Abstract
We consider a strongly nonlinear long wave model for large amplitude internal waves in a threelayer ow between two rigid boundaries. The model extends the twolayer MiyataChoiCamassa (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. Solitarywave 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 singlehump profiles can be described by the solitary wave solutions of the MCC model, originally developed for mode1 waves in a twolayer 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 mode2 solitary wave solutions of large amplitudes, characterized by multihumped wave problles, can be found. In contrast with the classical solitarywave solutions described by the MCC equation, such multihumped 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 language  English 

Article number  A16 
Number of pages  36 
Journal  Journal of Fluid Mechanics 
Volume  883 
Early online date  25 Nov 2019 
DOIs  
Publication status  Published  25 Jan 2020 
Keywords
 Geophysical and Geological Flows, Solitary waves
 Geophysical and Geological Flows, Stratified flows
 Internal waves
 Waves/Freesurface Flows
ASJC Scopus subject areas
 Condensed Matter Physics
 Mechanics of Materials
 Mechanical Engineering
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Paul Milewski
 Department of Mathematical Sciences  Professor
 EPSRC Centre for Doctoral Training in Statistical Applied Mathematics (SAMBa)
 Centre for Networks and Collective Behaviour
 Water Innovation and Research Centre (WIRC)
 Centre for Mathematical Biology
 Centre for Nonlinear Mechanics
 EPSRC Centre for Doctoral Training in Advanced Automotive Propulsion Systems (AAPS CDT)
Person: Research & Teaching, Affiliate staff