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Energy dissipation is highly intermittent in turbulent plasmas, being localized in coherent structures such as current sheets. The statistical analysis of spatial dissipative structures is an effective approach to studying turbulence. In this paper, we generalize this methodology to investigate four-dimensional spatiotemporal structures, i.e., dissipative processes representing sets of interacting coherent structures, which correspond to flares in astrophysical systems. We develop methods for identifying and characterizing these processes, and then perform a statistical analysis of dissipative processes in numerical simulations of driven magnetohydrodynamic turbulence. We find that processes are often highly complex, long-lived, and weakly asymmetric in time. They exhibit robust power-law probability distributions and scaling relations, including a distribution of dissipated energy with power-law index near -1.75, indicating that intense dissipative events dominate the overall energy dissipation. We compare our results with the previously observed statistical properties of solar flares.
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Energy dissipation in magnetohydrodynamic (MHD) turbulence is known to be highly intermittent in space, being concentrated in sheet-like coherent structures. Much less is known about intermittency in time, another fundamental aspect of turbulence which has great importance for observations of solar flares and other space/astrophysical phenomena. In this Letter, we investigate the temporal intermittency of energy dissipation in numerical simulations of MHD turbulence. We consider four-dimensional spatiotemporal structures, flare events, responsible for a large fraction of the energy dissipation. We find that although the flare events are often highly complex, they exhibit robust power-law distributions and scaling relations. We find that the probability distribution of dissipated energy has a power law index close to -1.75, similar to observations of solar flares, indicating that intense dissipative events dominate the heating of the system. We also discuss the temporal asymmetry of flare events as a signature of the turbulent cascade.
We study the spatio-temporal behavior of the Elsasser variables describing magnetic and velocity field fluctuations, using direct numerical simulations of three-dimensional magnetohydrodynamic turbulence. We consider cases with relatively small, intermediate, and large values of a mean background magnetic field, and with null, small, and high cross-helicity (correlations between the velocity and the magnetic field). Wavenumber-dependent time correlation functions are computed for the different simulations. From these correlation functions, the decorrelation time is computed and compared with different theoretical characteristic times: the local non-linear time, the random-sweeping time, and the Alfvenic time. It is found that decorrelation times are dominated by sweeping effects for low values of the mean magnetic field and for low values of the cross-helicity, while for large values of the background field or of the cross-helicity and for wave vectors sufficiently aligned with the guide field, decorrelation times are controlled by Alfvenic effects. Finally, we observe counter-propagation of Alfvenic fluctuations due to reflections produced by inhomogeneities in the total magnetic field. This effect becomes more prominent in flows with large cross-helicity, strongly modifying the propagation of waves in turbulent magnetohydrodynamic flows.
Observations of solar wind turbulence indicate the existence of multi-scale pressure-balanced structures (PBSs) in the solar wind. In this work, we conduct a numerical simulation to investigate multi-scale PBSs and in particular their formation in compressive MHD turbulence. By the use of a higher order Godunov code Athena,a driven compressible turbulence with an imposed uniform guide field is simulated. The simulation results show that both the magnetic pressure and the thermal pressure exhibit a turbulent spectrum with a Kolmogorov-like power law, and that in many regions of the simulation domain they are anti-correlated. The computed wavelet cross-coherence spectrum of the magnetic pressure and the thermal pressure, as well as their space series, indicate the existence of multi-scale PBSs, with the small PBSs being embedded in the large ones. These multi-scale PBSs are likely to be related with the highly oblique-propagating slow-mode waves, as the traced multi-scale PBS is found to be traveling in a certain direction at a speed consistent with that predicted theoretically for a slow-mode wave propagating in the same direction.
We develop a framework for studying the statistical properties of current sheets in numerical simulations of 3D magnetohydrodynamic (MHD) turbulence. We describe an algorithm that identifies current sheets in a simulation snapshot and then determines their geometrical properties (including length, width, and thickness) and intensities (peak current density and total energy dissipation rate). We then apply this procedure to simulations of reduced MHD turbulence and perform a statistical analysis on the obtained population of current sheets. We evaluate the role of reconnection by separately studying the populations of current sheets which contain magnetic X-points and those which do not. We find that the statistical properties of the two populations are different in general. We compare the scaling of these properties to phenomenological predictions obtained for the inertial range of MHD turbulence. Finally, we test whether the reconnecting current sheets are consistent with the Sweet-Parker model.
This article reviews recent studies of scale interactions in magnetohydrodynamic turbulence. The present day increase of computing power, which allows for the exploration of different configurations of turbulence in conducting flows, and the development of shell-to-shell transfer functions, has led to detailed studies of interactions between the velocity and the magnetic field and between scales. In particular, processes such as induction and dynamo action, the damping of velocity fluctuations by the Lorentz force, or the development of anisotropies, can be characterized at different scales. In this context we consider three different configurations often studied in the literature: mechanically forced turbulence, freely decaying turbulence, and turbulence in the presence of a uniform magnetic field. Each configuration is of interest for different geophysical and astrophysical applications. Local and non-local transfers are discussed for each case. While the transfer between scales of solely kinetic or solely magnetic energy is local, transfers between kinetic and magnetic fields are observed to be local or non-local depending on the configuration. Scale interactions in the cascade of magnetic helicity are also reviewed. Based on the results, the validity of several usual assumptions in hydrodynamic turbulence, such as isotropy of the small scales or universality, is discussed.
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