For more information about this meeting, contact Xiantao Li, Yuxi Zheng, Kris Jenssen, Jinchao Xu.

Title: | A new calculus for ideal ď¬‚uid dynamics |

Seminar: | Computational and Applied Mathematics Colloquium |

Speaker: | Darren Crowdy, Imperial College, UK |

Abstract: |

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. |

### Room Reservation Information

Room Number: | MB106 |

Date: | 12 / 03 / 2010 |

Time: | 03:35pm - 04:25pm |