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arXiv · 1810.13057

A local instability mechanism of the Navier-Stokes flow with swirl on the no-slip flat boundary

Leandro Lichtenfelz·Tsuyoshi Yoneda
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Abstract

Using numerical simulations of the axisymmetric Navier-Stokes equations with swirl on a no-slip flat boundary, Hsu-Notsu-Yoneda [J. Fluid Mech. 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.

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Leandro Lichtenfelz, Tsuyoshi Yoneda. 2018-10-31. A local instability mechanism of the Navier-Stokes flow with swirl on the no-slip flat boundary. https://doi.org/10.1007/s00021-019-0424-7

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