Underwater topography invisible for surface waves at given frequencies

Anne Sophie Bonnet-Ben Dhia; Sergey A. Nazarov; Jari Taskinen

doi:10.1016/j.wavemoti.2015.03.008

Underwater topography invisible for surface waves at given frequencies

Anne Sophie Bonnet-Ben Dhia, Sergey A. Nazarov, Jari Taskinen

Research output: Contribution to journal › Article › peer-review

Abstract

We consider scattering of surface waves modeled by the linear water wave equation in an unbounded two-dimensional domain of finite depth, at a given frequency and a given incidence. Using asymptotic analysis for small perturbations of the bottom shape, we build a fixed-point equation whose unique solution is a shape which cannot be detected by a distant observer. The method works at any incidence except π/4.

Original language	English
Pages (from-to)	129-142
Number of pages	14
Journal	Wave Motion
Volume	57
DOIs	https://doi.org/10.1016/j.wavemoti.2015.03.008
Publication status	Published - 1 Jan 2015

Keywords

Asymptotic analysis
Cloaking
Fixed point theorem
Invisibility
Linear water waves
Scattering problem

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10.1016/j.wavemoti.2015.03.008

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title = "Underwater topography invisible for surface waves at given frequencies",

abstract = "We consider scattering of surface waves modeled by the linear water wave equation in an unbounded two-dimensional domain of finite depth, at a given frequency and a given incidence. Using asymptotic analysis for small perturbations of the bottom shape, we build a fixed-point equation whose unique solution is a shape which cannot be detected by a distant observer. The method works at any incidence except π/4.",

keywords = "Asymptotic analysis, Cloaking, Fixed point theorem, Invisibility, Linear water waves, Scattering problem",

author = "\{Bonnet-Ben Dhia\}, \{Anne Sophie\} and Nazarov, \{Sergey A.\} and Jari Taskinen",

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year = "2015",

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doi = "10.1016/j.wavemoti.2015.03.008",

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T1 - Underwater topography invisible for surface waves at given frequencies

AU - Bonnet-Ben Dhia, Anne Sophie

AU - Nazarov, Sergey A.

AU - Taskinen, Jari

PY - 2015/1/1

Y1 - 2015/1/1

N2 - We consider scattering of surface waves modeled by the linear water wave equation in an unbounded two-dimensional domain of finite depth, at a given frequency and a given incidence. Using asymptotic analysis for small perturbations of the bottom shape, we build a fixed-point equation whose unique solution is a shape which cannot be detected by a distant observer. The method works at any incidence except π/4.

AB - We consider scattering of surface waves modeled by the linear water wave equation in an unbounded two-dimensional domain of finite depth, at a given frequency and a given incidence. Using asymptotic analysis for small perturbations of the bottom shape, we build a fixed-point equation whose unique solution is a shape which cannot be detected by a distant observer. The method works at any incidence except π/4.

KW - Asymptotic analysis

KW - Cloaking

KW - Fixed point theorem

KW - Invisibility

KW - Linear water waves

KW - Scattering problem

U2 - 10.1016/j.wavemoti.2015.03.008

DO - 10.1016/j.wavemoti.2015.03.008

M3 - Article

AN - SCOPUS:84946081431

SN - 0165-2125

VL - 57

SP - 129

EP - 142

JO - Wave Motion

JF - Wave Motion

ER -

Underwater topography invisible for surface waves at given frequencies

Abstract

Keywords

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