Guan, X; Vanden-Broeck, J-M; Wang, Z; Dias, F; (2021) A local model for the limiting configuration of interfacial solitary waves. Journal of Fluid Mechanics , 921 , Article A9. 10.1017/jfm.2021.521.

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Abstract

The limiting configuration of interfacial solitary waves between two homogeneous fluids consisting of a sharp 120∘ angle with an enclosed bubble of stagnant heavier fluid on top is investigated numerically. We use a boundary integral equation method to compute the almost limiting profiles which are nearly self-intersecting and thus extend the work of Pullin & Grimshaw (Phys. Fluids, vol. 31, 1988, pp. 3550–3559) by obtaining the overhanging solutions for very small density ratios. To further study the local configuration of the limiting profile, we propose a reduced model that replaces the 120∘ angle with two straight solid walls intersecting at the bottom of the bubble. Using a series truncation method, a one-parameter family of solutions depending on the angle between the two solid walls (denoted by γ) is found. When γ=2π/3, it is shown that the simplified model agrees well with the near-limiting wave profile if the density ratio is small, and thus provides a good local approximation to the assumed limiting configuration. Interesting solutions for other values of γ are also explored.

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