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

Ricardo Barros, Wooyoung Choi, Paul Milewski

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We consider a strongly nonlinear long wave model for large amplitude internal waves in a three-layer ow 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 mode-2 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 problles, 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.

Original languageEnglish
Article numberA16
Number of pages36
JournalJournal of Fluid Mechanics
Early online date25 Nov 2019
Publication statusPublished - 25 Jan 2020

Bibliographical note

Publisher Copyright:
© 2019 Cambridge University Press.


  • Geophysical and Geological Flows, Solitary waves
  • Geophysical and Geological Flows, Stratified flows
  • Internal waves
  • Waves/Free-surface Flows

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering


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