Type
ArticleKAUST Department
Applied Mathematics and Computational Science ProgramComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Date
2013-03-08Permanent link to this record
http://hdl.handle.net/10754/552862
Metadata
Show full item recordAbstract
We propose the following model equation, ut+1/2(u2−uus)x=f(x,us) 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, us(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.Citation
Model for Shock Wave Chaos 2013, 110 (10) Physical Review LettersPublisher
American Physical Society (APS)Journal
Physical Review LettersPubMed ID
23521260arXiv
1202.2989Additional Links
http://link.aps.org/doi/10.1103/PhysRevLett.110.104104ae974a485f413a2113503eed53cd6c53
10.1103/PhysRevLett.110.104104
Scopus Count
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