Applied Math. Colloquium A new calculus for two dimensional vortex dynamics

2009-12-21 17:40 - 2009-12-21 18:30
Prof. Darren Crowdy (Imperial College London, UK)
Abstract: In classical fluid dynamics, an important problem arising in avariety of applications is to understand how vorticity interacts with solid objects (e.g. aerofoils, obstacles or stirrers). For planar flows, a variety of powerful mathematical results exist but the constructions are usually restricted to problems with just one, or perhaps two, objects. The talk will show that there is a way to formulate the theory so that the relevant fluid dynamical formulae are exactly the same irrespective of the connectivity of the domain thereby leading to a flexible ``calculus'' for solving such problems. The approach is built on the methodologies expounded in the first talk. This application represents just one physical example where methods based on the Schottky-Klein prime function can be profitably employed.