Internal shear layers generated by a vertically oscillating cylinder in unbounded and bounded rotating fluids.
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| Title: | Internal shear layers generated by a vertically oscillating cylinder in unbounded and bounded rotating fluids. |
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| Authors: | He, Jiyang1,2 jiyanghe123@gmail.com, Favier, Benjamin2, Le Dizès, Stéphane2 |
| Source: | Journal of Fluid Mechanics. 7/25/2025, Vol. 1015, pA38-1-A38-36. 36p. |
| Subjects: | Rotating fluid, Fluid dynamics, Oscillations, Shear flow |
| Abstract: | In rotating fluids, the viscous smoothing of inviscid singular inertial waves leads to the formation of internal shear layers. In previous works, we analysed the internal shear layers excited by a viscous forcing (longitudinal libration) in a spherical shell geometry (He et al., 2022 J. Fluid Mech. 939, A3; He et al., 2023 J. Fluid Mech. 974, A3). We now consider the stronger inviscid forcing corresponding to the vertical oscillation of the inner boundary. We limit our analysis to two-dimensional geometries but examine three different configurations: freely propagating wave beams in an unbounded domain and two wave patterns (a periodic orbit and an attractor) in a cylindrical shell geometry. The asymptotic structures of the internal shear layers are assumed to follow the similarity solution of Moore & Saffman (1969 Phil. Trans. R. Soc. Lond. A, 264, 597–634) in the small viscous limit. The two undefined parameters of the similarity solution (singularity strength and amplitude) are derived by asymptotically matching the similarity solution with the inviscid solution. For each case, the derivation of the latter is achieved either through separation of variables combined with analytical continuation or the method of characteristics. Global inviscid solutions, when obtained, closely match numerical solutions for small Ekman numbers far from the critical lines, while viscous asymptotic solutions show excellent performance near those lines. The amplitude scalings of the internal shear layers excited by an inviscid forcing are found to be divergent as the Ekman number E decreases, specifically O(E−1/6) for the critical-point singularity and O(E−1/3) for attractors, in contrast to the convergent scalings found for a viscous forcing. [ABSTRACT FROM AUTHOR] |
| Copyright of Journal of Fluid Mechanics 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.) | |
| Database: | Engineering Source |
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| Header | DbId: egs DbLabel: Engineering Source An: 188032209 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Internal shear layers generated by a vertically oscillating cylinder in unbounded and bounded rotating fluids. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22He%2C+Jiyang%22">He, Jiyang</searchLink><relatesTo>1,2</relatesTo><i> jiyanghe123@gmail.com</i><br /><searchLink fieldCode="AR" term="%22Favier%2C+Benjamin%22">Favier, Benjamin</searchLink><relatesTo>2</relatesTo><br /><searchLink fieldCode="AR" term="%22Le+Dizès%2C+Stéphane%22">Le Dizès, Stéphane</searchLink><relatesTo>2</relatesTo> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Journal+of+Fluid+Mechanics%22">Journal of Fluid Mechanics</searchLink>. 7/25/2025, Vol. 1015, pA38-1-A38-36. 36p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Rotating+fluid%22">Rotating fluid</searchLink><br /><searchLink fieldCode="DE" term="%22Fluid+dynamics%22">Fluid dynamics</searchLink><br /><searchLink fieldCode="DE" term="%22Oscillations%22">Oscillations</searchLink><br /><searchLink fieldCode="DE" term="%22Shear+flow%22">Shear flow</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: In rotating fluids, the viscous smoothing of inviscid singular inertial waves leads to the formation of internal shear layers. In previous works, we analysed the internal shear layers excited by a viscous forcing (longitudinal libration) in a spherical shell geometry (He et al., 2022 J. Fluid Mech. 939, A3; He et al., 2023 J. Fluid Mech. 974, A3). We now consider the stronger inviscid forcing corresponding to the vertical oscillation of the inner boundary. We limit our analysis to two-dimensional geometries but examine three different configurations: freely propagating wave beams in an unbounded domain and two wave patterns (a periodic orbit and an attractor) in a cylindrical shell geometry. The asymptotic structures of the internal shear layers are assumed to follow the similarity solution of Moore & Saffman (1969 Phil. Trans. R. Soc. Lond. A, 264, 597–634) in the small viscous limit. The two undefined parameters of the similarity solution (singularity strength and amplitude) are derived by asymptotically matching the similarity solution with the inviscid solution. For each case, the derivation of the latter is achieved either through separation of variables combined with analytical continuation or the method of characteristics. Global inviscid solutions, when obtained, closely match numerical solutions for small Ekman numbers far from the critical lines, while viscous asymptotic solutions show excellent performance near those lines. The amplitude scalings of the internal shear layers excited by an inviscid forcing are found to be divergent as the Ekman number E decreases, specifically O(E−1/6) for the critical-point singularity and O(E−1/3) for attractors, in contrast to the convergent scalings found for a viscous forcing. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Journal of Fluid Mechanics 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/jfm.2025.10237 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 36 StartPage: A38-1 Subjects: – SubjectFull: Rotating fluid Type: general – SubjectFull: Fluid dynamics Type: general – SubjectFull: Oscillations Type: general – SubjectFull: Shear flow Type: general Titles: – TitleFull: Internal shear layers generated by a vertically oscillating cylinder in unbounded and bounded rotating fluids. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: He, Jiyang – PersonEntity: Name: NameFull: Favier, Benjamin – PersonEntity: Name: NameFull: Le Dizès, Stéphane IsPartOfRelationships: – BibEntity: Dates: – D: 25 M: 07 Text: 7/25/2025 Type: published Y: 2025 Identifiers: – Type: issn-print Value: 00221120 Numbering: – Type: volume Value: 1015 Titles: – TitleFull: Journal of Fluid Mechanics Type: main |
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