Hostname: page-component-cb9f654ff-mwwwr Total loading time: 0 Render date: 2025-09-01T02:40:10.088Z Has data issue: false hasContentIssue false
  • English
  • Français

Small water channel network for designing wave fields in shallow water

Published online by Cambridge University Press:  15 June 2018

Takahito Iida Open the ORCID record for Takahito Iida [Opens in a new window]  and
Masashi Kashiwagi
Takahito Iida*
Affiliation:
Department of Naval Architecture and Ocean Engineering, Osaka University, Osaka 5650871, Japan Research Fellow of Japan Society for the Promotion of Science, Japan
Masashi Kashiwagi
Affiliation:
Department of Naval Architecture and Ocean Engineering, Osaka University, Osaka 5650871, Japan
*
†Email address for correspondence: iida_takahito@naoe.eng.osaka-u.ac.jp
Get access Rights & Permissions [Opens in a new window]

Abstract

A small water channel network is proposed for designing shallow water fields, and the network is applied to attain water wave cloaking. The design formula is derived from an analogy between waves in a water channel and in an electric circuit; an approach of a transmission line metamaterial is extended to water waves and the water channel is used as an alternative of the transmission line. The size of the water channel is sufficiently smaller than the wavelength and a number of the channels are periodically connected as a network. This small water channel network makes artificial wave fields, and it works for a wide band of frequencies. First, we make an isotropic network equivalent to a shallow water space with constant depth in order to validate the proposed design method. It shows no wave reflection at the interface due to impedance matching. After that, the proposed theory is applied to designing an anisotropic small water channel network for demonstrating shallow water cloaking. A cylinder is cloaked from waves by the network surrounding the cylinder. Both cases are confirmed with numerical computations by solving the boundary-value problem based on linear potential theory.

JFM classification

Geophysical and Geological Flows: Shallow water flows Waves/Free-surface Flows: Waves/Free-surface Flows

Information

Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 849 , 25 August 2018 , pp. 90 - 110
Check for updates
Copyright
© 2018 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Berraquero, C. P., Maurel, A., Petitjeans, P. & Pagneux, V. 2013 Experimental realization of a water-wave metamaterial shifter. Phys. Rev. E 88 (5), 051002.Google Scholar
Brule, S., Javelaud, E. H., Enoch, S. & Guenneau, S. 2014 Experiments on seismic metamaterials: molding surface waves. Phys. Rev. Lett. 112 (13), 133901.Google Scholar
Caloz, C. & Itoh, T. 2002 Application of the transmission line theory of left-handed (LH) materials to the realization of a microstrip ‘LH line’. In Antennas and Propagation Society International Symposium, 2002, Vol. 2. IEEE.Google Scholar
Christopoulos, C. 1995 The Transmission-line Modeling Method. Oxford University Press.Google Scholar
Cummer, S. A. & Schurig, D. 2007 One path to acoustic cloaking. New J. Phys. 9 (3), 45.Google Scholar
Dupont, G., Guenneau, S., Kimmoun, O., Molin, B. & Enoch, S. 2016 Cloaking a vertical cylinder via homogenization in the mild-slope equation. J. Fluid Mech. 796, R1.Google Scholar
Eleftheriades, G. V., Iyer, A. K. & Kremer, P. C. 2002 Planar negative refractive index media using periodically LC loaded transmission lines. IEEE Trans. Microwave Theory Techniques 50 (12), 2702–2712.Google Scholar
Farhat, M., Enoch, S., Guenneau, S. & Movchan, A. B. 2008 Broadband cylindrical acoustic cloak for linear surface waves in a fluid. Phys. Rev. Lett. 101 (13), 134501.Google Scholar
Farhat, M., Guenneau, S., Enoch, S. & Movchan, A. B. 2009 Cloaking bending waves propagating in thin elastic plates. Phys. Rev. B 79 (3), 033102.Google Scholar
Fokin, V., Ambati, M., Sun, C. & Zhang, X. 2007 Method for retrieving effective properties of locally resonant acoustic metamaterials. Phys. Rev. B 76 (14), 144302.Google Scholar
Iida, T. & Kashiwagi, M. 2017 Design of small water channel network for shallow water cloaking. In Proc. 32nd Int. Workshop on Water Waves and Floating Bodies, Dalian, China, pp. 89–92.Google Scholar
Kiyokawa, S. & Mochizuki, H. 1994 Harou Filter Gata Kouzoubutsu Niyoru Harou Seigyo (wave controlling by wave filter based structure in Japanese). Proc. Coastal Engineering, JSCE 41, 616–620.Google Scholar
Mochizuki, H., Ando, S. & Mitsuhashi, W. 1990 A frequency filter for water waves (in Japanese). IEEJ Trans. Fundam. Mat. 110 (8), 493–500.Google Scholar
Nagayama, T. & Sanada, A. 2015 Planar distributed full-tensor anisotropic metamaterials for transformation electromagnetics. IEEE Trans. Microwave Theory Techniques 63 (12), 3851–3861.Google Scholar
Pendry, J. B. 2000 Negative refraction makes a perfect lens. Phys. Rev. Lett. 85 (18), 3966.Google Scholar
Pendry, J. B., Schurig, D. & Smith, D. R. 2006 Controlling electromagnetic fields. Science 312 (5781), 1780–1782.Google Scholar
Schurig, D., Mock, J. J., Justice, B. J., Cummer, S. A., Pendry, J. B., Starr, A. F. & Smith, D. R. 2006 Metamaterial electromagnetic cloak at microwave frequencies. Science 314 (5801), 977–980.Google Scholar
Shelby, R. A., Smith, D. R. & Schultz, S. 2001 Experimental verification of a negative index of refraction. Science 292 (5514), 77–79.Google Scholar
Smith, D. R., Padilla, W. J., Vier, D. C., Nemat-Nasser, S. C. & Schultz, S. 2000 Composite medium with simultaneously negative permeability and permittivity. Phys. Rev. Lett. 84 (18), 4184.Google Scholar
Stenger, N., Wilhelm, M. & Wegener, M. 2012 Experiments on elastic cloaking in thin plates. Phys. Rev. Lett. 108 (1), 014301.Google Scholar
Zareei, A. & Alam, M. R. 2015 Cloaking in shallow-water waves via nonlinear medium transformation. J. Fluid Mech. 778, 273–287.Google Scholar
Zareei, A. & Alam, R. 2016 Cloaking by a floating thin plate. In Proc. 31st Int. Workshop on Water Waves and Floating Bodies, Michigan, USA, pp. 197–200.Google Scholar
Zigoneanu, L., Popa, B. I. & Cummer, S. A. 2014 Three-dimensional broadband omnidirectional acoustic ground cloak. Nat. Mater. 13 (4), 352–355.Google Scholar