Laminar co-rotating Batchelor vortex merging
Abstract The dynamics of laminar co-rotating vortex pairs without axial flow have been recently thoroughly studied through theoretical, experimental and numerical studies, which revealed different instabilities contributing to the decay of the vortices. In this paper, the objective is to extend the...
Ausführliche Beschreibung
Autor*in: |
Ferreira de Sousa, Paulo J. S. A. [verfasserIn] |
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Format: |
Artikel |
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Sprache: |
Englisch |
Erschienen: |
2009 |
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Schlagwörter: |
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Anmerkung: |
© Springer-Verlag 2009 |
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Übergeordnetes Werk: |
Enthalten in: Theoretical and computational fluid dynamics - Springer-Verlag, 1989, 23(2009), 1 vom: 01. Feb., Seite 1-14 |
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Übergeordnetes Werk: |
volume:23 ; year:2009 ; number:1 ; day:01 ; month:02 ; pages:1-14 |
Links: |
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DOI / URN: |
10.1007/s00162-009-0091-z |
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Katalog-ID: |
OLC2071163354 |
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10.1007/s00162-009-0091-z doi (DE-627)OLC2071163354 (DE-He213)s00162-009-0091-z-p DE-627 ger DE-627 rakwb eng 530 620 VZ 510 530 VZ Ferreira de Sousa, Paulo J. S. A. verfasserin aut Laminar co-rotating Batchelor vortex merging 2009 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 2009 Abstract The dynamics of laminar co-rotating vortex pairs without axial flow have been recently thoroughly studied through theoretical, experimental and numerical studies, which revealed different instabilities contributing to the decay of the vortices. In this paper, the objective is to extend the analysis to the case of co-rotating vortices with axial flow at low Reynolds numbers. A high-order incompressible Navier–Stokes flow solver is used. The momentum equations are spatially discretized on a staggered mesh by finite differences and all derivatives are evaluated with 10th order compact finite difference schemes with RK-4 temporal discretization. The initial condition is a linear superposition of two co-rotating circular Batchelor vortices with q = 1. It is found that there is an initial evolution that resembles the evolution that single q = 1 vortices go through. Azimuthal disturbances grow and result in the appearance of large-scale helical sheets of vorticity. With the development of these instability waves, the axial velocity deficit is weakened. The redistribution of both angular and axial momentum between the core and the surroundings drives the vortex core to a more stable configuration, with a higher q value. After these processes, the evolution is somewhat similar to a pair of co-rotating Lamb–Oseen vortices. A three-dimensional instability develops, with a large band of unstable modes, with the most amplified mode corresponding scaling with the vortex initial separation distance. Vortices Flow simulation External flows Wakes Pereira, José C. F. aut Enthalten in Theoretical and computational fluid dynamics Springer-Verlag, 1989 23(2009), 1 vom: 01. Feb., Seite 1-14 (DE-627)130799521 (DE-600)1007949-X (DE-576)023042370 0935-4964 nnns volume:23 year:2009 number:1 day:01 month:02 pages:1-14 https://doi.org/10.1007/s00162-009-0091-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_20 GBV_ILN_70 GBV_ILN_267 GBV_ILN_2006 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_4116 GBV_ILN_4277 GBV_ILN_4307 AR 23 2009 1 01 02 1-14 |
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10.1007/s00162-009-0091-z doi (DE-627)OLC2071163354 (DE-He213)s00162-009-0091-z-p DE-627 ger DE-627 rakwb eng 530 620 VZ 510 530 VZ Ferreira de Sousa, Paulo J. S. A. verfasserin aut Laminar co-rotating Batchelor vortex merging 2009 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 2009 Abstract The dynamics of laminar co-rotating vortex pairs without axial flow have been recently thoroughly studied through theoretical, experimental and numerical studies, which revealed different instabilities contributing to the decay of the vortices. In this paper, the objective is to extend the analysis to the case of co-rotating vortices with axial flow at low Reynolds numbers. A high-order incompressible Navier–Stokes flow solver is used. The momentum equations are spatially discretized on a staggered mesh by finite differences and all derivatives are evaluated with 10th order compact finite difference schemes with RK-4 temporal discretization. The initial condition is a linear superposition of