These talks will be self-contained presentations of mathematical concepts and theorems. They are intended to be accessible to all mathematics students.

The study of fluid flows presents many interesting, and often extremely difficult, mathematical problems. A relatively small number of "simple" flows yield exact solutions, however the vast majority of "practical" flows must be studied either experimentally or using numerical techniques. In this talk the physical concepts and equations governing fluid flows will be introduced and discussed. The fluids group in mechanical engineering undertakes fundamental and applied research into a number of areas including: flows around bluff bodies, swirling flows, free-surface flows, fluid mixing, vortex structures, jet dynamics, multiphase and complex flows. A number of current research projects will be described in more detail, including studies of: the three-dimensionality of bluff body wakes, flow-induced motion and wind turbines. The mathematical techniques used in these investigations will be presented and discussed from an engineering perspective.