Unstable mode around the 3D boundary layer flow
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908524356829184 |
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| author | Liu, Cheng-Jie Ma, Mengjun Wu, Di Zhang, Zhu |
| author_facet | Liu, Cheng-Jie Ma, Mengjun Wu, Di Zhang, Zhu |
| contents | We study the stability properties of boundary layer-type shear flows for the three-dimensional Navier-Stokes equations in the limit of small viscosity $0<ν\ll 1$. When the streamwise and spanwise velocity profiles are linearly independent near the boundary, we construct an unstable mode that exhibits rapid growth at the rate of $e^{t/\sqrtν}$. Our results reveal an analytic instability in the three-dimensional Navier-Stokes equations around generic boundary layer profiles. This instability arises from the interplay between spanwise flow and three-dimensional perturbations, and does not occur in purely two-dimensional flows. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_06089 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Unstable mode around the 3D boundary layer flow Liu, Cheng-Jie Ma, Mengjun Wu, Di Zhang, Zhu Analysis of PDEs Fluid Dynamics We study the stability properties of boundary layer-type shear flows for the three-dimensional Navier-Stokes equations in the limit of small viscosity $0<ν\ll 1$. When the streamwise and spanwise velocity profiles are linearly independent near the boundary, we construct an unstable mode that exhibits rapid growth at the rate of $e^{t/\sqrtν}$. Our results reveal an analytic instability in the three-dimensional Navier-Stokes equations around generic boundary layer profiles. This instability arises from the interplay between spanwise flow and three-dimensional perturbations, and does not occur in purely two-dimensional flows. |
| title | Unstable mode around the 3D boundary layer flow |
| topic | Analysis of PDEs Fluid Dynamics |
| url | https://arxiv.org/abs/2509.06089 |