Three-dimensional coherent structures in a curved pipe flow
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
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2024
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| _version_ | 1866909541209210880 |
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| author | Song, Runjie Deguchi, Kengo |
| author_facet | Song, Runjie Deguchi, Kengo |
| contents | Dean's approximation for curved pipe flow, valid under loose coiling and high Reynolds numbers, is extended to study three-dimensional travelling waves. Two distinct types of solutions bifurcate from the Dean's classic two-vortex solution. The first type arises through a supercritical bifurcation from inviscid linear instability, and the corresponding self-consistent asymptotic structure aligns with the vortex-wave interaction theory. The second type emerges from a subcritical bifurcation by curvature-induced instabilities and satisfies the boundary region equations. Despite the subcritical nature of the second type of solutions, it is not possible to connect their solution branches to the zero-curvature limit of the pipe. However, by continuing from known self-sustained exact coherent structures in the straight pipe flow problem, another family of three-dimensional travelling waves can be shown to exist across all Dean numbers. The self-sustained solutions also possess the two high-Reynolds-number limits. While the vortex-wave interaction type of solutions can be computed at large Dean numbers, their branch remains unconnected to the Dean vortex solution branch. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2409_11105 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Three-dimensional coherent structures in a curved pipe flow Song, Runjie Deguchi, Kengo Fluid Dynamics Dean's approximation for curved pipe flow, valid under loose coiling and high Reynolds numbers, is extended to study three-dimensional travelling waves. Two distinct types of solutions bifurcate from the Dean's classic two-vortex solution. The first type arises through a supercritical bifurcation from inviscid linear instability, and the corresponding self-consistent asymptotic structure aligns with the vortex-wave interaction theory. The second type emerges from a subcritical bifurcation by curvature-induced instabilities and satisfies the boundary region equations. Despite the subcritical nature of the second type of solutions, it is not possible to connect their solution branches to the zero-curvature limit of the pipe. However, by continuing from known self-sustained exact coherent structures in the straight pipe flow problem, another family of three-dimensional travelling waves can be shown to exist across all Dean numbers. The self-sustained solutions also possess the two high-Reynolds-number limits. While the vortex-wave interaction type of solutions can be computed at large Dean numbers, their branch remains unconnected to the Dean vortex solution branch. |
| title | Three-dimensional coherent structures in a curved pipe flow |
| topic | Fluid Dynamics |
| url | https://arxiv.org/abs/2409.11105 |