De Giorgio Elisa, Servidio Sergio, Veltri Pierluigi
University of Calabria, Department of Physics, Rende, I-87036, Italy.
Sci Rep. 2017 Oct 23;7(1):13849. doi: 10.1038/s41598-017-13943-7.
Using high resolution 2D magnetohydrodynamic (MHD) simulations we analyze the formation of coherent structures induced by nonlinear interactions in turbulent flows. The properties of these coherent structures, which at the smallest scales are identified through a spatial intermittent behavior, turn out to be guided by the conservation of ideal quadratic (rugged) invariants of the 2D incompressible MHD equations. Different spatial regions can be identified, where the correlations predicted using the variational principles associated to the rugged invariants are locally displayed. These local correlated structures are produced rapidly, as soon as the turbulence is fully developed. It is worth speculating that the small scale structures under our investigation could give rise to singular weak solutions when letting the dissipative coefficients go to zero. In this case their properties could furnish a key to understand which mathematical conditions characterize singularity emergency in weak solutions of the MHD ideal case.
利用高分辨率二维磁流体动力学（MHD）模拟，我们分析了湍流中非线性相互作用所诱导的相干结构的形成。这些相干结构的特性，在最小尺度上通过空间间歇性行为得以识别，结果表明它们受二维不可压缩磁流体动力学方程理想二次（粗糙）不变量守恒的引导。可以识别出不同的空间区域，在这些区域中，使用与粗糙不变量相关的变分原理预测的相关性会局部显现。一旦湍流充分发展，这些局部相关结构就会迅速产生。值得推测的是，当耗散系数趋于零时，我们所研究的小尺度结构可能会产生奇异弱解。在这种情况下，它们的特性可能为理解磁流体动力学理想情况下弱解中奇异性出现的数学条件提供关键线索。
