dorsal/arxiv
View SchemaPattern selection in the absolutely unstable regime as a nonlinear eigenvalue problem: Taylor vortices in axial flow
| Authors | P. Buechel, M. Luecke, D. Roth, R. Schmitz |
|---|---|
| Categories | |
| ArXiv ID | patt-sol/9607004 |
| URL | https://arxiv.org/abs/patt-sol/9607004 |
| DOI | 10.1103/PhysRevE.53.4764 |
| Journal | Phys. Rev. E, 53, 4764-77 (1996) |
Abstract
A unique pattern selection in the absolutely unstable regime of a driven, nonlinear, open-flow system is analyzed: The spatiotemporal structures of rotationally symmetric vortices that propagate downstream in the annulus of the rotating Taylor-Couette system due to an externally imposed axial through-flow are investigated for two different axial boundary conditions at the in- and outlet. Unlike the stationary patterns in systems without through-flow the spatiotemporal structures of propagating vortices are independent of parameter history, initial conditions, and system's length. They do, however, depend on the axial boundary conditions, the driving rate of the inner cylinder and the through-flow rate. Our analysis of the amplitude equation shows that 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 one 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 a driven,\nnonlinear, open-flow system is analyzed: The spatiotemporal structures of\nrotationally symmetric vortices that propagate downstream in the annulus of the\nrotating Taylor-Couette system due to an externally imposed axial through-flow\nare investigated for two different axial boundary conditions at the in- and\noutlet. Unlike the stationary patterns in systems without through-flow the\nspatiotemporal structures of propagating vortices are independent of parameter\nhistory, initial conditions, and system\u0027s length. They do, however, depend on\nthe axial boundary conditions, the driving rate of the inner cylinder and the\nthrough-flow rate. Our analysis of the amplitude equation shows that the\npattern selection can be described by a nonlinear eigenvalue problem with the\nfrequency being the eigenvalue. Approaching the border between absolute and\nconvective instability the eigenvalue problem becomes effectively linear and\nthe selection mechanism approaches that one of linear front propagation.\nPACS:47.54.+r,47.20.Ky,47.32.-y,47.20.Ft",
"arxiv_id": "patt-sol/9607004",
"authors": [
"P. Buechel",
"M. Luecke",
"D. Roth",
"R. Schmitz"
],
"categories": [
"patt-sol",
"nlin.PS"
],
"doi": "10.1103/PhysRevE.53.4764",
"journal_ref": "Phys. Rev. E, 53, 4764-77 (1996)",
"title": "Pattern selection in the absolutely unstable regime as a nonlinear eigenvalue problem: Taylor vortices in axial flow",
"url": "https://arxiv.org/abs/patt-sol/9607004"
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