skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Temporal Intermittency of Energy Dissipation in Magnetohydrodynamic Turbulence

; ;
Publication Date:
Sponsoring Org.:
OSTI Identifier:
Grant/Contract Number:
Resource Type:
Journal Article: Publisher's Accepted Manuscript
Journal Name:
Physical Review Letters
Additional Journal Information:
Journal Volume: 114; Journal Issue: 6; Journal ID: ISSN 0031-9007
American Physical Society
Country of Publication:
United States

Citation Formats

Zhdankin, Vladimir, Uzdensky, Dmitri A., and Boldyrev, Stanislav. Temporal Intermittency of Energy Dissipation in Magnetohydrodynamic Turbulence. United States: N. p., 2015. Web. doi:10.1103/PhysRevLett.114.065002.
Zhdankin, Vladimir, Uzdensky, Dmitri A., & Boldyrev, Stanislav. Temporal Intermittency of Energy Dissipation in Magnetohydrodynamic Turbulence. United States. doi:10.1103/PhysRevLett.114.065002.
Zhdankin, Vladimir, Uzdensky, Dmitri A., and Boldyrev, Stanislav. 2015. "Temporal Intermittency of Energy Dissipation in Magnetohydrodynamic Turbulence". United States. doi:10.1103/PhysRevLett.114.065002.
title = {Temporal Intermittency of Energy Dissipation in Magnetohydrodynamic Turbulence},
author = {Zhdankin, Vladimir and Uzdensky, Dmitri A. and Boldyrev, Stanislav},
abstractNote = {},
doi = {10.1103/PhysRevLett.114.065002},
journal = {Physical Review Letters},
number = 6,
volume = 114,
place = {United States},
year = 2015,
month = 2

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record at 10.1103/PhysRevLett.114.065002

Citation Metrics:
Cited by: 9works
Citation information provided by
Web of Science

