Date/Time
Date(s) - 15/11/2024
11:30 am - 12:30 pm

Location: Hamilton Hall, Room 312

Speaker: Sergey Dyachenko (SUNY Buffalo)

Title: The Stokes wave on ideal fluid: modulational instability and wave breaking

Abstract: The long-standing problem of linear stability of surface waves on 2D fluid is solved in conformal variables for Stokes up to nearly extreme steepness. The stability spectrum of Stokes waves exhibits recurrent transitions, multiple modulation, or Benjamin-Feir instability branches. We show that all Stokes waves are, in fact, unstable, but the nature of these instabilities varies  — in some cases it leads directly to wave-breaking, and, in others, to modulational disturbance of ocean swell. We discuss the profound change in the numerical approach that allowed us to consider nearly extreme Stokes waves.