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Strongly nonlinear effects on internal solitary waves in three-layer flows

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journal contribution
posted on 07.11.2019, 11:12 by Ricardo Lopes-Barros, Wooyoung Choi, Paul Antoine Milewski
We consider a strongly nonlinear long wave model for large amplitude internal waves in a three-layer flow between two rigid boundaries. The model extends the two-layer Miyata-Choi-Camassa (MCC) model (Miyata 1988; Choi & Camassa 1999) and is able to describe the propagation of long internal waves of both the first and second baroclinic modes. Solitary-wave solutions of the model are shown to be governed by a Hamiltonian system with two degrees of freedom. Emphasis is given to the solitary waves of the second baroclinic mode (mode 2) and their strongly nonlinear characteristics that fail to be captured by weakly nonlinear models. In certain asymptotic limits relevant to oceanic applications and previous laboratory experiments, it is shown that large amplitude mode2 waves with single-hump profiles can be described by the solitary wave solutions of the MCC model, originally developed for mode-1 waves in a two-layer system. In other cases, however, e.g. when the density stratification is weak and the density transition layer is thin, the richness of the dynamical system with two degrees of freedom becomes apparent and new classes of mode-2 solitary wave solutions of large amplitudes, characterized by multi-humped wave profiles, can be found. In contrast with the classical solitary-wave solutions described by the MCC equation, such multi-humped solutions cannot exist for a continuum set of wave speeds for a given layer configuration. Our analytical predictions based on asymptotic theory are then corroborated by a numerical study of the original Hamiltonian system.

Funding

MACSI, the Mathematics Applications Consortium for Science and Industry (www.macsi.ul.ie) funded by the Science Foundation Ireland Investigator Award 12/IA/1683

US National Science Foundation through grant nos DMS-1517456 and OCE-1634939

Royal Society Wolfson award

History

School

  • Science

Department

  • Mathematical Sciences

Published in

Journal of Fluid Mechanics

Volume

883

Publisher

Cambridge University Press (CUP)

Version

AM (Accepted Manuscript)

Rights holder

© Cambridge University Press

Publisher statement

This article has been published in a revised form in Journal of Fluid Mechanics https://doi.org/10.1017/jfm.2019.795. This version is published under a Creative Commons CC-BY-NC-ND. No commercial re-distribution or re-use allowed. Derivative works cannot be distributed. © Cambridge University Press.

Acceptance date

26/10/2019

Publication date

2019-11-25

Copyright date

2019

ISSN

0022-1120

eISSN

1469-7645

Language

en

Depositor

Dr Ricardo Lopes Barros. Deposit date: 6 November 2019

Article number

A16

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