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Model for Shock Wave Chaos

Author(s)
Kasimov, Aslan R.; Faria, Luiz M.; Rosales, Rodolfo R.
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Abstract
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.
Date issued
2013-03
URI
http://hdl.handle.net/1721.1/79877
Department
Massachusetts Institute of Technology. Department of Mathematics
Journal
Physical Review Letters
Publisher
American Physical Society
Citation
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.
Version: Final published version
ISSN
0031-9007
1079-7114

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