Olga Trichtchenko | Physics and Astronomy, Western University
Solutions to nonlinear Euler equations and their stability
In this talk, we will discuss models that represent waves in the presence of gravity, surface tension as well as waves underneath a sheet of ice for an incompressible, inviscid and irrotational fluid. The resulting equations can be reformulated in a variety of ways and these lead to different approaches for numerically computing their solutions. We will show the different methods and illustrate with results for waves under a variety of conditions at the surface in both two and three dimensions. Once we obtain solutions, in order to understand how likely they are to occur in nature, we analyse their stability both analytically and numerically under various perturbations. We will conclude by showing which perturbations lead to exponentially growing instabilities and examine which simplified models exhibit the same instabilities as the full Euler equations.