September 28, 2010
Title: An Introduction to the Problem of Fluid Turbulence
Abstract: I will briefly explain two typical approaches to the problem of fluid turbulence, which are respectively based upon the structural and statistical descriptions of turbulence. The former has difficulty in reproducibility of chaotic evolution of turbulence structures, while the latter has difficulty obtaining a rigorous governing equation for turbulence statistics. Next I will propose a novel approach based on dynamical-system theory. In this approach turbulent flow is characterized in terms of simple invariant sets in phase space, which are represented by equilibrium and periodic solutions to the Navier-Stokes equation, the equation of fluid motion. Several invariant solutions have been found to exhibit similar statistical properties to turbulent flow. I will show reproducible dynamics of flow structures in the solutions to discuss their relevance with the appearance of universal statistical laws of turbulence.
Biography: Prof. Genta Kawahara received his PhD from Osaka University in 1994. In 2001, following assistant and associate professor positions in the Faculty of Engineering, Ehime University, he became an associate professor in the Graduate School of Engineering, Kyoto University. In 2001, he moved to the Graduate School of Engineering Science, Osaka University where he is now a professor and associate dean.