We present a systematic analysis of statistical properties of turbulent
current and vorticity structures at a given time using cluster analysis. The
data stems from numerical simulations of decaying three-dimensional (3D)
magnetohydrodynamic turbulence in the absence of an imposed uniform magnetic
field; the magnetic Prandtl number is taken equal to unity, and we use a
periodic box with grids of up to 1536^3 points, and with Taylor Reynolds
numbers up to 1100. The initial conditions are either an X-point configuration
embedded in 3D, the so-called Orszag-Tang vortex, or an
Arn'old-Beltrami-Childress configuration with a fully helical velocity and
magnetic field. In each case two snapshots are analyzed, separated by one
turn-over time, starting just after the peak of dissipation. We show that the
algorithm is able to select a large number of structures (in excess of 8,000)
for each snapshot and that the statistical properties of these clusters are
remarkably similar for the two snapshots as well as for the two flows under
study in terms of scaling laws for the cluster characteristics, with the
structures in the vorticity and in the current behaving in the same way. We
also study the effect of Reynolds number on cluster statistics, and we finally
analyze the properties of these clusters in terms of their velocity-magnetic
field correlation. Self-organized criticality features have been identified in
the dissipative range of scales. A different scaling arises in the inertial
range, which cannot be identified for the moment with a known self-organized
criticality class consistent with MHD. We suggest that this range can be
governed by turbulence dynamics as opposed to criticality, and propose an
interpretation of intermittency in terms of propagation of local instabilities.

本研究通过簇分析系统地分析了湍流电流和涡流结构的统计特性，同时研究了雷诺数对簇统计的影响以及如何解释间歇性，并发现自组织临界性特征在可耗散尺度范围内。