论文标题
部分可观测时空混沌系统的无模型预测
Scaling of the Hosking integral in decaying magnetically-dominated turbulence
论文作者
论文摘要
Saffman Helicity的Hosking and Schekochihin（2021，PRX 11，041005）（我们在这里称为Hosking Integral）已成为重要数量，它可能控制着磁性主导的非螺旋湍流的衰减特性。使用一系列不同的计算方法，我们确认该数量确实是衡量不变的，并且在大型Lundquist数字的极限中几乎完美保存。对于具有普通粘度和磁扩散率算子的直接数值模拟，我们发现该解决方案以几乎相似的方式发展。在量化磁能和积分尺度的瞬时衰减系数的图中，我们发现溶液沿线演变为确实暗示了Hosking积分的控制作用。该解决方案在该图中的一条线附近沉降，这是磁能谱的自相似演化所期望的。当磁扩散率随时间降低时，该溶液将在略有不同的位置沉降，这与由重新连接时间尺度而不是AlfVén时间兼容的衰减兼容。
The Saffman helicity invariant of Hosking and Schekochihin (2021, PRX 11, 041005), which we here call the Hosking integral, has emerged as an important quantity that may govern the decay properties of magnetically dominated nonhelical turbulence. Using a range of different computational methods, we confirm that this quantity is indeed gauge-invariant and nearly perfectly conserved in the limit of large Lundquist numbers. For direct numerical simulations with ordinary viscosity and magnetic diffusivity operators, we find that the solution develops in a nearly self-similar fashion. In a diagram quantifying the instantaneous decay coefficients of magnetic energy and integral scale, we find that the solution evolves along a line that is indeed suggestive of the governing role of the Hosking integral. The solution settles near a line in this diagram that is expected for a self-similar evolution of the magnetic energy spectrum. The solution will settle in a slightly different position when the magnetic diffusivity decreases with time, which would be compatible with the decay being governed by the reconnection time scale rather than the Alfvén time.
