Model for shock wave chaos

manta-ray4-big-01We propose a simple model equation that predicts chaotic shock waves, similar to those in detonations in chemically reacting mixtures. The equation is given on the half line, with the shock located at x=0.  This equation retains the essential physics needed to reproduce many properties of detonations in gaseous reactive mixtures: steady traveling wave solutions, instability of such solutions, and the onset of chaos. Our model is the first (to our knowledge) to describe chaos in shock waves by a scalar first-order partial differential equation. The chaos arises in the equation thanks to an interplay between the nonlinearity of the inviscid Burgers equation and a novel forcing term that is nonlocal in nature and has deep physical roots in reactive Euler equations.

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