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arXiv · 2110.09079

On vortex stretching for anti-parallel axisymmetric flows

Kyudong Choi·In-Jee Jeong
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Abstract

We consider axisymmetric incompressible inviscid flows without swirl in $\mathbb{R}^3$, under the assumption that the axial vorticity is non-positive in the upper half space and odd in the last coordinate, which corresponds to the flow setup for head-on collision of anti-parallel vortex rings. For any such data, we establish monotonicity and infinite growth of the vorticity impulse on the upper half-space. As an application, we achieve infinite growth of Sobolev norms for certain classical/smooth and compactly supported vorticity solutions in $\mathbb{R}^{3}$.

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Kyudong Choi, In-Jee Jeong. 2021-10-18. On vortex stretching for anti-parallel axisymmetric flows. https://arxiv.org/abs/2110.09079

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