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| Titel |
Propagation regimes of interfacial solitary waves in a three-layer fluid |
| VerfasserIn |
O. E. Kurkina, A. A. Kurkin, E. A. Rouvinskaya, T. Soomere  |
| Medientyp |
Artikel
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| Sprache |
Englisch
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| ISSN |
1023-5809
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| Digitales Dokument |
URL |
| Erschienen |
In: Nonlinear Processes in Geophysics ; 22, no. 2 ; Nr. 22, no. 2 (2015-03-04), S.117-132 |
| Datensatznummer |
250120967
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| Publikation (Nr.) |
 copernicus.org/npg-22-117-2015.pdf |
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| Zusammenfassung |
| Long weakly nonlinear finite-amplitude
internal waves in a fluid consisting of three inviscid layers of arbitrary
thickness and constant densities (stable configuration, Boussinesq
approximation) bounded by a horizontal rigid bottom from below and by a rigid
lid at the surface are described up to the second order of perturbation
theory in small parameters of nonlinearity and dispersion. First, a pair of
alternatives of appropriate KdV-type equations with the coefficients
depending on the parameters of the fluid (layer positions and thickness,
density jumps) are derived for the displacements of both modes of internal
waves and for each interface between the layers. These equations are
integrable for a very limited set of coefficients and do not allow for proper
description of several near-critical cases when certain coefficients vanish.
A more specific equation allowing for a variety of solitonic solutions and
capable of resolving most near-critical situations is derived by means of the
introduction of another small parameter that describes the properties of the
medium and rescaling of the ratio of small parameters. This procedure leads
to a pair of implicitly interrelated alternatives of Gardner equations
(KdV-type equations with combined nonlinearity) for the two interfaces. We
present a detailed analysis of the relationships for the solutions for the
disturbances at both interfaces and various regimes of the appearance and
propagation properties of soliton solutions to these equations depending on
the combinations of the parameters of the fluid. It is shown that both the
quadratic and the cubic nonlinear terms vanish for several realistic
configurations of such a fluid. |
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