dorsal/arxiv
View SchemaStructure And Dynamics Of Modulated Traveling Waves In Cellular Flames
| Authors | A. Bayliss, B. J. Matkowsky, H. Riecke |
|---|---|
| Categories | |
| ArXiv ID | patt-sol/9402001 |
| URL | https://arxiv.org/abs/patt-sol/9402001 |
| DOI | 10.1016/0167-2789(94)90023-X |
| Journal | Physica D 74 (1994) 1-23 |
Abstract
We describe spatial and temporal patterns in cylindrical premixed flames in the cellular regime, $Le < 1$, where the Lewis number $Le$ is the ratio of thermal to mass diffusivity of a deficient component of the combustible mixture. A transition from stationary, axisymmetric flames to stationary cellular flames is predicted analytically if $Le$ is decreased below a critical value. We present the results of numerical computations to show that as $Le$ is further decreased traveling waves (TWs) along the flame front arise via an infinite-period bifurcation which breaks the reflection symmetry of the cellular array. Upon further decreasing $Le$ different kinds of periodically modulated traveling waves (MTWs) as well as a branch of quasiperiodically modulated traveling waves (QPMTWs) arise. These transitions are accompanied by the development of different spatial and temporal symmetries including period doublings and period halvings. We also observe the apparently chaotic temporal behavior of a disordered cellular pattern involving creation and annihilation of cells. We analytically describe the stability of the TW solution near its onset+ using suitable phase-amplitude equations. Within this framework one of the MTW's can be identified as a localized wave traveling through an underlying stationary, spatially periodic structure. We study the Eckhaus instability of the TW and find that in general they are unstable at onset in infinite systems. They can, however, become stable for larger amplitudes.
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"abstract": "We describe spatial and temporal patterns in cylindrical premixed flames in\nthe cellular regime, $Le \u003c 1$, where the Lewis number $Le$ is the ratio of\nthermal to mass diffusivity of a deficient component of the combustible\nmixture. A transition from stationary, axisymmetric flames to stationary\ncellular flames is predicted analytically if $Le$ is decreased below a critical\nvalue. We present the results of numerical computations to show that as $Le$ is\nfurther decreased traveling waves (TWs) along the flame front arise via an\ninfinite-period bifurcation which breaks the reflection symmetry of the\ncellular array. Upon further decreasing $Le$ different kinds of periodically\nmodulated traveling waves (MTWs) as well as a branch of quasiperiodically\nmodulated traveling waves (QPMTWs) arise. These transitions are accompanied by\nthe development of different spatial and temporal symmetries including period\ndoublings and period halvings. We also observe the apparently chaotic temporal\nbehavior of a disordered cellular pattern involving creation and annihilation\nof cells. We analytically describe the stability of the TW solution near its\nonset+ using suitable phase-amplitude equations. Within this framework one of\nthe MTW\u0027s can be identified as a localized wave traveling through an underlying\nstationary, spatially periodic structure. We study the Eckhaus instability of\nthe TW and find that in general they are unstable at onset in infinite systems.\nThey can, however, become stable for larger amplitudes.",
"arxiv_id": "patt-sol/9402001",
"authors": [
"A. Bayliss",
"B. J. Matkowsky",
"H. Riecke"
],
"categories": [
"patt-sol",
"nlin.PS"
],
"doi": "10.1016/0167-2789(94)90023-X",
"journal_ref": "Physica D 74 (1994) 1-23",
"title": "Structure And Dynamics Of Modulated Traveling Waves In Cellular Flames",
"url": "https://arxiv.org/abs/patt-sol/9402001"
},
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