Structures in magnetohydrodynamic turbulence: Detection and scaling

Abstract

We present a systematic analysis of statistical properties of turbulent current and vorticity structures at a given time using cluster analysis. The data stem from numerical simulations of decaying three-dimensional 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 1536³ points and with Taylor Reynolds numbers up to 1100. The initial conditions are either an X -point configuration embedded in three dimensions, 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 8000) 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 magnetohydrodynamics. 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.

Reconnection-driven Magnetohydrodynamic Turbulence in a Simulated Coronal-hole Jet

“…Biskamp 2003). These and other observational hallmarks of the reconnection process have been identified in extreme ultraviolet (EUV) images of the corona from Solar and Heliospheric Observatory and Solar Terrestrial Relations Observatory spacecraft (Uritsky et al 2007(Uritsky et al , 2013, flyby time-series data from MErcury Surface, Space ENvironment, GEochemistry, and Ranging probe (Uritsky et al 2011), and numerical data from high-resolution 3D simulations of prescribed, vorticity-laden MHD flows (Uritsky et al 2010b). …”

“…The log-log slopes of the SFs estimated in this range serve as empirical proxies for the theoretical exponents ζ p describing the higher-order scaling of transverse v θϕ and B θϕ perturbations, as discussed in §2. The slope of the second-order SF has special significance as it yields the exponent ζ 2 directly related to the slope α = ζ 2 + 1 of the Fourier power spectrum of the fluctuations (see, e.g., Uritsky et al 2011).…”

Stochastic Coupling of Solar Photosphere and Corona

“…Instead, we start with detecting temporal traces of features in individual solar locations, and then verify their spatial adjacency. This algorithmic solution is fast and memory-efficient; see Uritsky et al (2010b) for its complete description and numerical validation. Both MDI and EUVI data sets are characterized by broad distributions of pixel values (Figure 3), encompassing more than three orders of magnitude for the magnetic field and about two orders of magnitude for the EUVI flux.…”

The Dynamical Generation of Current Sheets in Astrophysical Plasma Turbulence

“…Recent work investigating the statistics of these coherent structures, self-consistently generated by the plasma turbulence, has demonstrated that the dissipation of turbulent energy is largely concentrated in these current sheets (Uritsky et al 2010;Osman et al 2011;Zhdankin et al 2013). Since current sheets are associated with enhanced dissipation, illuminating their origin and nature is critical to identifying the dominant physical mechanisms of dissipation in plasma turbulence.…”