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le 11 octobre 2012
Paul Clavin, IRPHE, Aix-Marseille University
Gaseous shock waves have been discovered during the 19th century. Their planar front is known from a long time to be stable, but the relaxation mechanism is still not well understood and misunderstandings appear in the modern literature. The results obtained from 1955 to 1975 concern perturbations by acoustic waves occurring in shock diffraction. They indicate that the perturbations of the shock decay with time as 1/t3/2 or 1/t1/2. Experiments show also the systematic formation of Mach stems (triple points) propagating in the transverse direction during the relaxation process. No attention was paid to this phenomenon, which is not explained yet. Recent experiments at IUSTI in Marseille concerning the reflection of a shock on a wavy wall present long-living patterns of triple points that are quite similar to that observed in cellular detonations.
Using the same limiting case as that we have used in our previous work on detonations (strong shock in the Newtonian limit), I will present recent analytic results for the stability analysis of gaseous shock fronts, their nonlinear dynamics, and their interaction with vortices and turbulent flows. The result predicts the formation of singularities within a finite time travelling in the transverse direction with the sound speed of the shocked gas. They may be representative of the formation of Mach stems.