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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
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)

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
Copyright
Copyright © Royal Society of Edinburgh 2004

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