Abstract
Tornado is a destructive catastrophe. We use compressible isentropic Euler equations to describe this problem. A cylindrically symmetric special solution moving with a constant velocity in \(\mathbb {R}^3\) is given. It depicts how the vorticity function of the flow evolves. Even if the initial inward velocity and acceleration are both very small, the inward velocity could become very large and the vorticity could increase drastically in later time, and most of mass concentrates on a neighborhood of the moving center axis at this time. For this solution, cases when \(\gamma \ne 2\) and when \(\gamma =2\) (shallow water) have some differences, while their evolution dynamics are basically the same. When \(\gamma =2\), the initial vorticity could depend on the space variables.
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Acknowledgements
Thanks for the helpful discussion with Prof. ChangXing Miao. The author is supported by National Natural Science Foundation of China under contract 10931007 and 11771429.
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Li, TH. An analysis to a model of tornado. Z. Angew. Math. Phys. 73, 17 (2022). https://doi.org/10.1007/s00033-021-01647-y
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DOI: https://doi.org/10.1007/s00033-021-01647-y