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arXiv · 2203.03537

The wave stability of solitary waves over a bump for the full Euler equations

Marcelo V. Flamarion·Roberto Ribeiro-Jr
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Abstract

In this work, we present a numerical study of the wave stability of steady solitary waves over a localised topographic obstacle through the full Euler equations. There are two branches of the solutions: one from the perturbed uniform flow and the other from the perturbed solitary-wave flow. We find that steady waves from the perturbed uniform flow are always stable with respect to perturbations of its amplitude. Regarding the perturbed solitary-wave, when the perturbed initial condition has smaller amplitude than the steady solution we notice a certain type of stability. Yet, when the perturbed initial condition has larger amplitude than the steady solution an onset of wave-breaking seem to occur.

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Marcelo V. Flamarion, Roberto Ribeiro-Jr. 2022-03-07. The wave stability of solitary waves over a bump for the full Euler equations. https://arxiv.org/abs/2203.03537

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