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Abstract
A shallow water theory is developed which applies to surface wave propagation over structured bathymetry comprising rapid abrupt fluctuations in depth between two smoothly varying levels. Using a homogenization approach coupled to the depth-averaging process which underpins shallow water modelling, governing equations for the wave elevation are derived which explicitly relate local spatially varying anisotropy of wave speeds to properties of the microstructured bed. The model is applied to two water wave scattering problems both to demonstrate the complex wave propagation characteristics exhibited by structured beds and to provide examples of how to use structured beds to engineer bespoke wave propagation. This includes propagating waves with practically zero reflection and loss of form through circular bends in channels.
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Affiliation(s)
- C. Marangos
- School of Mathematics, University of Bristol, Fry Building, Woodland Road, Bristol BS8 1UG, UK
| | - R. Porter
- School of Mathematics, University of Bristol, Fry Building, Woodland Road, Bristol BS8 1UG, UK
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2
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Wang D, Ren Z, Chuang K. A review of gradient index metamaterials lenses. CHINESE SCIENCE BULLETIN-CHINESE 2021. [DOI: 10.1360/tb-2021-0523] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
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3
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Zou S, Xu Y, Zatianina R, Li C, Liang X, Zhu L, Zhang Y, Liu G, Liu QH, Chen H, Wang Z. Broadband Waveguide Cloak for Water Waves. PHYSICAL REVIEW LETTERS 2019; 123:074501. [PMID: 31491099 DOI: 10.1103/physrevlett.123.074501] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/07/2019] [Indexed: 06/10/2023]
Abstract
Inspired by electromagnetic waveguide cloaks with gradient index metamaterials, we fabricated a broadband cloak with simply a gradient depth profile on the bottom and without any other structures on the top to confine water waves in a certain area for cloaking regions. The new physics of mode conversion for water waves is first found. The experimental and numerical simulation results are in good agreement and show that the presented device has a nice performance for various situations and is feasible over a broadband of working frequencies. Being easy to construct, this design is potentially of significance for port applications.
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Affiliation(s)
- Siyuan Zou
- College of Civil Engineering and Architecture, Zhejiang University, Hangzhou 310058, China
- Institute of Electromagnetics and Acoustics and Key Laboratory of Electromagnetic Wave Science and Detection Technology, Xiamen University, Xiamen 361005, China
| | - Yadong Xu
- School of Physical Science and Technology and Jiangsu Key Laboratory of Thin Films, Soochow University, Suzhou 215006, China
| | - Razafizana Zatianina
- College of Civil Engineering and Architecture, Zhejiang University, Hangzhou 310058, China
| | - Chunyang Li
- College of Civil Engineering and Architecture, Zhejiang University, Hangzhou 310058, China
| | - Xu Liang
- Ocean College, Zhejiang University, Zhoushan 316021, China
| | - Lili Zhu
- College of Civil Engineering and Architecture, Zhejiang University, Hangzhou 310058, China
| | - Yongqiang Zhang
- College of Civil Engineering and Architecture, Zhejiang University, Hangzhou 310058, China
| | - Guohua Liu
- College of Civil Engineering and Architecture, Zhejiang University, Hangzhou 310058, China
| | - Qing Huo Liu
- Department of Electrical and Computer Engineering, Duke University, Durham, North Carolina 27708, USA
| | - Huanyang Chen
- Institute of Electromagnetics and Acoustics and Key Laboratory of Electromagnetic Wave Science and Detection Technology, Xiamen University, Xiamen 361005, China
| | - Zhenyu Wang
- College of Civil Engineering and Architecture, Zhejiang University, Hangzhou 310058, China
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Li C, Xu L, Zhu L, Zou S, Liu QH, Wang Z, Chen H. Concentrators for Water Waves. PHYSICAL REVIEW LETTERS 2018; 121:104501. [PMID: 30240256 DOI: 10.1103/physrevlett.121.104501] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/25/2018] [Indexed: 06/08/2023]
Abstract
By introducing concepts from transformation optics to the manipulation of water waves, we design and experimentally demonstrate two annular devices for concentrating waves, which employ gradient depth profiles based on Fabry-Pérot resonances. Our measurements and numerical simulations confirm the concentrating effect of the annular devices and show that they are effectively invisible to the water waves. We show that transformation optics is thus an effective framework for designing devices to improve the efficiency of wave energy collection, and we expect potential applications in coastline ocean engineering.
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Affiliation(s)
- Chunyang Li
- Institute of Electromagnetics and Acoustics and Department of Electronic Science, Xiamen University, Xiamen 361005, China
- College of Civil Engineering and Architecture, Zhejiang University, Hangzhou 310058, China
| | - Lin Xu
- Institute of Electromagnetics and Acoustics and Department of Electronic Science, Xiamen University, Xiamen 361005, China
- College of Civil Engineering and Architecture, Zhejiang University, Hangzhou 310058, China
- Institute of Physical Science and Information Technology & Key Laboratory of Opto-Electronic Information Acquisition and Manipulation of Ministry of Education, Anhui University, Hefei 230601, China
| | - Lili Zhu
- College of Civil Engineering and Architecture, Zhejiang University, Hangzhou 310058, China
| | - Siyuan Zou
- College of Civil Engineering and Architecture, Zhejiang University, Hangzhou 310058, China
| | - Qing Huo Liu
- Department of Electrical and Computer Engineering, Duke University, Durham, North Carolina 27708, USA
| | - Zhenyu Wang
- College of Civil Engineering and Architecture, Zhejiang University, Hangzhou 310058, China
| | - Huanyang Chen
- Institute of Electromagnetics and Acoustics and Department of Electronic Science, Xiamen University, Xiamen 361005, China
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Wang Z, Li C, Zatianina R, Zhang P, Zhang Y. Carpet cloak for water waves. Phys Rev E 2017; 96:053107. [PMID: 29347642 DOI: 10.1103/physreve.96.053107] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/23/2016] [Indexed: 06/07/2023]
Abstract
Cloaking is a challenging topic in the field of wave motion, and is of significant theoretical value. In this article, a type of carpet cloak has been theoretically designed for water waves by using the effective medium and transformation theory. This carpet cloak device, created by a three-dimensional printer, is composed of a periodic structure which realizes the equivalent anisotropic water depth. We demonstrate its excellent cloaking performance numerically and experimentally in a wide range of frequencies and angles of incidence, with low wave attenuation characteristics and simple device realization of this carpet cloak illustrating that water wave transformation is a powerful method with which to manipulate water waves.
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Affiliation(s)
- Zhenyu Wang
- College of Civil Engineering and Architecture, Zhejiang University, Hangzhou 310058, People's Republic of China
| | - Chunyang Li
- College of Civil Engineering and Architecture, Zhejiang University, Hangzhou 310058, People's Republic of China
| | - Razafizana Zatianina
- College of Civil Engineering and Architecture, Zhejiang University, Hangzhou 310058, People's Republic of China
| | - Pei Zhang
- College of Civil Engineering and Architecture, Zhejiang University, Hangzhou 310058, People's Republic of China
| | - Yongqiang Zhang
- College of Civil Engineering and Architecture, Zhejiang University, Hangzhou 310058, People's Republic of China
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