Self-similarity and recurrence in stability spectra of near-extreme Stokes waves

Bernard Deconinck; Sergey A. Dyachenko; Anastassiya Semenova

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arXiv · 2404.15481

Self-similarity and recurrence in stability spectra of near-extreme Stokes waves

Bernard Deconinck·Sergey A. Dyachenko·Anastassiya Semenova

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Abstract

We consider steady surface waves in an infinitely deep two--dimensional ideal fluid with potential flow, focusing on high-amplitude waves near the steepest wave with a 120 degree corner at the crest. The stability of these solutions with respect to coperiodic and subharmonic perturbations is studied, using new matrix-free numerical methods. We provide evidence for a plethora of conjectures on the nature of the instabilities as the steepest wave is approached, especially with regards to the self-similar recurrence of the stability spectrum near the origin of the spectral plane.

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Bernard Deconinck, Sergey A. Dyachenko, Anastassiya Semenova. 2024-04-23. Self-similarity and recurrence in stability spectra of near-extreme Stokes waves. https://arxiv.org/abs/2404.15481

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