Physics Forum - Spaciotemporal Tiling of Infinite Spacetime Kuramoto-Sivashinsky Equation
Physics Forum - Spaciotemporal Tiling of Infinite Spacetime Kuramoto-Sivashinsky EquationOctober 18, 2018 @ 2:30 pm - 3:30 pmInteraction Zone
Turbulence is one of the oldest unsolved problems of classical Physics.
In recent years, fluid turbulence has made great strides by using ideas from Dynamical Systems Theory, Periodic Orbit Theory, as well as direct numerical simulations; however, extending these results to large physical scales has been very challenging. Our attempt to circumvent this difficulty is to develop a theory that is truly spatiotemporal. We will accomplish this by finding, studying, and utilizing solutions to the spatiotemporal Kuramoto-Sivashinsky equation with doubly periodic boundary conditions. The Kuramoto-Sivashinsky equation is a good testing ground because it serves as a simpler, one-dimensional analog to to the Navier-Stokes equation. We believe that these doubly periodic solutions will serve as
the foundation for a spatiotemporal theory of turbulence on infinite spatiotemporal domains.