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Remarks on a strongly nonlinear model for two-layer flows with a top free surface

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posted on 2018-07-10, 12:21 authored by Ricardo Lopes-BarrosRicardo Lopes-Barros
We revisit in this paper the strongly nonlinear long wave model for large amplitude internal waves in two-layer flows with a free surface proposed by Choi and Camassa [1] and Barros et al. [2]. Its solitary-wave solutions were the object of the work by Barros and Gavrilyuk [3], who proved that such solutions are governed by a Hamiltonian system with two degrees of freedom. A detailed analysis of the critical points of the system is presented here, leading to some new results. It is shown that conjugate states for the long wave model are the same as those predicted by the fully nonlinear Euler equations. Some emphasis will be given to the baroclinic mode, where interfacial waves are known to change polarity according to different values of density and depth ratios. A critical depth ratio separates these two regimes and its analytical expression is derived directly from the model. In addition, we prove that such waves cannot exist throughout the whole range of speeds.

Funding

The author acknowledges the support of MACSI, the Mathematics Applications Consortium for Science and Industry (www.macsi.ul.ie) funded by the Science Foundation Ireland Investigator Award 12/IA/1683, and the Irish Research Council through the “New Foundations’ Scheme 2014”.

History

School

  • Science

Department

  • Mathematical Sciences

Published in

Studies in Applied Mathematics

Volume

136

Issue

3

Pages

263 - 287

Citation

BARROS, R., 2015. Remarks on a strongly nonlinear model for two-layer flows with a top free surface. Studies in Applied Mathematics, 136 (3), pp.263-287.

Publisher

© Wiley

Version

  • AM (Accepted Manuscript)

Publisher statement

This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/

Publication date

2015

Notes

This is the peer reviewed version of the following article: BARROS, R., 2015. Remarks on a strongly nonlinear model for two-layer flows with a top free surface. Studies in Applied Mathematics, 136 (3), pp.263-287, which has been published in final form at https://doi.org/10.1111/sapm.12104. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions.

ISSN

0022-2526

eISSN

1467-9590

Language

  • en

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