On the optimal rate of vortex stretching for axisymmetric Euler flows without swirl
Analysis of PDEs
2025-03-20 v2 Mathematical Physics
math.MP
Abstract
For axisymmetric flows without swirl and compactly supported initial vorticity, we prove the upper bound of for the growth of the vorticity maximum, which was conjectured by Childress [Phys. D, 2008] and supported by numerical computations from Childress--Gilbert--Valiant [J. Fluid Mech. 2016]. The key is to estimate the velocity maximum by the kinetic energy together with conserved quantities involving the vorticity.
Cite
@article{arxiv.2409.19497,
title = {On the optimal rate of vortex stretching for axisymmetric Euler flows without swirl},
author = {Deokwoo Lim and In-Jee Jeong},
journal= {arXiv preprint arXiv:2409.19497},
year = {2025}
}
Comments
24 pages, 2 figures, this version to appear in Arch. Rational Mech. Anal