From a vortex gas to a vortex crystal in instability-driven two-dimensional turbulence.
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| Title: | From a vortex gas to a vortex crystal in instability-driven two-dimensional turbulence. |
|---|---|
| Authors: | van Kan, Adrian1 (AUTHOR) avankan@berkeley.edu, Favier, Benjamin2 (AUTHOR), Julien, Keith3 (AUTHOR), Knobloch, Edgar1 (AUTHOR) |
| Source: | Journal of Fluid Mechanics. 4/10/2024, Vol. 984, p1-34. 34p. |
| Subjects: | Statistical physics, Turbulence, Crystals, Hybrid systems, Gases |
| Abstract: | We study structure formation in two-dimensional turbulence driven by an external force, interpolating between linear instability forcing and random stirring, subject to nonlinear damping. Using extensive direct numerical simulations, we uncover a rich parameter space featuring four distinct branches of stationary solutions: large-scale vortices, hybrid states with embedded shielded vortices (SVs) of either sign, and two states composed of many similar SVs. Of the latter, the first is a dense vortex gas where all SVs have the same sign and diffuse across the domain. The second is a hexagonal vortex crystal forming from this gas when the linear instability is sufficiently weak. These solutions coexist stably over a wide parameter range. The late-time evolution of the system from small-amplitude initial conditions is nearly self-similar, involving three phases: initial inverse cascade, random nucleation of SVs from turbulence and, once a critical number of vortices is reached, a phase of explosive nucleation of SVs, leading to a statistically stationary state. The vortex gas is continued in the forcing parameter, revealing a sharp transition towards the crystal state as the forcing strength decreases. This transition is analysed in terms of the diffusivity of individual vortices using ideas from statistical physics. The crystal can also decay via an inverse cascade resulting from the breakdown of shielding or insufficient nonlinear damping acting on SVs. Our study highlights the importance of the forcing details in two-dimensional turbulence and reveals the presence of non-trivial SV states in this system, specifically the emergence and melting of a vortex crystal. [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: 176764301 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: From a vortex gas to a vortex crystal in instability-driven two-dimensional turbulence. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22van+Kan%2C+Adrian%22">van Kan, Adrian</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> avankan@berkeley.edu</i><br /><searchLink fieldCode="AR" term="%22Favier%2C+Benjamin%22">Favier, Benjamin</searchLink><relatesTo>2</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Julien%2C+Keith%22">Julien, Keith</searchLink><relatesTo>3</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Knobloch%2C+Edgar%22">Knobloch, Edgar</searchLink><relatesTo>1</relatesTo> (AUTHOR) – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Journal+of+Fluid+Mechanics%22">Journal of Fluid Mechanics</searchLink>. 4/10/2024, Vol. 984, p1-34. 34p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Statistical+physics%22">Statistical physics</searchLink><br /><searchLink fieldCode="DE" term="%22Turbulence%22">Turbulence</searchLink><br /><searchLink fieldCode="DE" term="%22Crystals%22">Crystals</searchLink><br /><searchLink fieldCode="DE" term="%22Hybrid+systems%22">Hybrid systems</searchLink><br /><searchLink fieldCode="DE" term="%22Gases%22">Gases</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: We study structure formation in two-dimensional turbulence driven by an external force, interpolating between linear instability forcing and random stirring, subject to nonlinear damping. Using extensive direct numerical simulations, we uncover a rich parameter space featuring four distinct branches of stationary solutions: large-scale vortices, hybrid states with embedded shielded vortices (SVs) of either sign, and two states composed of many similar SVs. Of the latter, the first is a dense vortex gas where all SVs have the same sign and diffuse across the domain. The second is a hexagonal vortex crystal forming from this gas when the linear instability is sufficiently weak. These solutions coexist stably over a wide parameter range. The late-time evolution of the system from small-amplitude initial conditions is nearly self-similar, involving three phases: initial inverse cascade, random nucleation of SVs from turbulence and, once a critical number of vortices is reached, a phase of explosive nucleation of SVs, leading to a statistically stationary state. The vortex gas is continued in the forcing parameter, revealing a sharp transition towards the crystal state as the forcing strength decreases. This transition is analysed in terms of the diffusivity of individual vortices using ideas from statistical physics. The crystal can also decay via an inverse cascade resulting from the breakdown of shielding or insufficient nonlinear damping acting on SVs. Our study highlights the importance of the forcing details in two-dimensional turbulence and reveals the presence of non-trivial SV states in this system, specifically the emergence and melting of a vortex crystal. [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.2024.162 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 34 StartPage: 1 Subjects: – SubjectFull: Statistical physics Type: general – SubjectFull: Turbulence Type: general – SubjectFull: Crystals Type: general – SubjectFull: Hybrid systems Type: general – SubjectFull: Gases Type: general Titles: – TitleFull: From a vortex gas to a vortex crystal in instability-driven two-dimensional turbulence. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: van Kan, Adrian – PersonEntity: Name: NameFull: Favier, Benjamin – PersonEntity: Name: NameFull: Julien, Keith – PersonEntity: Name: NameFull: Knobloch, Edgar IsPartOfRelationships: – BibEntity: Dates: – D: 10 M: 04 Text: 4/10/2024 Type: published Y: 2024 Identifiers: – Type: issn-print Value: 00221120 Numbering: – Type: volume Value: 984 Titles: – TitleFull: Journal of Fluid Mechanics Type: main |
| ResultId | 1 |
