Model for Shock Wave Chaos
Author(s)Kasimov, Aslan R.; Faria, Luiz M.; Rosales, Rodolfo R.
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We propose the following model equation, u[subscript t]+1/2(u[superscript 2]-uu[subscript s])[subscript x]=f(x,u[subscript s]) that predicts chaotic shock waves, similar to those in detonations in chemically reacting mixtures. The equation is given on the half line, x<0, and the shock is located at x=0 for any t≥0. Here, u[subscript s](t) is the shock state and the source term f is taken to mimic the chemical energy release in detonations. 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.
DepartmentMassachusetts Institute of Technology. Department of Mathematics
Physical Review Letters
American Physical Society
Kasimov, Aslan R., Luiz M. Faria, and Rodolfo R. Rosales. Model for Shock Wave Chaos. Physical Review Letters 110, no. 10 (March 2013). © 2013 American Physical Society.
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