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Fully nonlinear higher-order model equations for long internal waves in a two-fluid system

Published online by Cambridge University Press:  11 May 2010

SUMA DEBSARMA ,
K. P. DAS  and
JAMES T. KIRBY
SUMA DEBSARMA
Affiliation:
Department of Applied Mathematics, University of Calcutta, 92 A.P.C. Road, Kolkata 700009, India
K. P. DAS
Affiliation:
Department of Applied Mathematics, University of Calcutta, 92 A.P.C. Road, Kolkata 700009, India
JAMES T. KIRBY*
Affiliation:
Center for Applied Coastal Research, University of Delaware, Newark, DE 19716, USA
*
†Email address for correspondence: [email protected]
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Abstract

Fully nonlinear model equations, including dispersive effects at one-order higher approximation than in the model of Choi & Camassa (J. Fluid Mech., vol. 396, 1999, pp. 1–36), are derived for long internal waves propagating in two spatial horizontal dimensions in a two-fluid system, where the lower layer is of infinite depth. The model equations consist of two coupled equations for the displacement of the interface and the horizontal velocity of the upper layer at an arbitrary elevation, and they are correct to O(μ2) terms, where μ is the ratio of thickness of the upper-layer fluid to a typical wavelength. For solitary waves propagating in one horizontal direction, the two coupled equations reduce to a single equation for the elevation of the interface. Solitary wave profiles obtained numerically from this equation for different wave speeds are in good agreement with computational results based on Euler's equations. A numerical approach for the propagation of solitary waves is provided in the weakly nonlinear case.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 654 , 10 July 2010 , pp. 281 - 303
Copyright
Copyright © Cambridge University Press 2010

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