On the optimal rate of vortex stretching for axisymmetric Euler flows without swirl

2024/09/29 by Deokwoo Lim, Lim, Deokwoo, In‐Jee Jeong +1 · 6 citations
Engineering · Mathematics · #Fluid Dynamics and Turbulent Flows #Computational Fluid Dynamics and Aerodynamics #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.2409.19497

Abstract

For axisymmetric flows without swirl and compactly supported initial vorticity, we prove the upper bound of t^4/3 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.

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• Support growth of vorticity for bi-rotational Euler flows in high dimensions
• On the upper bound for the vorticity growth of bi-rotational Euler flows without swirl
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