Applied PDE Seminar: Anastassiya Semenova, Almost extreme Stokes waves and their stability

Submitted by Anastassiya Semenova on

Speaker: Anastassiya Semenova, University of Washington

Date: May 11, 2023

Title:  Almost extreme Stokes waves and their stability

Abstract: We consider an ideal 2-dimensional fluid of infinite depth with potential flow and a free surface. Stokes waves are traveling waves on a free surface of the fluid. The equations of motion describing the free surface are linearized around Stokes waves in a moving frame, and we study the resulting eigenvalue problem. We present the eigenvalue spectrum of Stokes waves with various steepnesses and show the Benjamin-Feir, high-frequency and superharmonic (localized) instabilities of these waves. As we approach the wave of the greatest height, we discuss the growth rate of the instability with the largest real part.

Location: Residents of Lewis Hall can attend talks in the Wan Conference Room (Lewis 208). The talk will also be streamed live via Zoom.