two co-rotating circular Batchelor vortices with q = 1. It is found that there is an initial evolution that resembles the evolution that single q = 1 vortices go through. Azimuthal disturbances grow and result in the appearance of large-scale helical sheets of vorticity. With the development of these instability waves, the axial velocity deficit is weakened. The redistribution of both angular and axial momentum between the core and the surroundings drives the vortex core to a more stable configuration, with a higher q value. After these processes, the evolution is somewhat similar to a pair of co-rotating Lamb–Oseen vortices. A three-dimensional instability develops, with a large band of unstable modes, with the most amplified mode corresponding scaling with the vortex initial separation distance. Vortices Flow simulation External flows Wakes Pereira, José C. F. aut Enthalten in Theoretical and computational fluid dynamics Springer-Verlag, 1989 23(2009), 1 vom: 01. Feb., Seite 1-14 (DE-627)130799521 (DE-600)1007949-X (DE-576)023042370 0935-4964 nnns volume:23 year:2009 number:1 day:01 month:02 pages:1-14 https://doi.org/10.1007/s00162-009-0091-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_20 GBV_ILN_70 GBV_ILN_267 GBV_ILN_2006 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_4116 GBV_ILN_4277 GBV_ILN_4307 AR 23 2009 1 01 02 1-14 |
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10.1007/s00162-009-0091-z doi (DE-627)OLC2071163354 (DE-He213)s00162-009-0091-z-p DE-627 ger DE-627 rakwb eng 530 620 VZ 510 530 VZ Ferreira de Sousa, Paulo J. S. A. verfasserin aut Laminar co-rotating Batchelor vortex merging 2009 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 2009 Abstract The dynamics of laminar co-rotating vortex pairs without axial flow have been recently thoroughly studied through theoretical, experimental and numerical studies, which revealed different instabilities contributing to the decay of the vortices. In this paper, the objective is to extend the analysis to the case of co-rotating vortices with axial flow at low Reynolds numbers. A high-order incompressible Navier–Stokes flow solver is used. The momentum equations are spatially discretized on a staggered mesh by finite differences and all derivatives are evaluated with 10th order compact finite difference schemes with RK-4 temporal discretization. The initial condition is a linear superposition of two co-rotating circular Batchelor vortices with q = 1. It is found that there is an initial evolution that resembles the evolution that single q = 1 vortices go through. Azimuthal disturbances grow and result in the appearance of large-scale helical sheets of vorticity. With the development of these instability waves, the axial velocity deficit is weakened. The redistribution of both angular and axial momentum between the core and the surroundings drives the vortex core to a more stable configuration, with a higher q value. After these processes, the evolution is somewhat similar to a pair of co-rotating Lamb–Oseen vortices. A three-dimensional instability develops, with a large band of unstable modes, with the most amplified mode corresponding scaling with the vortex initial separation distance. Vortices Flow simulation External flows Wakes Pereira, José C. F. aut Enthalten in Theoretical and computational fluid dynamics Springer-Verlag, 1989 23(2009), 1 vom: 01. Feb., Seite 1-14 (DE-627)130799521 (DE-600)1007949-X (DE-576)023042370 0935-4964 nnns volume:23 year:2009 number:1 day:01 month:02 pages:1-14 https://doi.org/10.1007/s00162-009-0091-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_20 GBV_ILN_70 GBV_ILN_267 GBV_ILN_2006 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_4116 GBV_ILN_4277 GBV_ILN_4307 AR 23 2009 1 01 02 1-14 |
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10.1007/s00162-009-0091-z doi (DE-627)OLC2071163354 (DE-He213)s00162-009-0091-z-p DE-627 ger DE-627 rakwb eng 530 620 VZ 510 530 VZ Ferreira de Sousa, Paulo J. S. A. verfasserin aut Laminar co-rotating Batchelor vortex merging 2009 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 2009 Abstract The dynamics of laminar co-rotating vortex pairs without axial flow have been recently thoroughly studied through theoretical, experimental and numerical studies, which revealed different instabilities contributing to the decay of the vortices. In this paper, the objective is to extend the analysis to the case of co-rotating vortices with axial flow at low Reynolds numbers. A high-order incompressible Navier–Stokes flow solver is used. The momentum equations are spatially discretized on a staggered mesh by finite differences and all derivatives are evaluated with 10th order compact finite difference schemes with RK-4 