TY - JOUR

T1 - Nonlinear dynamics of cellular flames

AU - Bayliss, Alvin

AU - Matkowsky, Bernard J.

PY - 1992/1/1

Y1 - 1992/1/1

N2 - The problem of a flame stabilized by a line source of fuel in the cellular regime, i.e., L < 1, where L is the Lewis number, is solved numerically. It is found that as L is decreased, transitions from stationary axisymmetric to stationary cellular to nonstationary cellular flames occur. The nonstationary cellular flames can exhibit both periodic and quasi-periodic dynamics. In particular, as L is decreased successive transitions from stationary axisymmetric solutions, to stationary four-cell solutions, to spinning four-cell solutions are computed. The spinning four-cell solutions are very slowly traveling waves that arise due to an infinite period, symmetry breaking bifurcation, in which the reflection symmetry of the stationary four-cell solution is broken. Near the transition point, the traveling wave solution branch is unstable and perturbations evolve to either a stationary five-cell or a nonstationary mixed-mode solution exhibiting apparently quasi-periodic dynamics. If L is further decreased beyond a critical value Lx, the traveling wave solution branch becomes stable. Beyond another critical value LH, the traveling wave branch loses stability to a branch of mixed mode, apparently quasi-periodic, solutions that appear to arise due to the interaction of unstable three- and four-cell traveling wave solutions.

AB - The problem of a flame stabilized by a line source of fuel in the cellular regime, i.e., L < 1, where L is the Lewis number, is solved numerically. It is found that as L is decreased, transitions from stationary axisymmetric to stationary cellular to nonstationary cellular flames occur. The nonstationary cellular flames can exhibit both periodic and quasi-periodic dynamics. In particular, as L is decreased successive transitions from stationary axisymmetric solutions, to stationary four-cell solutions, to spinning four-cell solutions are computed. The spinning four-cell solutions are very slowly traveling waves that arise due to an infinite period, symmetry breaking bifurcation, in which the reflection symmetry of the stationary four-cell solution is broken. Near the transition point, the traveling wave solution branch is unstable and perturbations evolve to either a stationary five-cell or a nonstationary mixed-mode solution exhibiting apparently quasi-periodic dynamics. If L is further decreased beyond a critical value Lx, the traveling wave solution branch becomes stable. Beyond another critical value LH, the traveling wave branch loses stability to a branch of mixed mode, apparently quasi-periodic, solutions that appear to arise due to the interaction of unstable three- and four-cell traveling wave solutions.

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U2 - 10.1137/0152022

DO - 10.1137/0152022

M3 - Article

AN - SCOPUS:0026846050

VL - 52

SP - 396

EP - 415

JO - SIAM Journal on Applied Mathematics

JF - SIAM Journal on Applied Mathematics

SN - 0036-1399

IS - 2

ER -