Hopf bifurcation of a non-parallel Navier-Stokes flow
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909165659619328 |
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| author | Chen, Zhi-Min |
| author_facet | Chen, Zhi-Min |
| contents | A plane non-parallel flow in a square fluid domain exhibits an odd number of vortices. A spectral structure is found to have a non-real solution of the spectral problem linearized around the flow. With the use of this structure, Hopf bifurcation or secondary time periodic flows branching of a basic square eddy flow is found. In contrast to a square eddy flow involving an even number of vortices in earlier analytical and experimental investigations, instability of the flow leads to steady-state bifurcations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_07065 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hopf bifurcation of a non-parallel Navier-Stokes flow Chen, Zhi-Min Mathematical Physics Fluid Dynamics A plane non-parallel flow in a square fluid domain exhibits an odd number of vortices. A spectral structure is found to have a non-real solution of the spectral problem linearized around the flow. With the use of this structure, Hopf bifurcation or secondary time periodic flows branching of a basic square eddy flow is found. In contrast to a square eddy flow involving an even number of vortices in earlier analytical and experimental investigations, instability of the flow leads to steady-state bifurcations. |
| title | Hopf bifurcation of a non-parallel Navier-Stokes flow |
| topic | Mathematical Physics Fluid Dynamics |
| url | https://arxiv.org/abs/2404.07065 |