temporal discretization. The initial condition is a linear superposition of two co-rotating circular Batchelor vortices with q = 1. It is found that there is an initial evolution that resembles the evolution that single q = 1 vortices go through. Azimuthal disturbances grow and result in the appearance of large-scale helical sheets of vorticity. With the development of these instability waves, the axial velocity deficit is weakened. The redistribution of both angular and axial momentum between the core and the surroundings drives the vortex core to a more stable configuration, with a higher q value. After these processes, the evolution is somewhat similar to a pair of co-rotating Lamb–Oseen vortices. A three-dimensional instability develops, with a large band of unstable modes, with the most amplified mode corresponding scaling with the vortex initial separation distance. Vortices Flow simulation External flows Wakes Pereira, José C. F. aut Enthalten in Theoretical and computational fluid dynamics Springer-Verlag, 1989 23(2009), 1 vom: 01. Feb., Seite 1-14 (DE-627)130799521 (DE-600)1007949-X (DE-576)023042370 0935-4964 nnns volume:23 year:2009 number:1 day:01 month:02 pages:1-14 https://doi.org/10.1007/s00162-009-0091-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_20 GBV_ILN_70 GBV_ILN_267 GBV_ILN_2006 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_4116 GBV_ILN_4277 GBV_ILN_4307 AR 23 2009 1 01 02 1-14 |
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10.1007/s00162-009-0091-z doi (DE-627)OLC2071163354 (DE-He213)s00162-009-0091-z-p DE-627 ger DE-627 rakwb eng 530 620 VZ 510 530 VZ Ferreira de Sousa, Paulo J. S. A. verfasserin aut Laminar co-rotating Batchelor vortex merging 2009 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag 2009 Abstract The dynamics of laminar co-rotating vortex pairs without axial flow have been recently thoroughly studied through theoretical, experimental and numerical studies, which revealed different instabilities contributing to the decay of the vortices. In this paper, the objective is to extend the analysis to the case of co-rotating vortices with axial flow at low Reynolds numbers. A high-order incompressible Navier–Stokes flow solver is used. The momentum equations are spatially discretized on a staggered mesh by finite differences and all derivatives are evaluated with 10th order compact finite difference schemes with RK-4 temporal discretization. The initial condition is a linear superposition of two co-rotating circular Batchelor vortices with q = 1. It is found that there is an initial evolution that resembles the evolution that single q = 1 vortices go through. Azimuthal disturbances grow and result in the appearance of large-scale helical sheets of vorticity. With the development of these instability waves, the axial velocity deficit is weakened. The redistribution of both angular and axial momentum between the core and the surroundings drives the vortex core to a more stable configuration, with a higher q value. After these processes, the evolution is somewhat similar to a pair of co-rotating Lamb–Oseen vortices. A three-dimensional instability develops, with a large band of unstable modes, with the most amplified mode corresponding scaling with the vortex initial separation distance. Vortices Flow simulation External flows Wakes Pereira, José C. F. aut Enthalten in Theoretical and computational fluid dynamics Springer-Verlag, 1989 23(2009), 1 vom: 01. Feb., Seite 1-14 (DE-627)130799521 (DE-600)1007949-X (DE-576)023042370 0935-4964 nnns volume:23 year:2009 number:1 day:01 month:02 pages:1-14 https://doi.org/10.1007/s00162-009-0091-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_20 GBV_ILN_70 GBV_ILN_267 GBV_ILN_2006 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_4116 GBV_ILN_4277 GBV_ILN_4307 AR 23 2009 1 01 02 1-14 |
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Laminar co-rotating Batchelor vortex merging |
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Laminar co-rotating Batchelor vortex merging |
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Ferreira de Sousa, Paulo J. S. A. |
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Theoretical and computational fluid dynamics |
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2009 |
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Ferreira de Sousa, Paulo J. S. A. Pereira, José C. F. |
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Ferreira de Sousa, Paulo J. S. A. |
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laminar co-rotating batchelor vortex merging |
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Laminar co-rotating Batchelor vortex merging |
abstract |
