Date & Time: Wednesday, August 18, 2010, 16:30-17:15.

Venue: Ramanujan Hall

Title: Diffusion-driven flow in a stratified viscous fluid – and unexpected propulsion

Speaker: Michael Page

Biography: Associate Professor Michael Page is in the School of Mathematical Sciences at the Clayton campus of Monash University in Melbourne, Australia. He completed a BSc(Hons) in Mathematics at the University of Western Australia and then a PhD in Mathematics at University College London, on aspects of rapidly-rotating flows in a viscous fluid. This was followed by a Postdoctoral Fellowship at the University of East Anglia in Norwich, England on unsteady separating flows. His research activities include the mathematical and computational analysis of a range of viscous flows, for both high-Reynolds number non-rotating configurations and geophysical applications. His areas of interest span steady and unsteady boundary-layer motion (ranging from separated supersonic flows, to recirculation in curved-pipe flows, reattachment in incompressible flows and singularities which lead to eruption in unsteady boundary-layer flows), simple models of the ocean circulation (in particular in the western boundary layer) and the generation of ‘diffusion-driven’ flows in a contained density-stratified fluid. Most of his work combines techniques from computational fluid dynamics with asymptotic analysis in the limit of small or large parameters.

Abstract: In 1970, two independent studies (by Wunsch and Phillips) of the behaviour of a linear density-stratified viscous fluid in a closed container demonstrated a slow flow can be generated simply due to the container having a sloping boundary surface. This remarkable motion is generated as a result of the curvature of the lines of constant density near any sloping surface, which in turn enables a zero normal-flux condition on the density to be satisfied along that boundary. A recent experimental study, published in Nature Physics, has demonstrated that the same phenomenon can lead to the `diffusion driven propulsion' of a wedge-shaped object through a tank of stratified fluid. In this talk, the mathematical structure of these flows will be considered in a closed container in the limit when the Rayleigh number is large (or equivalently Wunsch's parameter R is small). It will be shown that this motion is concentrated in the near vicinity of the sloping surface, in a thin `buoyancy layer', which can then drive a broader-scale mass recirculation in a closed container. Further work on both the unsteady flow properties and the flow for other geometrical configurations will also be described.