2024/04/23 by Bernard Deconinck, Deconinck, Bernard, Sergey A. Dyachenko +3
Earth and Planetary Sciences · Environmental Science · Mathematics · #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Gas Dynamics and Kinetic Theory #Mathematical Physics (math-ph) #Methane Hydrates and Related Phenomena #Ocean Waves and Remote Sensing
paper · pdf · doi:10.48550/arxiv.2404.15481
openalex publication_date 2024/04/23 · openalex created_date 2024/04/26 · openalex updated_date 2026/07/28
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.