The scaling properties of two-dimensional compressible magnetohydrodynamic turbulence

2006 ◽  
Vol 13 (1) ◽  
pp. 012305 ◽  
Author(s):  
J. A. Merrifield ◽  
T. D. Arber ◽  
S. C. Chapman ◽  
R. O. Dendy
Keyword(s):  
Two Dimensional ◽  
Magnetohydrodynamic Turbulence ◽  
Scaling Properties

Scaling properties and intermittency of two-dimensional turbulence in pure electron plasmas

2013 ◽  
Vol 87 (6) ◽  
Author(s):  
F. Lepreti ◽  
M. Romé ◽  
G. Maero ◽  
B. Paroli ◽  
R. Pozzoli ◽  
...  
Keyword(s):  
Two Dimensional ◽  
Scaling Properties ◽  
Electron Plasmas

scholarly journals On energetics and inertial-range scaling laws of two-dimensional magnetohydrodynamic turbulence

2012 ◽  
Vol 703 ◽  
pp. 238-254 ◽  
Author(s):  
Luke A. K. Blackbourn ◽  
Chuong V. Tran
Keyword(s):  
Energy Transfer ◽  
Kinetic Energy ◽  
Energy Flux ◽  
Scaling Laws ◽  
Magnetic Energy ◽  
Inertial Range ◽  
Two Dimensional ◽  
Magnetohydrodynamic Turbulence ◽  
Direct Energy ◽  
Energy Equipartition

AbstractWe study two-dimensional magnetohydrodynamic turbulence, with an emphasis on its energetics and inertial-range scaling laws. A detailed spectral analysis shows that dynamo triads (those converting kinetic into magnetic energy) are associated with a direct magnetic energy flux while anti-dynamo triads (those converting magnetic into kinetic energy) are associated with an inverse magnetic energy flux. As both dynamo and anti-dynamo interacting triads are integral parts of the direct energy transfer, the anti-dynamo inverse flux partially neutralizes the dynamo direct flux, arguably resulting in relatively weak direct energy transfer and giving rise to dynamo saturation. This result is consistent with a qualitative prediction of energy transfer reduction due to Alfvén wave effects by the Iroshnikov–Kraichnan theory (which was originally formulated for magnetohydrodynamic turbulence in three dimensions). We numerically confirm the correlation between dynamo action and direct magnetic energy flux and investigate the applicability of quantitative aspects of the Iroshnikov–Kraichnan theory to the present case, particularly its predictions of energy equipartition and ${k}^{\ensuremath{-} 3/ 2} $ spectra in the energy inertial range. It is found that for turbulence satisfying the Kraichnan condition of magnetic energy at large scales exceeding total energy in the inertial range, the kinetic energy spectrum, which is significantly shallower than ${k}^{\ensuremath{-} 3/ 2} $, is shallower than its magnetic counterpart. This result suggests no energy equipartition. The total energy spectrum appears to depend on the energy composition of the turbulence but is clearly shallower than ${k}^{\ensuremath{-} 3/ 2} $ for $r\approx 2$, even at moderate resolutions. Here $r\approx 2$ is the magnetic-to-kinetic energy ratio during the stage when the turbulence can be considered fully developed. The implication of the present findings is discussed in conjunction with further numerical results on the dependence of the energy dissipation rate on resolution.

Algebraic probability density tails in decaying isotropic two-dimensional turbulence

1996 ◽  
Vol 313 ◽  
pp. 223-240 ◽  
Author(s):  
Javier Jiménez
Keyword(s):  
Isotropic Turbulence ◽  
Cauchy Distribution ◽  
Two Dimensional ◽  
Scaling Properties ◽  
Velocity Gradients ◽  
Random Arrangement ◽  
Coherent Vortices ◽  
Statistical Argument ◽  
Decaying Turbulence ◽  
The One

The p.d.f. of the velocity gradients in two-dimensional decaying isotropic turbulence is shown to approach a Cauchy distribution, with algebraic s−2 tails, as the flow becomes dominated by a large number of compact coherent vortices. The statistical argument is independent of the vortex structure, and depends only on general scaling properties. The same argument predicts a Gaussian p.d.f. for the velocity components. The convergence to these limits as a function of the number of vortices is analysed. It is found to be fast in the former case, but slow (logarithmic) in the latter, resulting in residual u−3 tails in all practical cases. The influence of a spread Gaussian vorticity distribution in the cores is estimated, and the relevant dimensionless parameter is identified as the area fraction covered by the cores. A comparison is made with the result of numerical simulations of two-dimensional decaying turbulence. The agreement of the p.d.f.s is excellent in the case of the gradients, and adequate in the case of the velocities. In the latter case the ratio between energy and enstrophy is computed, and agrees with the simulations. All the one-point statistics considered in this paper are consistent with a random arrangement of the vortex cores, with no evidence of energy screening.

