On the inverse cascade and flow speed scaling behaviour in rapidly rotating Rayleigh–Bénard convection.
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| Title: | On the inverse cascade and flow speed scaling behaviour in rapidly rotating Rayleigh–Bénard convection. |
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| Authors: | Maffei, S.1,2 (AUTHOR) s.maffei@leeds.ac.uk, Krouss, M.J.1 (AUTHOR), Julien, K.3 (AUTHOR), Calkins, M.A.1 (AUTHOR) |
| Source: | Journal of Fluid Mechanics. 4/25/2021, Vol. 913, p1-30. 30p. |
| Subjects: | Rayleigh-Bénard convection, Convective flow, Buoyancy, Rayleigh number, Prandtl number, Viscosity |
| Abstract: | Rotating Rayleigh–Bénard convection is investigated numerically with the use of an asymptotic model that captures the rapidly rotating, small Ekman number limit, $Ek \rightarrow 0$. The Prandtl number ($Pr$) and the asymptotically scaled Rayleigh number ($\widetilde {Ra} = Ra Ek^{4/3}$ , where $Ra$ is the typical Rayleigh number) are varied systematically. For sufficiently vigorous convection, an inverse kinetic energy cascade leads to the formation of a pair of large-scale vortices of opposite polarity, in agreement with previous studies of rapidly rotating convection. With respect to the kinetic energy, we find a transition from convection dominated states to a state dominated by large-scale vortices at an asymptotically reduced (small-scale) Reynolds number of $\widetilde {Re} \approx 6$ ($\widetilde {Re} = Re Ek^{1/3}$ , where $Re$ is the Reynolds number associated with vertical flows) for all investigated values of $Pr$. The ratio of the depth-averaged kinetic energy to the kinetic energy of the convection reaches a maximum at $\widetilde {Re} \approx 24$ , then decreases as $\widetilde {Ra}$ is increased. This decrease in the relative kinetic energy of the large-scale vortices is associated with a decrease in the convective correlations with increasing Rayleigh number. The scaling behaviour of the convective flow speeds is studied; although a linear scaling of the form $\widetilde {Re} \sim \widetilde {Ra}/Pr$ is observed over a limited range in Rayleigh number and Prandtl number, a clear departure from this scaling is observed at the highest accessible values of $\widetilde {Ra}$. Calculation of the forces present in the governing equations shows that the ratio of the viscous force to the buoyancy force is an increasing function of $\widetilde {Ra}$ , that approaches unity over the investigated range of parameters. [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: 149512610 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: On the inverse cascade and flow speed scaling behaviour in rapidly rotating Rayleigh–Bénard convection. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Maffei%2C+S%2E%22">Maffei, S.</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<i> s.maffei@leeds.ac.uk</i><br /><searchLink fieldCode="AR" term="%22Krouss%2C+M%2EJ%2E%22">Krouss, M.J.</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Julien%2C+K%2E%22">Julien, K.</searchLink><relatesTo>3</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Calkins%2C+M%2EA%2E%22">Calkins, M.A.</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>. 4/25/2021, Vol. 913, p1-30. 30p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Rayleigh-Bénard+convection%22">Rayleigh-Bénard convection</searchLink><br /><searchLink fieldCode="DE" term="%22Convective+flow%22">Convective flow</searchLink><br /><searchLink fieldCode="DE" term="%22Buoyancy%22">Buoyancy</searchLink><br /><searchLink fieldCode="DE" term="%22Rayleigh+number%22">Rayleigh number</searchLink><br /><searchLink fieldCode="DE" term="%22Prandtl+number%22">Prandtl number</searchLink><br /><searchLink fieldCode="DE" term="%22Viscosity%22">Viscosity</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: Rotating Rayleigh–Bénard convection is investigated numerically with the use of an asymptotic model that captures the rapidly rotating, small Ekman number limit, $Ek \rightarrow 0$. The Prandtl number ($Pr$) and the asymptotically scaled Rayleigh number ($\widetilde {Ra} = Ra Ek^{4/3}$ , where $Ra$ is the typical Rayleigh number) are varied systematically. For sufficiently vigorous convection, an inverse kinetic energy cascade leads to the formation of a pair of large-scale vortices of opposite polarity, in agreement with previous studies of rapidly rotating convection. With respect to the kinetic energy, we find a transition from convection dominated states to a state dominated by large-scale vortices at an asymptotically reduced (small-scale) Reynolds number of $\widetilde {Re} \approx 6$ ($\widetilde {Re} = Re Ek^{1/3}$ , where $Re$ is the Reynolds number associated with vertical flows) for all investigated values of $Pr$. The ratio of the depth-averaged kinetic energy to the kinetic energy of the convection reaches a maximum at $\widetilde {Re} \approx 24$ , then decreases as $\widetilde {Ra}$ is increased. This decrease in the relative kinetic energy of the large-scale vortices is associated with a decrease in the convective correlations with increasing Rayleigh number. The scaling behaviour of the convective flow speeds is studied; although a linear scaling of the form $\widetilde {Re} \sim \widetilde {Ra}/Pr$ is observed over a limited range in Rayleigh number and Prandtl number, a clear departure from this scaling is observed at the highest accessible values of $\widetilde {Ra}$. Calculation of the forces present in the governing equations shows that the ratio of the viscous force to the buoyancy force is an increasing function of $\widetilde {Ra}$ , that approaches unity over the investigated range of parameters. [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.2020.1058 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 30 StartPage: 1 Subjects: – SubjectFull: Rayleigh-Bénard convection Type: general – SubjectFull: Convective flow Type: general – SubjectFull: Buoyancy Type: general – SubjectFull: Rayleigh number Type: general – SubjectFull: Prandtl number Type: general – SubjectFull: Viscosity Type: general Titles: – TitleFull: On the inverse cascade and flow speed scaling behaviour in rapidly rotating Rayleigh–Bénard convection. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Maffei, S. – PersonEntity: Name: NameFull: Krouss, M.J. – PersonEntity: Name: NameFull: Julien, K. – PersonEntity: Name: NameFull: Calkins, M.A. IsPartOfRelationships: – BibEntity: Dates: – D: 25 M: 04 Text: 4/25/2021 Type: published Y: 2021 Identifiers: – Type: issn-print Value: 00221120 Numbering: – Type: volume Value: 913 Titles: – TitleFull: Journal of Fluid Mechanics Type: main |
| ResultId | 1 |
