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Large mode-2 internal solitary waves in three-layer flows

Published online by Cambridge University Press:  16 December 2022

A. Doak Open the ORCID record for A. Doak [Opens in a new window] ,
R. Barros Open the ORCID record for R. Barros [Opens in a new window]  and
P.A. Milewski Open the ORCID record for P.A. Milewski [Opens in a new window]
A. Doak*
Affiliation:
Department of Mathematical Sciences, Univesity of Bath, Bath BA2 7AY, UK
R. Barros
Affiliation:
Department of Mathematical Sciences, Loughborough University, Loughborough LE11 3TU, UK
P.A. Milewski
Affiliation:
Department of Mathematical Sciences, Univesity of Bath, Bath BA2 7AY, UK
*
†Email address for correspondence: add49@bath.ac.uk
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Abstract

In this paper, we investigate mode-2 solitary waves in a three-layer stratified flow model. Localised travelling wave solutions to both the fully nonlinear problem (Euler equations), and the three-layer Miyata–Choi–Camassa equations are found numerically and compared. Mode-2 solitary waves with speeds slower than the linear mode-1 long-wave speed are typically generalised solitary waves with infinite tails consisting of a resonant mode-1 periodic wave train. Herein, we evidence the existence of mode-2 embedded solitary waves, that is, we show that for specific values of the parameters, the amplitude of the oscillations in the tail are zero. For sufficiently thick middle layers, we also find branches of mode-2 solitary waves with speeds that extend beyond the mode-1 linear waves and are no longer embedded. In addition, we show how large amplitude embedded solitary waves are intimately linked to the conjugate states of the problem.

JFM classification

Geophysical and Geological Flows: Stratified flows Nonlinear Dynamical Systems: Bifurcation Waves/Free-surface Flows: Solitary waves
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 953 , 25 December 2022 , A42
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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References

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