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Instability of boundary layers with the Navier boundary condition
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Quarisa, Lorenzo and Rodrigo Diez, José L. (2022) Instability of boundary layers with the Navier boundary condition. Journal of Mathematical Fluid Mechanics, 24 . 91. doi:10.1007/s00021-022-00714-2 ISSN 1422-6928.
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Official URL: https://doi.org/10.1007/s00021-022-00714-2
Abstract
We study the L∞- stability of the Navier-Stokes equations in the half-plane with a viscosity-dependent Navier friction boundary condition around shear profiles which are linearly unstable for the Euler equation. The dependence from the viscosity is given in the Navier boundary condition as ∂yu=ν−γu for some γ∈R, where u is the tangential velocity. With the no-slip boundary condition, which corresponds to the limit γ→+∞, a celebrated result from E. Grenier provides an instability of order ν1/4. M. Paddick proved the same result in the case γ= 1/2, furthermore improving the instability to order one. In this paper, we extend these two results to allγ∈R, obtaining an instability of order νθ, where in particular θ= 0 for γ≤1/2 and θ= 1/4 for γ≥3/4. When γ≥1/2, the result denies the validity of the Prandtl boundary layer expansion around the chosen shear profile.
| Item Type: | Journal Article | ||||||
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| Subjects: | Q Science > QA Mathematics | ||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||
| Library of Congress Subject Headings (LCSH): | Navier-Stokes equations , Boundary layer, Fluid dynamics -- Approximation methods | ||||||
| Journal or Publication Title: | Journal of Mathematical Fluid Mechanics | ||||||
| Publisher: | Birkhaeuser Verlag AG | ||||||
| ISSN: | 1422-6928 | ||||||
| Official Date: | 26 July 2022 | ||||||
| Dates: |
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| Volume: | 24 | ||||||
| Article Number: | 91 | ||||||
| DOI: | 10.1007/s00021-022-00714-2 | ||||||
| Status: | Peer Reviewed | ||||||
| Publication Status: | Published | ||||||
| Access rights to Published version: | Open Access (Creative Commons) | ||||||
| Date of first compliant deposit: | 13 July 2022 | ||||||
| Date of first compliant Open Access: | 2 August 2022 | ||||||
| RIOXX Funder/Project Grant: |
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