Title: Ideal evolution of MHD turbulence when imposing Taylor-Green symmetries Show Chinese title

Title: 施加Taylor-Green对称性时MHD湍流的理想演化

Abstract: 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. Show Chinese abstract

Abstract: 我们研究了三维空间中的理想不可压缩磁流体力学（MHD）方程，以探索可能的奇异性结构的发展。 该方法包括实现泰勒-格林涡流的四重对称性推广到MHD，这在给定分辨率下可以显著节省计算机时间和内存；我们还使用了一种重网格化方法，在早期时间可以进行较低分辨率的运行，同时不会损失谱精度。 在相当于$6144^3$点的分辨率下检查了一种磁配置，并在$4096^3$点的网格上检查了三种不同的配置。 在最高分辨率下，发现了两种不同的电流和涡度片系统碰撞，导致小尺度发展过程出现两次连续加速。 在最后的时间点，磁场线的汇聚可能正在最大电流位置附近局部导致这些线的强烈弯曲和方向变化。 基于尖锐分析不等式的新型解析方法被用来评估有限时间奇异性情景的有效性。 这种方法允许通过评估解析性条带法的对数减幅趋于零的速度来排除虚假奇异性。 结果表明，不能排除有限时间奇异性情景，奇异时间可能在$t=2.33$和$t=2.70.$之间。更有力的结论需要更高分辨率的运行以及最大电流和涡度的网格点插值测量。