We study the time evolution of an incompressible fluid with an axial symmetry without swirl when the vorticity is sharply concentrated on N annuli of radii ≈r₀ and thickness ɛ. We prove that when r₀ = |log ɛ|^α, α > 2, the vorticity field of the fluid converges as ɛ → 0 to the point-vortex model, at least for a small but positive time. This result generalizes a previous paper that assumed a power law for the relation between r₀ and ɛ.

中文翻译：

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具有大半径和非常集中涡度的涡环的时间演化

我们研究了当涡量急剧集中在半径 ≈ r ₀和厚度ɛ 的N圆环上时，具有轴对称无涡流的不可压缩流体的时间演化。我们证明当r ₀ = |log  ɛ | ^α , α > 2，流体的涡量场随着ɛ → 0收敛到点涡模型，至少在一小段时间是正的。这个结果概括了之前的一篇论文，该论文假设了r ₀和ɛ之间的关系的幂律。