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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 languageEnglish
Pages (from-to)84-97
Number of pages14
JournalWave Motion
Volume85
Early online date27 Nov 2018
DOIs
Publication statusPublished - 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

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