dorsal/arxiv
View SchemaPattern selection as a nonlinear eigenvalue problem
| Authors | P. Buechel, M. Luecke |
|---|---|
| Categories | |
| ArXiv ID | patt-sol/9610001 |
| URL | https://arxiv.org/abs/patt-sol/9610001 |
| DOI | 10.1007/BFb0105427 |
Abstract
A unique pattern selection in the absolutely unstable regime of driven, nonlinear, open-flow systems is reviewed. It has recently been found in numerical simulations of propagating vortex structures occuring in Taylor-Couette and Rayleigh-Benard systems subject to an externally imposed through-flow. Unlike the stationary patterns in systems without through-flow the spatiotemporal structures of propagating vortices are independent of parameter history, initial conditions, and system length. They do, however, depend on the boundary conditions in addition to the driving rate and the through-flow rate. Our analysis of the Ginzburg-Landau amplitude equation elucidates how the pattern selection can be described by a nonlinear eigenvalue problem with the frequency being the eigenvalue. Approaching the border between absolute and convective instability the eigenvalue problem becomes effectively linear and the selection mechanism approaches that of linear front propagation. PACS: 47.54.+r,47.20.Ky,47.32.-y,47.20.Ft
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"abstract": "A unique pattern selection in the absolutely unstable regime of driven,\nnonlinear, open-flow systems is reviewed. It has recently been found in\nnumerical simulations of propagating vortex structures occuring in\nTaylor-Couette and Rayleigh-Benard systems subject to an externally imposed\nthrough-flow. Unlike the stationary patterns in systems without through-flow\nthe spatiotemporal structures of propagating vortices are independent of\nparameter history, initial conditions, and system length. They do, however,\ndepend on the boundary conditions in addition to the driving rate and the\nthrough-flow rate. Our analysis of the Ginzburg-Landau amplitude equation\nelucidates how the pattern selection can be described by a nonlinear eigenvalue\nproblem with the frequency being the eigenvalue. Approaching the border between\nabsolute and convective instability the eigenvalue problem becomes effectively\nlinear and the selection mechanism approaches that of linear front propagation.\nPACS: 47.54.+r,47.20.Ky,47.32.-y,47.20.Ft",
"arxiv_id": "patt-sol/9610001",
"authors": [
"P. Buechel",
"M. Luecke"
],
"categories": [
"patt-sol",
"nlin.PS"
],
"doi": "10.1007/BFb0105427",
"title": "Pattern selection as a nonlinear eigenvalue problem",
"url": "https://arxiv.org/abs/patt-sol/9610001"
},
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