On December 1, 2009 Bruce Boghosian (Tufts University) will be delivering a lecture entitled “The Dynamical Systems Approach to Turbulence – Challenges for High-Performance Computing “.

Location: 2231 French Family Science Center

Time: 4:30pm

Abstract: Turbulence is sometimes call the “last unsolved problem of classical mechanics”. While it has long been understood that the details of turbulent flow are essentially unpredictable beyond a number of Lyapunov times due to the so-called “Butterfly effect”, hope remains for a comprehensive statistical description of turbulence. Two developments in dynamical systems theory over the past twenty years provide solid foundation for that hope. The first is the observation, placed on firm foundation in the 1980s, that Navier-Stokes flow has a finite-dimensional attracting set of states. The second is the development of the dynamical zeta function formalism by Ruelle, and its deployment by Cvitanovic, Pollicott, Eckhardt, Yorke and others, enabling statistical descriptions of chaotic dynamical systems, given knowledge of their unstable periodic orbits (UPOs). For this reason, the efficient numerical computation of UPOs has gained great importance over the past decade, in both the dynamical systems and turbulence literature. Periodic orbits for high-dimensional state spaces are devilishly difficult to calculate, requiring high-performance computing and placing new demands on algorithms, accuracy and hardware. This talk will discuss some of these computational challenges and demonstrate the successful computation of UPOs of driven Navier-Stokes turbulence in two spatial dimensions.