A Local Instability Mechanism of the Navier-Stokes Flow with Swirl on the No-Slip Flat Boundary
Abstract
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∞-norm of derivatives of the velocity field on the boundary.
- Publication:
-
Journal of Mathematical Fluid Mechanics
- Pub Date:
- June 2019
- DOI:
- 10.1007/s00021-019-0424-7
- arXiv:
- arXiv:1810.13057
- Bibcode:
- 2019JMFM...21...20L
- Keywords:
-
- Mathematics - Analysis of PDEs;
- Mathematics - Differential Geometry;
- Physics - Fluid Dynamics
- E-Print:
- doi:10.1007/s00021-019-0424-7