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Title
On the Optimal Rate of Vortex Stretching for Axisymmetric Euler Flows Without Swirl
KIAS Author
Jeong, In-Jee
Journal
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2025
Archive
Abstract
For axisymmetric flows without swirl and compactly supported initial vorticity, we prove the upper bound of t4/3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$t<^>{4/3}$$\end{document} for the growth of the vorticity maximum, which was conjectured by Childress (Phys. D 237(14-17):1921-1925, 2008) and supported by numerical computations from Childress-Gilbert-Valiant (J. Fluid Mech. 805:1-30, 2016). The key is to estimate the velocity maximum by the kinetic energy together with conserved quantities involving the vorticity.