Barros_Choi_Milewski_ISW.pdf (3.62 MB)
Strongly nonlinear effects on internal solitary waves in three-layer flows
journal contribution
posted on 2019-11-07, 11:12 authored by Ricardo Lopes-BarrosRicardo Lopes-Barros, Wooyoung Choi, Paul Antoine MilewskiWe 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 MechanicsVolume
883Publisher
Cambridge University Press (CUP)Version
- AM (Accepted Manuscript)
Rights holder
© Cambridge University PressPublisher 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
2019-10-26Publication date
2019-11-25Copyright date
2019ISSN
0022-1120eISSN
1469-7645Publisher version
Language
- en
Depositor
Dr Ricardo Lopes Barros. Deposit date: 6 November 2019Article number
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