IF 1.3 3区 物理与天体物理 Q3 PHYSICS, MATHEMATICAL
Paolo Buttà, Guido Cavallaro, Carlo Marchioro
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引用次数: 0

摘要

我们研究了具有轴对称性的不可压缩流体在无漩涡情况下的时间演化,当涡度急剧集中在N个半径为\(r_0\)、厚度为\(\varepsilon \)的环上时。我们证明当\(r_0= |\log \varepsilon |^\alpha \),\(\alpha >1\)时,流体的涡度场对于\(\varepsilon \rightarrow 0\)收敛于点涡模型,时间间隔发散为\(\log |\log \varepsilon |\)。这概括了卡瓦拉罗和马奇奥罗之前在(J Math Phys 62:053102,2021)中的结果,该结果假定了\(\alpha >2\),并且只在短时间内证明了收敛性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Long Time Evolution of Concentrated Vortex Rings with Large Radius

We study the time evolution of an incompressible fluid with axial symmetry without swirl when the vorticity is sharply concentrated on N annuli of radii of the order of \(r_0\) and thickness \(\varepsilon \). We prove that when \(r_0= |\log \varepsilon |^\alpha \), \(\alpha >1\), the vorticity field of the fluid converges for \(\varepsilon \rightarrow 0\) to the point vortex model, in an interval of time which diverges as \(\log |\log \varepsilon |\). This generalizes previous result by Cavallaro and Marchioro in (J Math Phys 62:053102, 2021), that assumed \(\alpha >2\) and in which the convergence was proved for short times only.

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来源期刊
Journal of Statistical Physics
Journal of Statistical Physics 物理-物理:数学物理
CiteScore
3.10
自引率
12.50%
发文量
152
审稿时长
3-6 weeks
期刊介绍: The Journal of Statistical Physics publishes original and invited review papers in all areas of statistical physics as well as in related fields concerned with collective phenomena in physical systems.
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