Save / Share:
  • Direct numerical simulations (DNS) provide a means to test phenomenological models for the scaling properties of intermittent MHD turbulence. The well-known model of She and Leveque, when generalized to MHD, is in good agreement with the DNS in three dimensions, however, it does not coincide with DNS in two dimensions (2D). This is resolved here using the results of recent DNS of driven MHD turbulence in 2D which directly determine the scaling of the rate of dissipation. Specifically, a simple modification to generalized refined similarity is proposed that captures the results of the 2D MHD simulations. This leads to amore » new generalization of She and Leveque in MHD that is coincident with the DNS results in 2D. A key feature of this model is that the most intensely dissipating structures, which are responsible for the intermittency, are thread-like in 2D, independent of whether the underlying phenomenology of the cascade is Kolmogorov or Iroshnikov Kraichnan.« less
  • We investigate the intermittency of energy dissipation in magnetohydrodynamic (MHD) turbulence by identifying dissipative structures and measuring their characteristic scales. We find that the probability distribution of energy dissipation rates exhibits a power-law tail with an index very close to the critical value of –2.0, which indicates that structures of all intensities contribute equally to energy dissipation. We find that energy dissipation is uniformly spread among coherent structures with lengths and widths in the inertial range. At the same time, these structures have thicknesses deep within the dissipative regime. As the Reynolds number is increased, structures become thinner and moremore » numerous, while the energy dissipation continues to occur mainly in large-scale coherent structures. This implies that in the limit of high Reynolds number, energy dissipation occurs in thin, tightly packed current sheets which nevertheless span a continuum of scales up to the system size, exhibiting features of both coherent structures and nanoflares previously conjectured as a coronal heating mechanism.« less
  • Collisionless dissipation in turbulent plasmas such as the solar wind and the solar corona has been an intensively studied subject recently, with new insights often emerging from numerical simulation. Here we report results from high resolution, fully kinetic simulations of plasma turbulence in both two (2D) and three (3D) dimensions, studying the relationship between intermittency and dissipation. The simulations show development of turbulent coherent structures, characterized by sheet-like current density structures spanning a range of scales. An approximate dissipation measure is employed, based on work done by the electromagnetic field in the local electron fluid frame. This surrogate dissipation measuremore » is highly concentrated in small subvolumes in both 2D and 3D simulations. Fully kinetic simulations are also compared with magnetohydrodynamics (MHD) simulations in terms of coherent structures and dissipation. The interesting result emerges that the conditional averages of dissipation measure scale very similarly with normalized current density J in 2D and 3D particle-in-cell and in MHD. To the extent that the surrogate dissipation measure is accurate, this result implies that on average dissipation scales as ∼J{sup 2} in turbulent kinetic plasma. Multifractal intermittency is seen in the inertial range in both 2D and 3D, but at scales ∼ion inertial length, the scaling is closer to monofractal.« less
  • We investigate the intermittency of anisotropic magnetohydrodynamic (MHD) turbulence in high-speed solar wind. Using the data recorded by the Ulysses spacecraft, we apply the Castaing function to model the probability density functions of the fluctuating magnetic field and calculate the magnetic structure functions (SFs) S{sup p} of the order p in the coordinates (r, {Theta}), with r being the length scale and {Theta} the direction of the local mean field. The scaling exponent {zeta}, from S{sup p} (r, {Theta}){proportional_to}r {sup {zeta}(p,{Theta})}, has an anomalous nonlinear dependence on p, implying the intermittent scaling of solar wind turbulence, which has been observedmore » for decades. Furthermore, we study the anisotropy of solar wind turbulence introduced by the strong mean magnetic field. From S{sup p} ({Theta} = 0){proportional_to}S{sup p} ({Theta} = {pi}/2), we obtain r{sub perpendicular{proportional_to}r {sup {alpha}}p||} with {alpha}{sub p} = {zeta}{sub ||}/{zeta}{sub perpendicular} denoting the perpendicular-parallel spatial correlation of the moment of the pth order. For the magnetic field difference {delta}B, we find {alpha}{sub 2} = 1.78 {+-} 0.26, consistent with recent theories and observations. However, when the contribution from the intermittent fluctuations begins to dominate the scaling, {alpha} is not a constant but increases with p, e.g., {alpha}{sub 5} = 1.97 {+-} 0.41 and {alpha}{sub 8} {approx} 2.42 {+-} 0.64. This complication of the perpendicular-parallel spatial correlation due to the intermittency raises new questions for MHD turbulence theory.« less
  • Scale-dependent and geometrical statistics of three-dimensional incompressible homogeneous magnetohydrodynamic turbulence without mean magnetic field are examined by means of the orthogonal wavelet decomposition. The flow is computed by direct numerical simulation with a Fourier spectral method at resolution 512{sup 3} and a unit magnetic Prandtl number. Scale-dependent second and higher order statistics of the velocity and magnetic fields allow to quantify their intermittency in terms of spatial fluctuations of the energy spectra, the flatness, and the probability distribution functions at different scales. Different scale-dependent relative helicities, e.g., kinetic, cross, and magnetic relative helicities, yield geometrical information on alignment between themore » different scale-dependent fields. At each scale, the alignment between the velocity and magnetic field is found to be more pronounced than the other alignments considered here, i.e., the scale-dependent alignment between the velocity and vorticity, the scale-dependent alignment between the magnetic field and its vector potential, and the scale-dependent alignment between the magnetic field and the current density. Finally, statistical scale-dependent analyses of both Eulerian and Lagrangian accelerations and the corresponding time-derivatives of the magnetic field are performed. It is found that the Lagrangian acceleration does not exhibit substantially stronger intermittency compared to the Eulerian acceleration, in contrast to hydrodynamic turbulence where the Lagrangian acceleration shows much stronger intermittency than the Eulerian acceleration. The Eulerian time-derivative of the magnetic field is more intermittent than the Lagrangian time-derivative of the magnetic field.« less