Topics in the Mathematical Analysis of Vortex Dynamics

2014/10/07 Tue 15:00 - 18:00
2014/10/28 Tue 15:00 - 18:00
2014/11/17 Mon 15:00 - 18:00
2014/11/25 Tue 15:00 - 18:00
2014/12/11 Thu 15:00 - 18:00
Room 108, Building No.3
Robert Krasny
Kyoto University / University of Michigan

Topics in the Mathematical Analysis of Vortex Dynamics
After introducing the incompressible fluid equations, we present the following topics in the mathematical analysis of vortex dynamics,

(1) asymptotic analysis of singularity formation in an evolving vortex sheet (Moore 1979),
(2) dynamical systems analysis of transport, mixing, and chaos in the flow of an oscillating vortex pair (Rom-Kedar, Leonard, and Wiggins 1990).

Since these lectures are intended for students with diverse backgrounds in math and science, we present some background material, warm-up examples, and experimental results to motivate the interest in vortex dynamics. We also discuss related computations using vortex particle methods.