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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 |
2198-5634
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| Digitales Dokument |
URL |
| Erschienen |
In: Nonlinear Processes in Geophysics Discussions ; 2, no. 1 ; Nr. 2, no. 1 (2015-01-06), S.1-41 |
| Datensatznummer |
250115141
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| Publikation (Nr.) |
 copernicus.org/npgd-2-1-2015.pdf |
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| Zusammenfassung |
| Long weakly nonlinear finite-amplitude internal waves in a fluid
consisting of three inviscid immiscible 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 of 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 equation (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 both the quadratic and the cubic nonlinear terms
vanish for several realistic configurations of such a fluid. |
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