Microturbulence close to marginality with inclusion of electron dynamics and in the electrostatic limit [A. Weikl et al., Phys. Plasmas 25, 072305 (2018)] is revisited. In such states the E × B shearing rate ${\omega }_{\mathrm{E}\times \mathrm{B}}$, i.e., the second radial derivative of the zonal electrostatic potential, a quantity often applied to study zonal flow structure formation, has been found to be dominated by radial fine scale features. Those features are significantly different from the mesoscale E × B staircase structures [G. Dif-Pradalier et al., Phys. Rev. E 82, 025401(R) (2010)] normally occurring close to the threshold. Instead of the E × B shearing rate, here, zonal flow structure formation is studied through the zonal flow shear induced tilt of turbulent structures, which is measured by director field methods. In contrast to dominant fine scale features in ${\omega }_{\mathrm{E}\times \mathrm{B}}$, mesoscale zonal flow pattern formation on two disparate scales is identified: (i) A zonal flow with radial scale of the boxsize develops, (ii) superposed by zonal flow corrugations in form of shear layers emerging in the vicinity of lowest order rational layers. This mesoscale zonal flow pattern exhibits properties of E × B staircases: (i) A shearing rate of $\sim {10}^{-1}\hspace{0.17em}{v}_{\text{th},\mathrm{i}}/R_0$ ($v_{\text{th},\mathrm{i}}$ is the ion thermal velocity and R₀ is the major radius), comparable to typical growth rates, can be attributed to both components of the mesoscale pattern. (ii) Avalanche-like turbulent transport events organize spatially on the same mesoscales. (iii) Shear stabilization by a background E × B shear flow requires values of the background shearing rate exceeding those connected to the mesoscale pattern. In conclusion, this work demonstrates that E × B staircases do develop, even when the E × B shearing rate ${\omega }_{\mathrm{E}\times \mathrm{B}}$ is dominated by radial fine scale features. The E × B shearing rate ${\omega }_{\mathrm{E}\times \mathrm{B}}$, therefore, fails to estimate the shear provided by zonal flows when fine scale structures dominate its radial profile.

中文翻译：

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边缘湍流回旋动力学中的纬向流型形成和阶梯状态修正的分析

微湍流接近边缘，包含电子动力学和静电极限 [A. 魏克尔等人。，物理。等离子体25，072305（2018）]被重新考虑。在这种状态下，E  ×  B剪切速率${\omega }_{\mathrm{乙}\times \mathrm{乙}}$，即纬向静电势的二阶径向导数，一个经常用于研究纬向流结构形成的量，已被发现由径向精细尺度特征主导。这些特征与中尺度E  ×  B阶梯结构 [G. 迪夫-普拉达利埃等人。，物理。Rev. E 82 , 025401(R) (2010)] 通常发生在阈值附近。在这里，不是E  ×  B剪切速率，而是通过由导向场方法测量的湍流结构的纬向流剪切引起的倾斜来研究纬向流结构的形成。与占主导地位的精细尺度特征相反${\omega }_{\mathrm{乙}\times \mathrm{乙}}$，确定了两个不同尺度上的中尺度带状流模式形成：（i）具有箱形径向尺度的带状流发展，（ii）由在最低阶合理层附近出现的剪切层形式的带状流波纹叠加。这种中尺度纬向流动模式表现出E  ×  B阶梯的特性：(i) 剪切速率为$～{10}^{-1}\hspace{0.17em}{v}_{\text{日},\mathrm{一世}}/{\mathrm{电阻}}_0$ ($v_{\text{日},\mathrm{一世}}$是离子热速度，R ₀是主半径），与典型的增长率相当，可归因于中尺度模式的两个组成部分。(ii) 类似雪崩的湍流运输事件在相同的中尺度上在空间上组织。(iii) 背景E  ×  B剪切流的剪切稳定需要背景剪切速率的值超过与中尺度模式相关的值。总之，这项工作表明E  ×  B阶梯确实发展，即使E  ×  B剪切速率${\omega }_{\mathrm{乙}\times \mathrm{乙}}$以径向精细尺度特征为主。所述ë  × 乙剪切速率${\omega }_{\mathrm{乙}\times \mathrm{乙}}$因此，当细尺度结构主导其径向剖面时，无法估计纬向流提供的剪切。