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Applied Mathematics Seminar
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Jim Denier
School of Mathematical Sciences, University of Adelaide

Anomalous behaviour in boundary-layers: short-scale instabilities, finite distance breakdown and non-uniqueness

Wednesday 24th September 14:05-14:55pm, Eastern Avenue Lecture Theatre.

This talk will present some new results on an old problem of (very) short-scale instabilities in boundary-layer flows. Starting with a rather simple flow over a heated surface we can show that the boundary-layer equations predict an anomalous short scale instability that is independent of the Reynolds number, a non-dimensional parameter that defines the dynamics of our fluid system. The origin of this short scale instability is explored and shown to be linked to a finite distance singularity which arises in the boundary-layer equations. We'll then go on to show that this singularity occurs in a wide range of boundary-layer problems and attempt (but perhaps fail) to argue that it is non-physical by presenting some calculations from a full numerical solution of the Navier-Stokes equations.