2006, 314: 977-980

[24] Schurig D, Pendry JB, Smith DR. Calculation of material properties and ray tracing in transformation media. Optics Express, 2006, 14(21): 9794-9804

[25] Wiel RVD, Kramer J, Ven PVD, Borsboom M, Jong MPCD. Influence of a parabolic reflector wall on the sea state in an array of point absorber wave energy converters. Proceedings of the 2nd International Conference on Renewable Energies Offshore (RENEW2016), Lisbon, Portugal, 2016 24-26

[26] Wang Z, Li C, Zatianina R, Zhang P, Zhang Y. Carpet cloak for water waves. Physical Review E, 2017, 96: 053107

[27] Xu H, Shi X, Gao F, Sun H, Zhang B. Ultrathin three-dimensional thermal cloak. Physical Review Letters, 2014, 112(5): 054301

[28] Zareei A, Alam MR. Cloaking in shallow-water waves via nonlinear medium transformation. Journal of Fluid Mechanics, 2015, 778: 273-287

[29] Zhang C, Ning D. Hydrodynamic study of a novel breakwater with parabolic openings for wave energy harvest. Ocean Engineering, 2019, 182: 540-551

[30] Zhang Z, He G, Gou Y, Luan Z, Liu S, He R. Wavelength manipulation in shallow water via space transformation method. Physics of Fluids, 2023, 35: 117108

[31] Zhang Z, He G, Wang W, Liu S, Wang Z. Broadband cloaking of multiple truncated cylinders in water waves using the arrangement defects. Physics of Fluids, 2020, 32: 067111

[32] Zhang Z, Iida T, He G, Mo W, Liu S, Luan Z, Jing P. Boundary effects of anisotropic medium on cloaking under shallow-water waves. Ocean Engineering, 2024, 291: 116485

[33] Zhang Z, Liu S, Luan Z, Wang Z, He G. Invisibility concentrator for water waves. Physics of Fluids, 2020, 32: 081701

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Harbin Engineering University and Springer-Verlag GmbH Germany, part of Springer Nature