EVENT DETAILS AND ABSTRACT

Title: Characterizing spatiotemporal chaos in the Kuramoto-Sivashinsky and related equations
Speaker: Ralf Wittenberg
Speaker Info: University of Michigan
Brief Description:
Special Note: More current information may be available at Plan-it Purple
Abstract:

We discuss some aspects of spatiotemporal chaos (STC) in the one-dimensional Kuramoto-Sivashinsky (KS) equation. In particular, we will describe how a wavelet projection may be used to elucidate features of the dynamics, and we will discuss some numerical experiments to probe the localization of the dynamics in space and scale. These experiments have motivated the construction of relatively low-dimensional, spatially localized models for a minimal "chaotic box", in the form of externally excited, periodized wavelet projections of the KS evolution equation. We will particularly comment on the importance of the large scales in maintaining the spatiotemporal disorder, and illustrate this with two other examples: The KS equation in the presence of an additional destabilizing linear term displays a transition from STC to a stationary shock-like solution, due to excitation at the large scales. We will also briefly discuss a sixth-order analogue of the KS equation in which STC is maintained by the coupling to large scales.