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Applied Mathematics Colloquium

Friday, October 14,  2005, 11:30 am
Cullimore Lecture Hall II
New Jersey Institute of Technology

Do Forcing and Viscosity Drive Chaotic Advection?

Christopher K. R. T. Jones

Department of Mathematics

University of North Carolina - Chapel Hill

Chapel Hill, NC

Abstract

The particle trajectories of a steady Euler flow in 2D are determined by an integrable system and hence exhibit no chaotic motion. The question then naturally arises as to whether a perturbed flow that incorporates the physical effects of viscosity and forcing can be chaotic. This problem is non-trivial since the perturbation is added at the level of the full partial differential equation but the potential chaos is at the level of Lagrangian trajectories. It brings up many issues including long-time existence for 2D Navier-Stokes and finite-time Melnikov theory.