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

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.  

http://www.maths.usyd.edu.au/u/AppliedSeminar/abstracts/2008/denier.html