Manchester Applied Mathematics and Numerical Analysis Seminars Spring 1999/2000

March 8, 2000, 4.00 pm

Lecture Theatre OF/B9 Oddfellows Hall (Material Science)

Feedback instabilities in boundary-layer flows

Dr. Sergei Timoshin, Dept. of Mathematics, UCL

Slowly varying flows which exhibit instability to infinitesimal disturbances can be classified as convectively unstable or absolutely unstable depending on the flow response to a pulse perturbation. The flow geometries of concern in this presentation have extended regions of slow variation (where the classical stability analysis can be used) and localised regions of fast spatial variations such as entrance/exit sections in a channel, constirctions/expansions in a pipe, or isolated obstacles on a flat plate. We aim to establish the conditions under which the 'end effects' introduced by the spatial inhomogeneity can lead to a non-local (feedback) instability in the flow. The analysis is restricted to flows with asymptotically large Reynolds numbers (where properties of the feedback modes can be derived analytically or with minimum computation) and relies on model examples from compressible boundary layer theory, incompressible two-fluid flow and, if time allows, incompressible boundary layer. The common feature in all the cases considered is an interaction between slow upstream influence in the flow and relatively fast downstream growth of instability waves. The interaction takes place in the regions of spatial inhomogeneity where downstream travelling disturbances are converted into upstream travelling modes and vice versa, leading to self-sustained instability in the flow as a whole.

For further info contact either Matthias Heil (mheil@ma.man.ac.uk), Mark Muldoon (M.Muldoon@umist.ac.uk)or the seminar secretary (Tel. 0161 275 5800).