Numerical study of interfacial solitary waves propagating under an elastic sheet

Steady solitary and generalized solitary waves of a two-fluid problem where the upper layer is under a flexible elastic sheet are considered as a model for internal waves under an ice-covered ocean. The fluid consists of two layers of constant densities, separated by an interface. The elastic sheet...

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Bibliographic Details
Published in:Proceedings of the Royal Society. A, Mathematical, physical, and engineering sciences Mathematical, physical, and engineering sciences, 2014-08, Vol.470 (2168), p.20140111-20140111
Main Authors: Wang, Zhan, P r u, Emilian I., Milewski, Paul A., Vanden-Broeck, Jean-Marc
Format: Article
Language:English
Subjects:
Computation
Constants
Density
Elastic sheets
Generalized Solitary Wave
Gravity-Flexural
Interfacial Wave
Mathematical models
Solitary Wave
Solitary waves
Thin walled shells
Trains
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Summary:Steady solitary and generalized solitary waves of a two-fluid problem where the upper layer is under a flexible elastic sheet are considered as a model for internal waves under an ice-covered ocean. The fluid consists of two layers of constant densities, separated by an interface. The elastic sheet resists bending forces and is mathematically described by a fully nonlinear thin shell model. Fully localized solitary waves are computed via a boundary integral method. Progression along the various branches of solutions shows that barotropic (i.e. surface modes) wave-packet solitary wave branches end with the free surface approaching the interface. On the other hand, the limiting configurations of long baroclinic (i.e. internal) solitary waves are characterized by an infinite broadening in the horizontal direction. Baroclinic wave-packet modes also exist for a large range of amplitudes and generalized solitary waves are computed in a case of a long internal mode in resonance with surface modes. In contrast to the pure gravity case (i.e without an elastic cover), these generalized solitary waves exhibit new Wilton-ripple-like periodic trains in the far field.
ISSN:1364-5021
1471-2946
DOI:10.1098/rspa.2014.0111