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A reformulation and applications of interfacial fluids with a free surface

Published online by Cambridge University Press:  17 July 2009

T. S. HAUT  and
M. J. ABLOWITZ
T. S. HAUT
Affiliation:
Department of Applied Mathematics, University of Colorado at Boulder, 526 UCB, Boulder, CO 80209-0526, USA
M. J. ABLOWITZ*
Affiliation:
Department of Applied Mathematics, University of Colorado at Boulder, 526 UCB, Boulder, CO 80209-0526, USA
*
†Email address for correspondence: [email protected]
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Abstract

A non-local formulation, depending on a free spectral parameter, is presented governing two ideal fluids separated by a free interface and bounded above either by a free surface or by a rigid lid. This formulation is shown to be related to the Dirichlet–Neumann operators associated with the two-fluid equations. As an application, long wave equations are obtained; these include generalizations of the Benney–Luke and intermediate long wave equations, as well as their higher order perturbations. Computational studies reveal that both equations possess lump-type solutions, which indicate the possible existence of fully localized solitary waves in interfacial fluids with sufficient surface tension.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 631 , 25 July 2009 , pp. 375 - 396
Copyright
Copyright © Cambridge University Press 2009

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