Large Internal Solitary Waves in Shallow Waters

Liapidevskii, V. Yu.; Гаврилов, Н. М.

doi:10.1007/978-3-319-71934-4_9

Cited by 14 publications

(9 citation statements)

References 23 publications

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“…In addition to single-humped profiles, we find branches of exotic multi-hump solutions for both the fully nonlinear Euler equations and the MCC3 equations. For MCC3, this extends the work of Liapidevskii & Gavrilov (2018) and Barros et al (2020), who previously computed multi-humped waves within the strongly nonlinear regime, but limited to small depths of the intermediate layer. In fact, such solutions are revealed to be prolific throughout the parameter space.…”

Section: Discussionsupporting

confidence: 80%

“…They were recovered in the asymptotic limit H 2 → 0, but were found numerically to persist for finite values of H 2 . Such solutions were coined multi-hump solitary waves, and appear to have been observed in the laboratory by Liapidevskii & Gavrilov (2018) and Gavrilov et al (2013).…”

Section: Multi-hump Solitary Wavesmentioning

confidence: 92%

“…Mode-2 ISW Euler computations without these symmetries have thus far yielded only GSWs (Vanden-Broeck & Turner 1992;Rusås & Grue 2002). Hence, numerical evidence for generic mode-2 'true' solitary waves was lacking, but recent laboratory observations point to their existence (Gavrilov, Liapidevskii & Liapidevskaya 2013;Liapidevskii & Gavrilov 2018).…”

Section: Introductionmentioning

confidence: 99%

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

2022

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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.

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Section: Discussionsupporting

confidence: 80%

Section: Multi-hump Solitary Wavesmentioning

confidence: 92%

Section: Introductionmentioning

confidence: 99%

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

2022

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“…In addition to single-humped profiles, we find branches of exotic multi-hump solutions for both the fully nonlinear Euler equations and the reduced MCC3 equations. For MCC, this extends the work of Liapidevskii and Gavrilov [2018] and Barros et al [2020], who previously computed multi-humped waves within the strongly nonlinear regime, but limited to small depths of the intermediate layer. In fact, such solutions reveal to be prolific throughout the parameter space.…”

Section: Discussionsupporting

confidence: 84%

“…These solutions are related to the curious 'multi-hump' solutions found in Barros et al [2020], which are solitary waves characterised by multiple oscillations on one or both interfaces. Multi-hump waves have also been witnessed in experimental conditions by Liapidevskii and Gavrilov [2018], who also found numerical solutions to a modified MCC3 system, which includes the additional assumption that the pressure in the middle layer is purely hydrostatic. The insight gained by exploring critical points of the potential of the MCC3 system extend to the full Euler system: it is found that, although the MCC3 solutions are at times quantitatively poor, the qualitative similarities are remarkable.…”

Section: Introductionmentioning

confidence: 82%

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

Doak¹,

Barros²,

Milewski³

2022

Preprint

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In this paper, we investigate mode-2 solitary waves in a three-layer stratified flow model. Travelling wave solutions to both the fully nonlinear problem (Euler equations), and a three-layer extension of the strongly nonlinear two-layer Miyata-Choi-Camassa equations are found numerically. Mode-2 solitary waves with speeds slower than the linear mode-1 long-wave speed are typically expected to be generalised solitary waves: that is, their tails consist of a resonant modeone 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 exceed the mode-1 linear long wave speed. Further, we show how some forms of the embedded solitary waves are intimately linked to the conjugate states of the problem.

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Laboratory Experiments on an Internal Solitary Wave over a Triangular Barrier

2019

J. Ocean Univ. China

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Large Internal Solitary Waves in Shallow Waters

Cited by 14 publications

References 23 publications

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

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

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

Laboratory Experiments on an Internal Solitary Wave over a Triangular Barrier

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