Water Waves: Instabilities of Stokes Waves

The study of ocean waves, particularly surface waves, is crucial for predicting and preparing for natural disasters such as tsunamis. Although ocean waves naturally occur in three dimensions, there are instances when they can be analyzed within a two-dimensional framework. For example, waves that propagate from the epicenter of a storm can be treated as unidirectional. In this presentation, we will examine periodic traveling waves that occur at the free surface of an ideal (incompressible and inviscid) two-dimensional fluid of infinite depth. Specifically, we will introduce surface waves of permanent shape, also known as Stokes waves and discuss their stability.