Locality of Vortex Stretching for the 3D Euler Equations

Yuuki Shimizu; Tsuyoshi Yoneda

doi:10.1007/s00021-023-00763-1

Locality of Vortex Stretching for the 3D Euler Equations

Yuuki Shimizu, Tsuyoshi Yoneda^*

^*この論文の責任著者

理学科　数学プログラム

研究成果: ジャーナルへの寄稿 › 学術論文 › 査読

1 被引用数 (Scopus)

抄録

We consider the 3D incompressible Euler equations under the following situation: small-scale vortex blob being stretched by a prescribed large-scale stationary flow. More precisely, we clarify what kind of large-scale stationary flows really stretch small-scale vortex blobs in alignment with the straining direction. The key idea is constructing a Lagrangian coordinate so that the Lie bracket is identically zero (c.f. the Frobenius theorem), and investigate the locality of the pressure term by using it.

本文言語	英語
論文番号	18
ジャーナル	Journal of Mathematical Fluid Mechanics
巻	25
号	1
DOI	https://doi.org/10.1007/s00021-023-00763-1
出版ステータス	出版済み - 2023/02

ASJC Scopus 主題領域

数理物理学
凝縮系物理学
計算数学
応用数学

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10.1007/s00021-023-00763-1

引用スタイル

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keywords = "Euler equations, Frenet–Serret formulas, Frobenius theorem, Vortex stretching",

author = "Yuuki Shimizu and Tsuyoshi Yoneda",

note = "Publisher Copyright: {\textcopyright} 2023, The Author(s), under exclusive licence to Springer Nature Switzerland AG.",

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doi = "10.1007/s00021-023-00763-1",

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N2 - We consider the 3D incompressible Euler equations under the following situation: small-scale vortex blob being stretched by a prescribed large-scale stationary flow. More precisely, we clarify what kind of large-scale stationary flows really stretch small-scale vortex blobs in alignment with the straining direction. The key idea is constructing a Lagrangian coordinate so that the Lie bracket is identically zero (c.f. the Frobenius theorem), and investigate the locality of the pressure term by using it.

AB - We consider the 3D incompressible Euler equations under the following situation: small-scale vortex blob being stretched by a prescribed large-scale stationary flow. More precisely, we clarify what kind of large-scale stationary flows really stretch small-scale vortex blobs in alignment with the straining direction. The key idea is constructing a Lagrangian coordinate so that the Lie bracket is identically zero (c.f. the Frobenius theorem), and investigate the locality of the pressure term by using it.

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KW - Frenet–Serret formulas

KW - Frobenius theorem

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Locality of Vortex Stretching for the 3D Euler Equations

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