# Meeting Details

Title: A new calculus for ideal ﬂuid dynamics Computational and Applied Mathematics Colloquium Darren Crowdy, Imperial College, UK In classical fluid dynamics, an important basic problem is to understand how solid bodies (e.g. aerofoils, obstacles or stirrers) immersed in an ideal fluid interact by communicating'' with each other through the ambient fluid. Also of interest is how vortices interact with such solid bodies (and each other). There is great interest in such problems in areas such as aerodynamics, biolocomotion and oceanography. For two-dimensional flows, a variety of powerful mathematical results exist (complex variable methods, conformal mapping, Kirchhoff-Routh theory) that have been used to study such problems, but the constructions are usually restricted to problems with just one, or perhaps two, objects. Expressed mathematically, most studies deal only with fluid regions that are simply or doubly connected. There has been a general and longstanding perception that problems involving fluid regions of higher connectivity -- that is, more than two interacting objects -- are too intractable to be tackled analytically (and that numerical methods must be used). The lecture 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 number of interacting objects (i.e., the approach is relevant to fluid domains of any finite connectivity). This provides a flexible and unified tool (a calculus'') for modelling the fluid dynamical interaction of multiple objects/aerofoils/obstacles in ideal flow as well as their interaction with free vortices. Examples of how to apply the calculus to specific problems will be given to illustrate its flexibility. More generally, the results have wider reaching applications beyond fluid dynamics and essentially provide a new calculus for two-dimensional potential theory.