Unsteady fronts in an auto catalytic system

N. J. Balmforth, R. V. Craster, S. J. A. Malham

Research output: Contribution to journalArticlepeer-review

27 Citations (Scopus)

Abstract

Travelling waves in a model for autocatalytic reactions have, for some parameter regimes, been suggested to have oscillatory instabilities. These instabilities are confirmed by various methods, including linear-stability analysis (exploiting Evans's function) and direct numerical simulations. The front instability sets in when the order of the reaction, m, exceeds some threshold, mc(τ), that depends on the inverse of the Lewis number, τ. The stability boundary, m = mc(τ), is found numerically for m order one. In the limit m ≫ 1 (in which the system becomes similar to combustion systems with Arrhenius kinetics), the method of matched asymptotic expansions is employed to find the asymptotic front speed and show that mc ∼ (V -1)-1 as τ rarr;1. Just beyond the stability boundary, the unstable rocking of the front saturates supercritically. If the order is increased still further, period-doubling bifurcations occur, and for small τ there is a transition to chaos through intermittency after the disappearance of a period-4 orbit.

Original languageEnglish
Pages (from-to)1401-1433
Number of pages33
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume455
Issue number1984
DOIs
Publication statusPublished - 8 Apr 1999

Keywords

  • Combustion
  • Instability
  • Travelling waves

ASJC Scopus subject areas

  • Mathematics(all)
  • Engineering(all)
  • Physics and Astronomy(all)

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