Title: Water Waves: Instabilities of Steep Stokes Waves

Abstract: The study of ocean waves, particularly surface waves, is essential for predicting and preparing for natural disasters such as tsunamis, storm surges, hurricanes, and others. Although ocean waves naturally occur in three dimensions, there are instances when water waves can be considered in a two-dimensional framework. For example, waves that travel away from an epicenter of a storm can be considered unidirectional waves. In this talk, we consider periodic traveling waves occurring at the free surface of an ideal two-dimensional fluid of infinite depth. In particular, we will introduce surface waves of permanent shape commonly referred to as Stokes waves and discuss their stability. We will show how to examine stability of these waves and present the growth rate of the dominant instability and discuss the Benjamin-Feir, high-frequency and superharmonic instabilities associated with these waves.

About the Speaker:  Dr. Anastassiya Semenova, is a UNM Alumni (BS 2013 Summa Cum Laude, MS 2016 and PhD 2020). Her PhD advisors were Alex Korotkevich and Pavel Lushnikov and her Dissertation was titled "Numerical Simulations of Nonlinear Waves and Their Stability: Stokes Waves and Nonlinear Schroedinger Equation".  Dr. Semenova spent a year (2021-22) as a Postdoc at the Institute for Computational and Experimental Research in Mathematics (ICERM) at Brown University, Providence, RI.  She is currently PIMS-Simons Postdoctoral Fellow at the Department of Applied Mathematics, University of Washington, Seattle. Dr. Semenova has already sevaral publications including a recent one in the Proceedings of the National Academy of Sciences, in the Journal of Computational Physics and Studies in Applied Mathematics.