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Proceedings of the Royal Society of Edinburgh Section A: Mathematics Proceedings of the Royal Society of Edinburgh Section A: Mathematics

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On the transverse linear instability of solitary water waves with large surface tension

Published online by Cambridge University Press:  12 July 2007

Robert L. Pego  and
S. M. Sun
Robert L. Pego
Affiliation:
Department of Mathematics, University of Maryland, College Park, MD 20742, USA (rlp@math.umd.edu)
S. M. Sun
Affiliation:
Department of Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, USA (sun@math.vt.edu)
Corresponding
E-mail address:
rlp@math.umd.edu
sun@math.vt.edu
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Abstract

The paper considers an incompressible and irrotational flow of a fluid with constant density bounded below by a rigid horizontal bottom and above by a free surface under the influence of gravity and surface tension. It is known that the full Euler equations have travelling two-dimensional solitary-wave solutions of small amplitude for large surface tension (Bond number greater than ⅓). This paper shows that these waves are linearly unstable to three-dimensional perturbations which oscillate along the wave crest with wavenumber in a finite band. The growth rates of these unstable modes are well approximated using the linearized Kadomtsev–Petviashvili equation with positive disper

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 134 , Issue 4 , August 2004 , pp. 733 - 752
Copyright
Copyright © Royal Society of Edinburgh 2004

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