Plenary Talk: Mode-2 solitary waves in 3-layer flows

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• Paul Milewski (University of Bath)
• Thursday 08 December 2022, 09:00-10:00
• Seminar Room 1, Newton Institute.

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HY2W05 - Physical applications

Stratified fluids with narrow regions of rapid density variation with respect to depth (pycnoclines) are often modelled as layered flows. In this talk we shall examine horizontally propagating internal waves of the second baroclinic mode (mode-2), by computing travelling wave solutions within three-layer fluid. We will be presenting numerical solutions to both the full Euler equations and to a reduced fully-nonlinear, weakly dispersive model, the three-layer Miyata-Choi-Camassa (MCC3) equations. Mode-2 nonlinear waves (typically) occur within the linear spectrum of mode-1 waves, and are hence generically associated with an infinite energy resonant mode-1 oscillatory tail. However, in line with recent results for the MCC3 system by Barros, Choi & Milewski (JFM, 2020), we will present numerical evidence that these oscillations can be found to have zero amplitude, resulting in families of truly localised solutions (so called embedded solitary waves) in the Euler equations. We also discuss limiting solutions which are related to heteroclinic connections between the so called conjugate states of the system (which are identical in Euler and MCC3 ). This is joint work with Ricardo Barros and Alex Doak.

This talk is part of the Isaac Newton Institute Seminar Series series.

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