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arXiv · 2409.19497

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

Deokwoo Lim·In-Jee Jeong
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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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Deokwoo Lim, In-Jee Jeong. 2024-09-29. On the optimal rate of vortex stretching for axisymmetric Euler flows without swirl. https://arxiv.org/abs/2409.19497

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