Speaker: Ryan Creedon, University of Washington
Date: April 27, 2023
Title: An Asymptotic Description of the Spectral Instabilities of Stokes Waves
Abstract: Euler's equations govern the behavior of gravity waves on the surface of an incompressible, inviscid, and irrotational fluid. In this talk, we consider the small-amplitude, periodic traveling-wave solutions of Euler's equations known as the Stokes waves. We investigate the instabilities of Stokes waves present in the spectrum of the linearized Euler's equations about these solutions. These instabilities encompass the Benjamin-Feir (or modulational) instability as well as the recently discovered high-frequency instabilities. A perturbation method is developed to approximate the unstable spectral elements associated with each of these instabilities in both finite and infinite depth, allowing us to obtain desirable asymptotic properties that connect recent numerical and rigorous studies. In all cases, we compare our asymptotic results with direct numerical computations of these instabilities and find excellent agreement, giving confidence in the validity of the perturbation method.
Location: Residents of Lewis Hall can attend talks in the Wan Conference Room (Lewis 208). The talk will also be streamed live via Zoom.