We investigate the ideal and incompressible magnetohydrodynamic (MHD) equations in three space dimensions for the development of potentially singular structures. The methodology consists in implementing the four-fold symmetries of the Taylor-Green vortex generalized to MHD, leading to substantial computer time and memory savings at a given resolution; we also use a re-gridding method that allows for lower-resolution runs at early times, with no loss of spectral accuracy. One magnetic configuration is examined at an equivalent resolution of $6144^3$ points, and three different configurations on grids of $4096^3$ points. At the highest resolution, two different current and vorticity sheet systems are found to collide, producing two successive accelerations in the development of small scales. At the latest time, a convergence of magnetic field lines to the location of maximum current is probably leading locally to a strong bending and directional variability of such lines. A novel analytical method, based on sharp analysis inequalities, is used to assess the validity of the finite-time singularity scenario. This method allows one to rule out spurious singularities by evaluating the rate at which the logarithmic decrement of the analyticity-strip method goes to zero. The result is that the finite-time singularity scenario cannot be ruled out, and the singularity time could be somewhere between $t=2.33$ and $t=2.70.$ More robust conclusions will require higher resolution runs and grid-point interpolation measurements of maximum current and vorticity.
Plasmoid solutions of the Hahm--Kulsrud--Taylor equilibrium model
The Hahm-Kulsrud（HK）[T. S. Hahm和R. M. Kulsrud，Phys. Fluids { \bf 28}，2412（1985）]，由共振周期边界扰动驱动的磁剪切等离子体板的解示出了完全屏蔽（电流片）和完全重连（磁岛）响应。在全球范围内，重联涉及解决磁流体动力学（MHD）平衡问题。在具有连续对称性的系统中，这种MHD平衡通常通过求解Grad-Shafranov方程来找到，而在平板几何中，该方程中的椭圆算子是2-D拉普拉斯算子。因此，假设适当的压力和极向电流分布，保角映射方法可以用来将一个解决方案转化为另一个不同的边界条件，给出一个连续的解决方案序列的形式部分重新连接的磁岛（等离子体团）分离的Syrovatsky电流片。这两个HK解决方案似乎是特殊情况。
Princeton University（普林斯顿大学）；University of Maryland, College Park（马里兰大学帕克分校）；National Aeronautics and Space Administration Goddard Space Flight Center（美国国家航空航天局戈达德太空飞行中心）
Investigating prominence turbulence with Hinode SOT Dopplergrams
静止湍流有各种各样的流动，包括瑞利-泰勒不稳定性驱动的上升流和脉冲下降流，因此湍流运动也存在也就不足为奇了。由于磁流体湍流被认为具有平均水平引导场，因此研究它们所承载的任何湍流都可以揭示在广泛的天体物理系统中MHD湍流的性质。本文利用Hinode SOT观测资料构造的H $α$多普勒图，用结构函数分析方法研究了湍流日珥运动的性质。速度增量的pdf显示，当我们看到越来越小的空间间隔时，分布显示出与参考高斯分布的更大偏离，暗示了速度场的不稳定性。水平和垂直分离的偶数阶结构函数的分析表明，存在两个不同的区域，显示不同的幂律指数，在幂律中的突破约2000公里。我们假设这是一个结果的内部湍流激发的日珥的动态流动的系统在这个空间尺度。我们发现这两个区域的p阶结构函数的标度指数一般遵循p/2（小尺度）和p/4（大尺度）定律，这与弱MHD湍流和Kraichnan-Iroshnikov湍流的标度指数分别相同。然而，在比p/2标度更大的尺度上，p/4标度的存在与MHD湍流中预期的非线性增加不一致。从湍流能量耗散估算加热表明，这种湍流加热将是非常低效的，但是通过湍流驱动的重联的质量扩散是$10^{10}$ cm $^2$/s的量级。
