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.

翻译：本文重新审视了二维不可压缩欧拉方程在涡层初始数据下近似解序列$u^\epsilon$在$\epsilon \to 0$时的能量集中问题。基于涡量结构函数的一个新恒等式，提出将涡量极大函数作为检测近似解序列中集中效应的定量工具。将该工具应用于基于涡团法的数值实验，其中考虑了不带明确符号的涡层初始数据，如文献\emph{[R.~Krasny, J. Fluid Mech. \textbf{167}:65-93 (1986)]}所述。数值证据表明，对于所考虑的初始数据，在涡团正则化极限$\epsilon \to 0$下未出现能量集中现象。