Anastassiya Semenova: Superharmonic instabilities of Stokes waves

Submitted by Jorge Cisneros on

Speaker: Anastassiya Semenova, Institute for Computational and Experimental Research in Mathematics

Date: January 20, 2022

Title: Superharmonic instabilities of Stokes waves

Abstract: We consider the classical problem of water waves on the surface of an ideal fluid in 2D and in particular, we study the growth of perturbations to nearly limiting Stokes waves at infinite depth. The stability of Stokes waves is determined by the linearization of the equations of motion of fluid around a Stokes wave. The eigenvalue problem is solved numerically via shift and invert method. We identify each positive eigenvalue with an unstable eigenmode in the equations of motion, and find that real positive eigenvalues of the linearized problem converge to a self-similar curve as a function of steepness. The power law is suggested for unstable eigenmodes in the immediate vicinity of the limiting Stokes wave. We will discuss the topic of Stokes waves in the finite depth fluid.