The gap-size influence on the excitation of magnetorotational instability in cylindricTaylor–Couette flows.
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| Title: | The gap-size influence on the excitation of magnetorotational instability in cylindricTaylor–Couette flows. |
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| Authors: | Rüdiger, G.1,2 (AUTHOR) gruediger@aip.de, Schultz, M.2 (AUTHOR) |
| Source: | Journal of Plasma Physics. Jan2024, Vol. 90 Issue 1, p1-14. 14p. 1 Chart, 6 Graphs. |
| Subjects: | Princeton University, Flow instability, Taylor vortices, Reynolds number, Prandtl number, Magnetic fields, Insulating materials |
| Abstract: | The excitation conditions of the magnetorotational instability (MRI) are studied for axially unbounded Taylor–Couette (TC) flows of various gap widths between the cylinders. The cylinders are considered as made from both perfect-conducting or insulating material and the conducting fluid with a finite but small magnetic Prandtl number rotates with a quasi-Keplerian velocity profile. The solutions are optimized with respect to the wavenumber and the Reynolds number of the rotation of the inner cylinder. For the axisymmetric modes, we find the critical Lundquist number of the applied axial magnetic field: the lower, the wider the gap between the cylinders. A similar result is obtained for the induced cell structure: the wider the gap, the more spherical the cells are. The marginal rotation rate of the inner cylinder – for a fixed size of the outer cylinder – always possesses a minimum for not too wide and not too narrow gap widths. For perfect-conducting walls the minimum lies at 𝑟in ≃0.4, where 𝑟in is the ratio of the radii of the two rotating cylinders. The lowest magnetic field amplitudes to excite the instability are required for TC flows between perfect-conducting cylinders with gaps corresponding to 𝑟in ≃ 0.2. For even wider and also for very thin gaps the needed magnetic fields and rotation frequencies are shown to become rather huge. Also the non-axisymmetric modes with |𝑚| =1 have been considered. Their excitation generally requires stronger magnetic fields and higher magnetic Reynolds numbers in comparison with those for the axisymmetric modes. If TC experiments with too slow rotation for the applied magnetic fields yield unstable modes of any azimuthal symmetry, such as the currently reported Princeton experiment (Wang et al., Phys. Rev. Lett., vol. 129, 115001), then also other players, including axial boundary effects, than the MRI-typical linear combination of current-free fields and differential rotation should be in the game. [ABSTRACT FROM AUTHOR] |
| Copyright of Journal of Plasma Physics is the property of Cambridge University Press and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
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| Items | – Name: Title Label: Title Group: Ti Data: The gap-size influence on the excitation of magnetorotational instability in cylindricTaylor–Couette flows. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Rüdiger%2C+G%2E%22">Rüdiger, G.</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<i> gruediger@aip.de</i><br /><searchLink fieldCode="AR" term="%22Schultz%2C+M%2E%22">Schultz, M.</searchLink><relatesTo>2</relatesTo> (AUTHOR) – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Journal+of+Plasma+Physics%22">Journal of Plasma Physics</searchLink>. Jan2024, Vol. 90 Issue 1, p1-14. 14p. 1 Chart, 6 Graphs. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Princeton+University%22">Princeton University</searchLink><br /><searchLink fieldCode="DE" term="%22Flow+instability%22">Flow instability</searchLink><br /><searchLink fieldCode="DE" term="%22Taylor+vortices%22">Taylor vortices</searchLink><br /><searchLink fieldCode="DE" term="%22Reynolds+number%22">Reynolds number</searchLink><br /><searchLink fieldCode="DE" term="%22Prandtl+number%22">Prandtl number</searchLink><br /><searchLink fieldCode="DE" term="%22Magnetic+fields%22">Magnetic fields</searchLink><br /><searchLink fieldCode="DE" term="%22Insulating+materials%22">Insulating materials</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: The excitation conditions of the magnetorotational instability (MRI) are studied for axially unbounded Taylor–Couette (TC) flows of various gap widths between the cylinders. The cylinders are considered as made from both perfect-conducting or insulating material and the conducting fluid with a finite but small magnetic Prandtl number rotates with a quasi-Keplerian velocity profile. The solutions are optimized with respect to the wavenumber and the Reynolds number of the rotation of the inner cylinder. For the axisymmetric modes, we find the critical Lundquist number of the applied axial magnetic field: the lower, the wider the gap between the cylinders. A similar result is obtained for the induced cell structure: the wider the gap, the more spherical the cells are. The marginal rotation rate of the inner cylinder – for a fixed size of the outer cylinder – always possesses a minimum for not too wide and not too narrow gap widths. For perfect-conducting walls the minimum lies at 𝑟in ≃0.4, where 𝑟in is the ratio of the radii of the two rotating cylinders. The lowest magnetic field amplitudes to excite the instability are required for TC flows between perfect-conducting cylinders with gaps corresponding to 𝑟in ≃ 0.2. For even wider and also for very thin gaps the needed magnetic fields and rotation frequencies are shown to become rather huge. Also the non-axisymmetric modes with |𝑚| =1 have been considered. Their excitation generally requires stronger magnetic fields and higher magnetic Reynolds numbers in comparison with those for the axisymmetric modes. If TC experiments with too slow rotation for the applied magnetic fields yield unstable modes of any azimuthal symmetry, such as the currently reported Princeton experiment (Wang et al., Phys. Rev. Lett., vol. 129, 115001), then also other players, including axial boundary effects, than the MRI-typical linear combination of current-free fields and differential rotation should be in the game. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Journal of Plasma Physics is the property of Cambridge University Press and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1017/S0022377823001356 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 14 StartPage: 1 Subjects: – SubjectFull: Princeton University Type: general – SubjectFull: Flow instability Type: general – SubjectFull: Taylor vortices Type: general – SubjectFull: Reynolds number Type: general – SubjectFull: Prandtl number Type: general – SubjectFull: Magnetic fields Type: general – SubjectFull: Insulating materials Type: general Titles: – TitleFull: The gap-size influence on the excitation of magnetorotational instability in cylindricTaylor–Couette flows. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Rüdiger, G. – PersonEntity: Name: NameFull: Schultz, M. IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 01 Text: Jan2024 Type: published Y: 2024 Identifiers: – Type: issn-print Value: 00223778 Numbering: – Type: volume Value: 90 – Type: issue Value: 1 Titles: – TitleFull: Journal of Plasma Physics Type: main |
| ResultId | 1 |
