« Nonlinear waves and fronts in flows: From flames, shocks and detonations to the explosion of stars »
By Paul Clavin, Aix-Marseille Université, CNRS, Centrale Marseille, IRPHE UMR7342
This seminar presents a review of recent analytical studies of reacting flows, including the dynamics of unstable flames and detonations as well as thermo-acoustic instabilities. These topics that are essential in many applied domains (safety of nuclear plants, in-stabilities of gas turbines and rocket engines, super knocking,..), involve stiff problems concerning complex systems. By using multiple-scale methods the problems are reduced to study the coupled dynamics of fronts and flows, the coupling resulting from the density change through the fronts. The attention is focused on the formation and dynamics of the singularities of slope that characterize these unstable fronts (cusped flames, cellular detonations, Mach-stems of wrinkled shock waves,..). Generally speaking, the objective is to perform a systematic reduction of the complexity to set up a simplified nonlinear PDE for the front dynamics that can then be investigated accurately by numerical analyses. The essential ingredients for a successful input are deep physical insights into the problem and comparison with small-scale carefully controlled experiments. The purely mathematical contents are neither the most difficult nor the most essential parts. Different examples will be presented ranging from unsteady propagation of flames in tubes, initiation of detonations… to explosion of the iron core of massive stars at the end of their life time (supernovae SN IIa).