On two-dimensional magnetohydrodynamic turbulence

2001 ◽  
Vol 8 (7) ◽  
pp. 3282-3292 ◽  
Author(s):  
D. Biskamp ◽  
E. Schwarz
Keyword(s):  
Two Dimensional ◽  
Magnetohydrodynamic Turbulence

scholarly journals Magnetic dynamo action in two-dimensional turbulent magneto-hydrodynamics

1977 ◽  
Vol 17 (2) ◽  
pp. 317-335 ◽  
Author(s):  
David Fyfe ◽  
Glenn Joyce ◽  
David Montgomery
Keyword(s):  
Initial Conditions ◽  
Magnetic Energy ◽  
Field Energy ◽  
Magnetic Excitation ◽  
External Forcing ◽  
Two Dimensional ◽  
Dynamo Action ◽  
Magnetohydrodynamic Turbulence ◽  
Long Wavelength ◽  
Magnetic Field Energy

Two-dimensional magnetohydrodynamic turbulence is explored by means of numerical simulation. Previous analytical theory, based on non-dissipative constants of the motion in a truncated Fourier representation, is verified by following the evolution of highly non-equilibrium initial conditions numerically. Dynamo action (conversion of a significant fraction of turbulent kinetic energy into long-wavelength magnetic field energy) is observed. It is conjectured that in the presence of dissipation and external forcing; a dual cascade will be observed for zero-helicity situations. Energy will cascade to higher wavenumbers simultaneously with a cascade of mean square vector potential to lower wavenumbers, leading to an omni-directional magnetic energy spectrum which varies as k-⅓ at lower wavenumbers, simultaneously with a build-up of magnetic excitation at the lowest wavenumber of the system. Equipartition of kinetic and magnetic energies is expected at the highest wavenumbers in the system.

scholarly journals The scaling properties of dissipation in incompressible isotropic three-dimensional magnetohydrodynamic turbulence

2005 ◽  
Vol 12 (2) ◽  
pp. 022301 ◽  
Author(s):  
J. A. Merrifield ◽  
W.-C. Müller ◽  
S. C. Chapman ◽  
R. O. Dendy
Keyword(s):  
Three Dimensional ◽  
Magnetohydrodynamic Turbulence ◽  
Scaling Properties

Inverse cascade of kinetic energy in two-dimensional β-Plane magnetohydrodynamic turbulence

2020 ◽  
Author(s):  
Timofey Zinyakov ◽  
Arakel Petrosyan
Keyword(s):  
Numerical Simulation ◽  
Kinetic Energy ◽  
Cascade Process ◽  
Two Dimensional ◽  
Mhd Turbulence ◽  
Self Similarity ◽  
Magnetohydrodynamic Turbulence ◽  
Zonal Flows ◽  
Inverse Cascade ◽  
Kolmogorov Spectrum

<p>Numerical studies of two-dimensional β-plane homogeneous magnetohydrodynamic turbulence are presented. The study of the fundamental properties of such turbulence allows understanding the evolution of various astrophysical objects from the Sun and stars to planetary systems, galaxies, and galaxy clusters. Energy spectra and cascade process in two-dimensional β-plane MHD are studied.</p><p>In this work the equations of two-dimensional magnetohydrodynamics with the Coriolis force in the β-plane approximation are used for the qualitative analysis and numerical simulation of processes in plasma astrophysics. The equations are solved on a square box of edge size 2π with periodic boundary conditions applying a the pseudospectral method using the 2/3 rule for dealiasing. The results of numerical simulation of two-dimensional β-plane MHD turbulence with a spatial resolution of 1024 × 1024 and 4096 × 4096 with different Rossby parameters β and different Reynolds numbers are presented.</p><p>It is found that only unsteady zonal flows with complex temporal dynamics are formed in two-dimensional β-plane magnetohydrodynamic turbulence. It is shown that flow nonstationarity is due to the appearance of isotropic magnetic islands caused by the Lorentz force in the system. The formation of Iroshnikov–Kraichnan spectrum is shown in the early stages of evolution of two-dimensional β-plane magnetohydrodynamic turbulence. The self-similarity of the decay of Iroshnikov–Kraichnan spectrum is studied. On long time scale violation of self-similarity of the decay and formation of Kolmogorov spectrum is discovered. The inverse cascade of kinetic energy, which is characteristic of the detected Kolmogorov spectrum, provides the formation of zonal flows.</p><p>This work was supported by the Russian Foundation for Basic Research (project no. 19-02-00016).</p>

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