Abstract The dynamics of laminar co-rotating vortex pairs without axial flow have been recently thoroughly studied through theoretical, experimental and numerical studies, which revealed different instabilities contributing to the decay of the vortices. In this paper, the objective is to extend the analysis to the case of co-rotating vortices with axial flow at low Reynolds numbers. A high-order incompressible Navier–Stokes flow solver is used. The momentum equations are spatially discretized on a staggered mesh by finite differences and all derivatives are evaluated with 10th order compact finite difference schemes with RK-4 temporal discretization. The initial condition is a linear superposition of two co-rotating circular Batchelor vortices with q = 1. It is found that there is an initial evolution that resembles the evolution that single q = 1 vortices go through. Azimuthal disturbances grow and result in the appearance of large-scale helical sheets of vorticity. With the development of these instability waves, the axial velocity deficit is weakened. The redistribution of both angular and axial momentum between the core and the surroundings drives the vortex core to a more stable configuration, with a higher q value. After these processes, the evolution is somewhat similar to a pair of co-rotating Lamb–Oseen vortices. A three-dimensional instability develops, with a large band of unstable modes, with the most amplified mode corresponding scaling with the vortex initial separation distance. © Springer-Verlag 2009 |
abstractGer |
Abstract The dynamics of laminar co-rotating vortex pairs without axial flow have been recently thoroughly studied through theoretical, experimental and numerical studies, which revealed different instabilities contributing to the decay of the vortices. In this paper, the objective is to extend the analysis to the case of co-rotating vortices with axial flow at low Reynolds numbers. A high-order incompressible Navier–Stokes flow solver is used. The momentum equations are spatially discretized on a staggered mesh by finite differences and all derivatives are evaluated with 10th order compact finite difference schemes with RK-4 temporal discretization. The initial condition is a linear superposition of two co-rotating circular Batchelor vortices with q = 1. It is found that there is an initial evolution that resembles the evolution that single q = 1 vortices go through. Azimuthal disturbances grow and result in the appearance of large-scale helical sheets of vorticity. With the development of these instability waves, the axial velocity deficit is weakened. The redistribution of both angular and axial momentum between the core and the surroundings drives the vortex core to a more stable configuration, with a higher q value. After these processes, the evolution is somewhat similar to a pair of co-rotating Lamb–Oseen vortices. A three-dimensional instability develops, with a large band of unstable modes, with the most amplified mode corresponding scaling with the vortex initial separation distance. © Springer-Verlag 2009 |
abstract_unstemmed |
Abstract The dynamics of laminar co-rotating vortex pairs without axial flow have been recently thoroughly studied through theoretical, experimental and numerical studies, which revealed different instabilities contributing to the decay of the vortices. In this paper, the objective is to extend the analysis to the case of co-rotating vortices with axial flow at low Reynolds numbers. A high-order incompressible Navier–Stokes flow solver is used. The momentum equations are spatially discretized on a staggered mesh by finite differences and all derivatives are evaluated with 10th order compact finite difference schemes with RK-4 temporal discretization. The initial condition is a linear superposition of two co-rotating circular Batchelor vortices with q = 1. It is found that there is an initial evolution that resembles the evolution that single q = 1 vortices go through. Azimuthal disturbances grow and result in the appearance of large-scale helical sheets of vorticity. With the development of these instability waves, the axial velocity deficit is weakened. The redistribution of both angular and axial momentum between the core and the surroundings drives the vortex core to a more stable configuration, with a higher q value. After these processes, the evolution is somewhat similar to a pair of co-rotating Lamb–Oseen vortices. A three-dimensional instability develops, with a large band of unstable modes, with the most amplified mode corresponding scaling with the vortex initial separation distance. © Springer-Verlag 2009 |
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Laminar co-rotating Batchelor vortex merging |
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