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Modulated Traveling Waves in Combustion

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Asymptotic and Numerical Methods for Partial Differential Equations with Critical Parameters

Part of the book series: NATO ASI Series ((ASIC,volume 384))

Abstract

We describe the formation of spatial and temporal patterns in cylindrical premixed flames. In particular, we consider the formation of rotating cellular flames described by modulated traveling waves (MTWs) along the flame front. We find different types of MTWs, distinguished by their symmetries, in different parameter regimes of the Lewis number, Le, the ratio of thermal diffusivity to mass diffusivity of a deficient component of the mixture. The nature and evolution of the MTWs are described for each case. The adaptive pseudo-spectral method, which we developed for these and other computations, is motivated by the asymptotic notion of “stretching” a layer in the method of matched asymptotic expansions for treating singular perturbation problems.

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Author information

Authors and Affiliations

  1. Department of Engineering Sciences and Applied Mathematics, Northwestern University, Evanston, IL, 60208, USA

    Alvin Bayliss, Bernard J. Matkowsky & Hermann Riecke

Authors
  1. Alvin Bayliss
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  2. Bernard J. Matkowsky
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  3. Hermann Riecke
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Editors and Affiliations

  1. Argonne National Laboratory, Argonne, Illinois, USA

    Hans G. Kaper  & Gail W. Pieper  & 

  2. Université Claude Bernard, Lyon, France

    Marc Garbey

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© 1993 Springer Science+Business Media Dordrecht

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Bayliss, A., Matkowsky, B.J., Riecke, H. (1993). Modulated Traveling Waves in Combustion. In: Kaper, H.G., Garbey, M., Pieper, G.W. (eds) Asymptotic and Numerical Methods for Partial Differential Equations with Critical Parameters. NATO ASI Series, vol 384. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-1810-1_9

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  • DOI: https://doi.org/10.1007/978-94-011-1810-1_9

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-4798-2

  • Online ISBN: 978-94-011-1810-1

  • eBook Packages: Springer Book Archive

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