Speaker: Dr. Katie Oliveras, Associate Professor at Seattle University

Title: The Instability of Surface Water Waves

Abstract:  Euler’s equations describe the shape of waves in an ideal fluid.  These equations admit waves of unchanging shape that move at a constant speed.  But what happens to these waves when they are perturbed?  While direct numerical simulation of the equations of motion yields insight, they are computational expensive.  In this talk, we discuss the spectral stability or instability of periodic traveling wave solutions for the full set of Euler’s equations as various physical parameters such as gravity, fluid depth, surface tension, and vorticity are varied.  This allows us to explore a broader parameter space in a systematic, less computational expensive, manner.  With this approach, the role of various boundary conditions is also explored and will highlight dramatic differences in stability when considering a single versus a multi-layer, density-stratified fluid.