The question of energy concentration in approximate solution sequences $u^\epsilon$, as $\epsilon \to 0$, of the two-dimensional incompressible Euler equations with vortex-sheet initial data is revisited. Building on a novel identity for the structure function in terms of vorticity, the vorticity maximal function is proposed as a quantitative tool to detect concentration effects in approximate solution sequences. This tool is applied to numerical experiments based on the vortex-blob method, where vortex sheet initial data without distinguished sign are considered, as introduced in \emph{[R.~Krasny, J. Fluid Mech. \textbf{167}:65-93 (1986)]}. Numerical evidence suggests that no energy concentration appears in the limit of zero blob-regularization $\epsilon \to 0$, for the considered initial data.

中文翻译：

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关于涡流片中的浓度

重新讨论了具有涡片初始数据的二维不可压缩欧拉方程的近似解序列$u^\epsilon$, as $\epsilon \to 0$ 中的能量集中问题。基于涡度方面的结构函数的新身份，涡度最大函数被提议作为一种定量工具来检测近似溶液序列中的浓度效应。该工具应用于基于涡团法的数值实验，其中考虑了没有区分符号的涡流片初始数据，如 \emph{[R.~Krasny, J. Fluid Mech. \textbf{167}:65-93 (1986)]}。数值证据表明，对于所考虑的初始数据，在零 blob 正则化 $\epsilon \to 0$ 的极限内没有出现能量集中。