dorsal/arxiv
View SchemaBoundary Limitation of Wavenumbers in Taylor-Vortex Flow
| Authors | Marcus Linek, Guenter Ahlers |
|---|---|
| Categories | |
| ArXiv ID | patt-sol/9805008 |
| URL | https://arxiv.org/abs/patt-sol/9805008 |
| DOI | 10.1103/PhysRevE.58.3168 |
Abstract
We report experimental results for a boundary-mediated wavenumber-adjustment mechanism and for a boundary-limited wavenumber-band of Taylor-vortex flow (TVF). The system consists of fluid contained between two concentric cylinders with the inner one rotating at an angular frequency $\Omega$. As observed previously, the Eckhaus instability (a bulk instability) is observed and limits the stable wavenumber band when the system is terminated axially by two rigid, non-rotating plates. The band width is then of order $\epsilon^{1/2}$ at small $\epsilon$ ($\epsilon \equiv \Omega/\Omega_c - 1$) and agrees well with calculations based on the equations of motion over a wide $\epsilon$-range. When the cylinder axis is vertical and the upper liquid surface is free (i.e. an air-liquid interface), vortices can be generated or expelled at the free surface because there the phase of the structure is only weakly pinned. The band of wavenumbers over which Taylor-vortex flow exists is then more narrow than the stable band limited by the Eckhaus instability. At small $\epsilon$ the boundary-mediated band-width is linear in $\epsilon$. These results are qualitatively consistent with theoretical predictions, but to our knowledge a quantitative calculation for TVF with a free surface does not exist.
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"abstract": "We report experimental results for a boundary-mediated wavenumber-adjustment\nmechanism and for a boundary-limited wavenumber-band of Taylor-vortex flow\n(TVF). The system consists of fluid contained between two concentric cylinders\nwith the inner one rotating at an angular frequency $\\Omega$. As observed\npreviously, the Eckhaus instability (a bulk instability) is observed and limits\nthe stable wavenumber band when the system is terminated axially by two rigid,\nnon-rotating plates. The band width is then of order $\\epsilon^{1/2}$ at small\n$\\epsilon$ ($\\epsilon \\equiv \\Omega/\\Omega_c - 1$) and agrees well with\ncalculations based on the equations of motion over a wide $\\epsilon$-range.\nWhen the cylinder axis is vertical and the upper liquid surface is free (i.e.\nan air-liquid interface), vortices can be generated or expelled at the free\nsurface because there the phase of the structure is only weakly pinned. The\nband of wavenumbers over which Taylor-vortex flow exists is then more narrow\nthan the stable band limited by the Eckhaus instability. At small $\\epsilon$\nthe boundary-mediated band-width is linear in $\\epsilon$. These results are\nqualitatively consistent with theoretical predictions, but to our knowledge a\nquantitative calculation for TVF with a free surface does not exist.",
"arxiv_id": "patt-sol/9805008",
"authors": [
"Marcus Linek",
"Guenter Ahlers"
],
"categories": [
"patt-sol",
"nlin.PS"
],
"doi": "10.1103/PhysRevE.58.3168",
"title": "Boundary Limitation of Wavenumbers in Taylor-Vortex Flow",
"url": "https://arxiv.org/abs/patt-sol/9805008"
},
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