dorsal/arxiv
View SchemaSpiral Vortices and Taylor Vortices in the Annulus between Rotating Cylinders and the Effect of an Axial Flow
| Authors | Ch. Hoffmann, M. Lücke, A. Pinter |
|---|---|
| Categories | |
| ArXiv ID | physics/0505164 |
| URL | https://arxiv.org/abs/physics/0505164 |
| DOI | 10.1103/PhysRevE.69.056309 |
| Journal | Phys. Rev. E 69, 056309 (2004). |
Abstract
We present numerical simulations of vortices that appear via primary bifurcations out of the unstructured circular Couette flow in the Taylor-Couette system with counter-rotating as well as with co-rotating cylinders. The full, time dependent Navier-Stokes equations are solved with a combination of a finite difference and a Galerkin method for a fixed axial periodicity length of the vortex patterns and for a finite system of aspect ratio 12 with rigid nonrotating ends in a setup with radius ratio eta=0.5. Differences in structure, dynamics, symmetry properties, bifurcation and stability behavior between spiral vortices with azimuthal wave numbers M=+-1 and M=0 Taylor vortices are elucidated and compared in quantitative detail. Simulations in axially periodic systems and in finite systems with stationary rigid ends are compared with experimental spiral data. In a second part of the paper we determine how the above listed properties of the M=-1,0,1 vortex structures are changed by an externally imposed axial through-flow with Reynolds numbers in the range -40 <= Re <= 40. Among others we investigate when left handed or right handed spirals or toroidally closed vortices are preferred.
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"abstract": "We present numerical simulations of vortices that appear via primary\nbifurcations out of the unstructured circular Couette flow in the\nTaylor-Couette system with counter-rotating as well as with co-rotating\ncylinders. The full, time dependent Navier-Stokes equations are solved with a\ncombination of a finite difference and a Galerkin method for a fixed axial\nperiodicity length of the vortex patterns and for a finite system of aspect\nratio 12 with rigid nonrotating ends in a setup with radius ratio eta=0.5.\nDifferences in structure, dynamics, symmetry properties, bifurcation and\nstability behavior between spiral vortices with azimuthal wave numbers M=+-1\nand M=0 Taylor vortices are elucidated and compared in quantitative detail.\nSimulations in axially periodic systems and in finite systems with stationary\nrigid ends are compared with experimental spiral data. In a second part of the\npaper we determine how the above listed properties of the M=-1,0,1 vortex\nstructures are changed by an externally imposed axial through-flow with\nReynolds numbers in the range -40 \u003c= Re \u003c= 40. Among others we investigate when\nleft handed or right handed spirals or toroidally closed vortices are\npreferred.",
"arxiv_id": "physics/0505164",
"authors": [
"Ch. Hoffmann",
"M. L\u00fccke",
"A. Pinter"
],
"categories": [
"physics.flu-dyn",
"nlin.PS",
"physics.comp-ph"
],
"doi": "10.1103/PhysRevE.69.056309",
"journal_ref": "Phys. Rev. E 69, 056309 (2004).",
"title": "Spiral Vortices and Taylor Vortices in the Annulus between Rotating Cylinders and the Effect of an Axial Flow",
"url": "https://arxiv.org/abs/physics/0505164"
},
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