A Local Instability Mechanism of the Navier–Stokes Flow with Swirl on the No-Slip Flat Boundary

  • Leandro LichtenfelzEmail author
  • Tsuyoshi Yoneda


Using numerical simulations of the axisymmetric Navier–Stokes equations with swirl on a no-slip flat boundary, Hsu et al. (J Fluid Mech 794:444–459, 2016) observed the creation of a high-vorticity region on the boundary near the axis of symmetry. In this paper, using a differential geometric approach, we prove that such flows indeed have a destabilizing effect, which is formulated in terms of a lower bound on the \(L^\infty \)-norm of derivatives of the velocity field on the boundary.



The authors would like to thank Doctor Pen-Yuan Hsu for helpful comments. TY was partially supported by Grant-in-Aid for Young Scientists A (17H04825) and Scientific Research B (18H01135), Japan Society for the Promotion of Science (JSPS).

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Conflict of interest

The authors declare that they have no conflicts of interest in the present work.


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Authors and Affiliations

  1. 1.Department of MathematicsUniversity of PennsylvaniaPhiladelphiaUSA
  2. 2.Graduate School of Mathematical SciencesUniversity of TokyoMeguroJapan

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