Hydroelastic solitary waves with constant vorticity

Tao Gao; Paul Milewski; Jean Marc Vanden-Broeck

doi:10.1016/j.wavemoti.2018.11.005

Hydroelastic solitary waves with constant vorticity

Tao Gao, Paul Milewski, Jean Marc Vanden-Broeck

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Abstract

In this work, two-dimensional hydroelastic solitary waves in the presence of constant vorticity are studied. Time-dependent conformal mapping techniques first developed for irrotational waves are applied subject to appropriate modification. An illustrative high-order Nonlinear Schrödinger Equation is presented to investigate whether a given envelope collapses into a singular point in finite time by using the virial theory. Travelling solitary waves on water of infinite depth are computed for different values of vorticity and new generalised solitary waves are discovered. The stabilities of these waves are examined numerically by using fully nonlinear time-dependent computations which confirm the virial theory analysis.

Original language	English
Pages (from-to)	84-97
Number of pages	14
Journal	Wave Motion
Volume	85
Early online date	27 Nov 2018
DOIs	https://doi.org/10.1016/j.wavemoti.2018.11.005
Publication status	Published - 1 Jan 2019

Bibliographical note

Funding Information:
J.-M.V.-B. acknowledges the support from EPSRC, UK Grant No. EP/N018559/1 . P.M. was supported by EPSRC, UK under Grant No. EP/N018176/1 .

Funding Information:
J.-M.V.-B. acknowledges the support from EPSRC, UK Grant No. EP/N018559/1. P.M. was supported by EPSRC, UK under Grant No. EP/N018176/1.

Publisher Copyright:
© 2018 Elsevier B.V.

Keywords

Asymmetric waves
Elastic waves
Solitary waves
Surface gravity waves

ASJC Scopus subject areas

Modelling and Simulation
General Physics and Astronomy
Computational Mathematics
Applied Mathematics

Access to Document

10.1016/j.wavemoti.2018.11.005

GMV_acceptedAccepted author manuscript, 1.06 MBLicence: CC BY-NC-ND

Cite this

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title = "Hydroelastic solitary waves with constant vorticity",

abstract = "In this work, two-dimensional hydroelastic solitary waves in the presence of constant vorticity are studied. Time-dependent conformal mapping techniques first developed for irrotational waves are applied subject to appropriate modification. An illustrative high-order Nonlinear Schr{\"o}dinger Equation is presented to investigate whether a given envelope collapses into a singular point in finite time by using the virial theory. Travelling solitary waves on water of infinite depth are computed for different values of vorticity and new generalised solitary waves are discovered. The stabilities of these waves are examined numerically by using fully nonlinear time-dependent computations which confirm the virial theory analysis.",

keywords = "Asymmetric waves, Elastic waves, Solitary waves, Surface gravity waves",

author = "Tao Gao and Paul Milewski and Vanden-Broeck, {Jean Marc}",

note = "Funding Information: J.-M.V.-B. acknowledges the support from EPSRC, UK Grant No. EP/N018559/1 . P.M. was supported by EPSRC, UK under Grant No. EP/N018176/1 . Funding Information: J.-M.V.-B. acknowledges the support from EPSRC, UK Grant No. EP/N018559/1. P.M. was supported by EPSRC, UK under Grant No. EP/N018176/1. Publisher Copyright: {\textcopyright} 2018 Elsevier B.V.",

year = "2019",

month = jan,

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doi = "10.1016/j.wavemoti.2018.11.005",

language = "English",

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journal = "Wave Motion",

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AU - Gao, Tao

AU - Milewski, Paul

AU - Vanden-Broeck, Jean Marc

N1 - Funding Information: J.-M.V.-B. acknowledges the support from EPSRC, UK Grant No. EP/N018559/1 . P.M. was supported by EPSRC, UK under Grant No. EP/N018176/1 . Funding Information: J.-M.V.-B. acknowledges the support from EPSRC, UK Grant No. EP/N018559/1. P.M. was supported by EPSRC, UK under Grant No. EP/N018176/1. Publisher Copyright: © 2018 Elsevier B.V.

PY - 2019/1/1

Y1 - 2019/1/1

N2 - In this work, two-dimensional hydroelastic solitary waves in the presence of constant vorticity are studied. Time-dependent conformal mapping techniques first developed for irrotational waves are applied subject to appropriate modification. An illustrative high-order Nonlinear Schrödinger Equation is presented to investigate whether a given envelope collapses into a singular point in finite time by using the virial theory. Travelling solitary waves on water of infinite depth are computed for different values of vorticity and new generalised solitary waves are discovered. The stabilities of these waves are examined numerically by using fully nonlinear time-dependent computations which confirm the virial theory analysis.

AB - In this work, two-dimensional hydroelastic solitary waves in the presence of constant vorticity are studied. Time-dependent conformal mapping techniques first developed for irrotational waves are applied subject to appropriate modification. An illustrative high-order Nonlinear Schrödinger Equation is presented to investigate whether a given envelope collapses into a singular point in finite time by using the virial theory. Travelling solitary waves on water of infinite depth are computed for different values of vorticity and new generalised solitary waves are discovered. The stabilities of these waves are examined numerically by using fully nonlinear time-dependent computations which confirm the virial theory analysis.

KW - Asymmetric waves

KW - Elastic waves

KW - Solitary waves

KW - Surface gravity waves

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U2 - 10.1016/j.wavemoti.2018.11.005

DO - 10.1016/j.wavemoti.2018.11.005

M3 - Article

AN - SCOPUS:85057462606

SN - 0165-2125

VL - 85

SP - 84

EP - 97

JO - Wave Motion

JF - Wave Motion

ER -

Hydroelastic solitary waves with constant vorticity

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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Modelling, Computation ahnd Analysis of Droplets Guided by Faraday Waves: A Complex System with Macroscopic Quantum Analogies

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Hydroelastic solitary waves with constant vorticity

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Projects

Modelling, Computation ahnd Analysis of Droplets Guided by Faraday Waves: A Complex System with Macroscopic Quantum Analogies

Cite this