Traveling waves are a powerful framework for analyzing physical phenomena described by PDEs, even as they pertain to numerical solvers. In this talk, I will look at traveling wave solutions to the incompressible Navier-Stokes equations for fluids with free surfaces and significant surface tension. These waves provide insight into the physics of the solutions, revealing how surface tension, gravity, and viscosity compete to set how a disturbance propagates and decays. Moreover, Free-surface flows have few known solutions, and traveling waves instead follow from the governing physics, and they can be posed across a wide range of Reynolds and Bond numbers and on both flat and curved geometries. Furthermore, understanding the behavior of traveling waves informs us of time-step restrictions our solvers may face.
About the Speaker
Gabriel is a 2nd year math PhD student, working with Professors J. Banks, W. Henshaw, and D. Schwendeman here at RPI and A. Alvarez Loya, D. Serino, and J. Bonilla in the T-5 group at Los Alamos.
