A general kinematic theory of fluid-element rotation and intrinsic vorticity decompositions.
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| Title: | A general kinematic theory of fluid-element rotation and intrinsic vorticity decompositions. |
|---|---|
| Authors: | Chen, Tao1 (AUTHOR) chentao2023@njust.edu.cn, Wu, Jie-Zhi2 (AUTHOR), Mao, Feng3 (AUTHOR), Liu, Tianshu4 (AUTHOR) |
| Source: | Journal of Fluid Mechanics. 4/10/2026, Vol. 1032, p1-57. 57p. |
| Subjects: | Vortex motion, Rotational flow, Rotational motion, Fluid dynamics, Shearing force, Kinematics, Tensor algebra |
| Abstract: | The present study establishes a general theory for fluid-element rotation and intrinsic vorticity decompositions within the framework of vorticity kinematics. We propose two direction-dependent vorticity decompositions (DVDs) based on the analysis of rotation of directed material line and surface elements, with the rigid-rotation and spin modes of vorticity being explicitly defined. Intrinsic coupling relations are then derived for a pair of orthogonal line and surface elements, demonstrating their complementary roles in both kinematics and geometry. Notably, the surface-element-based spin mode is shown to coincide with the relative vorticity in the generalized Caswell formula, thereby providing a faithful representation of surface shear stress in Newtonian fluids. Correspondingly, another two DVDs are constructed based on the geometry of streamlines and streamsurfaces in the field description. Furthermore, within the characteristic algebraic description, in terms of the rotational invariants $(\psi ,\gamma)$ in the real Schur form of the velocity gradient tensor, two invariant vorticity decompositions (IVDs) are formulated. The first IVD with positive spin aligns with the Liutex-shear decomposition, which corresponds to the Klein–Kaden–Betz (KKB) mechanism by which wrapping shear layers form axial vortices. The second IVD is indispensable for understanding unidirectional swirling motion around a point on the rotation-axis-normal plane ${\mathcal{P}}$ , corresponding to an anti-KKB mechanism/phenomenon characterized by the negative spin. Importantly, it is proved that the DVD vorticity modes are rigorously bounded by the IVD vorticity modes $(R_{N}^{\pm },s_{N}^{\pm })=(2\psi ^{\pm },\gamma ^{\pm })$ on ${\mathcal{P}}$. Finally, distinctive features and applicability of these kinematic tools are demonstrated with representative examples. The results indicate that a coupled IVD–DVD approach provides a powerful diagnostic tool for unravelling the subtle structures and fundamental physics inherent to complex flow fields. [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 |
| FullText | Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 193224703 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: A general kinematic theory of fluid-element rotation and intrinsic vorticity decompositions. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Chen%2C+Tao%22">Chen, Tao</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> chentao2023@njust.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Wu%2C+Jie-Zhi%22">Wu, Jie-Zhi</searchLink><relatesTo>2</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Mao%2C+Feng%22">Mao, Feng</searchLink><relatesTo>3</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Liu%2C+Tianshu%22">Liu, Tianshu</searchLink><relatesTo>4</relatesTo> (AUTHOR) – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Journal+of+Fluid+Mechanics%22">Journal of Fluid Mechanics</searchLink>. 4/10/2026, Vol. 1032, p1-57. 57p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Vortex+motion%22">Vortex motion</searchLink><br /><searchLink fieldCode="DE" term="%22Rotational+flow%22">Rotational flow</searchLink><br /><searchLink fieldCode="DE" term="%22Rotational+motion%22">Rotational motion</searchLink><br /><searchLink fieldCode="DE" term="%22Fluid+dynamics%22">Fluid dynamics</searchLink><br /><searchLink fieldCode="DE" term="%22Shearing+force%22">Shearing force</searchLink><br /><searchLink fieldCode="DE" term="%22Kinematics%22">Kinematics</searchLink><br /><searchLink fieldCode="DE" term="%22Tensor+algebra%22">Tensor algebra</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: The present study establishes a general theory for fluid-element rotation and intrinsic vorticity decompositions within the framework of vorticity kinematics. We propose two direction-dependent vorticity decompositions (DVDs) based on the analysis of rotation of directed material line and surface elements, with the rigid-rotation and spin modes of vorticity being explicitly defined. Intrinsic coupling relations are then derived for a pair of orthogonal line and surface elements, demonstrating their complementary roles in both kinematics and geometry. Notably, the surface-element-based spin mode is shown to coincide with the relative vorticity in the generalized Caswell formula, thereby providing a faithful representation of surface shear stress in Newtonian fluids. Correspondingly, another two DVDs are constructed based on the geometry of streamlines and streamsurfaces in the field description. Furthermore, within the characteristic algebraic description, in terms of the rotational invariants $(\psi ,\gamma)$ in the real Schur form of the velocity gradient tensor, two invariant vorticity decompositions (IVDs) are formulated. The first IVD with positive spin aligns with the Liutex-shear decomposition, which corresponds to the Klein–Kaden–Betz (KKB) mechanism by which wrapping shear layers form axial vortices. The second IVD is indispensable for understanding unidirectional swirling motion around a point on the rotation-axis-normal plane ${\mathcal{P}}$ , corresponding to an anti-KKB mechanism/phenomenon characterized by the negative spin. Importantly, it is proved that the DVD vorticity modes are rigorously bounded by the IVD vorticity modes $(R_{N}^{\pm },s_{N}^{\pm })=(2\psi ^{\pm },\gamma ^{\pm })$ on ${\mathcal{P}}$. Finally, distinctive features and applicability of these kinematic tools are demonstrated with representative examples. The results indicate that a coupled IVD–DVD approach provides a powerful diagnostic tool for unravelling the subtle structures and fundamental physics inherent to complex flow fields. [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.2026.11406 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 57 StartPage: 1 Subjects: – SubjectFull: Vortex motion Type: general – SubjectFull: Rotational flow Type: general – SubjectFull: Rotational motion Type: general – SubjectFull: Fluid dynamics Type: general – SubjectFull: Shearing force Type: general – SubjectFull: Kinematics Type: general – SubjectFull: Tensor algebra Type: general Titles: – TitleFull: A general kinematic theory of fluid-element rotation and intrinsic vorticity decompositions. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Chen, Tao – PersonEntity: Name: NameFull: Wu, Jie-Zhi – PersonEntity: Name: NameFull: Mao, Feng – PersonEntity: Name: NameFull: Liu, Tianshu IsPartOfRelationships: – BibEntity: Dates: – D: 10 M: 04 Text: 4/10/2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 00221120 Numbering: – Type: volume Value: 1032 Titles: – TitleFull: Journal of Fluid Mechanics Type: main |
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