scholarly journals Exact scaling laws and the local structure of isotropic magnetohydrodynamic turbulence

2007 ◽  
Vol 575 ◽  
pp. 111-120 ◽  
Author(s):  
T. A. YOUSEF ◽  
F. RINCON ◽  
A. A. SCHEKOCHIHIN
Keyword(s):  
Scaling Laws ◽  
Linear Scaling ◽  
Mhd Turbulence ◽  
Third Order ◽  
Magnetohydrodynamic Turbulence ◽  
Kolmogorov Turbulence ◽  
Non Local ◽  
Prandtl Numbers ◽  
The Magnetic Field ◽  
Exact Scaling

This paper examines the consistency of the exact scaling laws for isotropic magnetohydrodynamic (MHD) turbulence in numerical simulations with large magnetic Prandtl numbers Pm and with Pm = 1. The exact laws are used to elucidate the structure of the magnetic and velocity fields. Despite the linear scaling of certain third-order correlation functions, the situation is not analogous to the case of Kolmogorov turbulence. The magnetic field is adequately described by a model of a stripy (folded) field with direction reversals at the resistive scale. At currently available resolutions, the cascade of kinetic energy is short-circuited by the direct exchange of energy between the forcing-scale motions and the stripy magnetic fields. This non-local interaction is the defining feature of isotropic MHD turbulence.

INFRARED PROPERTIES OF AN ANISOTROPICALLY DRIVEN MHD TURBULENCE

1995 ◽  
Vol 09 (26) ◽  
pp. 3401-3419 ◽  
Author(s):  
L. Ts. ADZHEMYAN ◽  
M. HNATICH ◽  
D. HORVÁTH ◽  
M. STEHLIK
Keyword(s):  
Magnetic Field ◽  
Lorentz Force ◽  
Large Scale ◽  
Isotropic Case ◽  
Kinetic Regime ◽  
Mhd Turbulence ◽  
Magnetohydrodynamic Turbulence ◽  
Passive Admixture ◽  
Scale Properties ◽  
The Magnetic Field

The model of anisotropic magnetohydrodynamic turbulence is investigated by the renormalization group approach. It is demonstrated that the inclusion of small anisotropy into the model leads to increasing of the Lorentz force influence. This effect is especially important in the kinetic regime in which the Kolmogorov spectrum of pulsation energy takes place. It is quite different from the isotropic case where the Lorentz force has no influence on large scale properties of magnetohydrodynamic turbulence, even if the external injection of energy is very intensive. Therefore, the magnetic field behaves like a passive admixture. In the anisotropic MHD, nonlinear interactions generate modified "anisotropic Lorentz forces". These forces are relevant for certain values of dimensionless parameter a, which describes the spectrum of the magnetic noise, and the magnetic field ceases to be a passive admixture. In particular, this statement is true for the most realistic value of a = 1 when the random magnetic force amplitude has the same dimensionality as the energy injection rate.

SCALING LAWS IN MAGNETOHYDRODYNAMIC TURBULENCE

2002 ◽  
Vol 11 (08) ◽  
pp. 1183-1188
Author(s):  
QING-ZENG FENG
Keyword(s):  
Solar Wind ◽  
Observational Data ◽  
Scaling Laws ◽  
The Other ◽  
Mhd Turbulence ◽  
Magnetohydrodynamic Turbulence ◽  
New Model

Based on the criticism of existing models of intermittency in magnetohydrodynamic (MHD) turbulence,2,4,5 a new model for the description of intermittency corrections in MHD turbulence is presented and compared with the other models, and is consistent with observational data in the solar wind.

DYNAMIC ALIGNMENT AND EXACT SCALING LAWS IN MAGNETOHYDRODYNAMIC TURBULENCE

2009 ◽  
Vol 699 (1) ◽  
pp. L39-L42 ◽  
Author(s):  
Stanislav Boldyrev ◽  
Joanne Mason ◽  
Fausto Cattaneo
Keyword(s):  
Scaling Laws ◽  
Magnetohydrodynamic Turbulence ◽  
Dynamic Alignment ◽  
Exact Scaling

scholarly journals Scaling laws in Hall inertial-range turbulence

2019 ◽  
Vol 37 (5) ◽  
pp. 825-834 ◽  
Author(s):  
Yasuhito Narita ◽  
Wolfgang Baumjohann ◽  
Rudolf A. Treumann
Keyword(s):  
Magnetic Field ◽  
Electric Field ◽  
Scaling Laws ◽  
Magnetic Energy ◽  
Electric Energy ◽  
Power Spectra ◽  
Inertial Range ◽  
Energy Spectra ◽  
Mhd Turbulence ◽  
The Magnetic Field

Abstract. There is an increasing amount of observational evidence in space plasmas for the breakdown of inertial-range spectra of magnetohydrodynamic (MHD) turbulence on spatial scales smaller than the ion-inertial length. Magnetic energy spectra often exhibit a steepening, which is reminiscent of dissipation of turbulence energy, for example in wave–particle interactions. Electric energy spectra, on the other hand, tend to be flatter than those of MHD turbulence, which is indicative of a dispersive process converting magnetic into electric energy in electromagnetic wave excitation. Here we develop a model of the scaling laws and the power spectra for the Hall inertial range in plasma turbulence. In the present paper we consider a two-dimensional geometry with no wave vector component parallel to the magnetic field as is appropriate in Hall MHD. A phenomenological approach is taken. The Hall electric field attains an electrostatic component when the wave vectors are perpendicular to the mean magnetic field. The power spectra of Hall turbulence are steep for the magnetic field with a slope of -7/3 for compressible magnetic turbulence; they are flatter for the Hall electric field with a slope of -1/3. Our model for the Hall turbulence gives a possible explanation for the steepening of the magnetic energy spectra in the solar wind as an indication of neither the dissipation range nor the dispersive range but as the Hall inertial range. Our model also reproduces the shape of energy spectra in Kelvin–Helmholtz turbulence observed at the Earth's magnetopause.

scholarly journals Perturbative linearization of super-Yang-Mills theories in general gauges

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Hannes Malcha ◽  
Hermann Nicolai
Keyword(s):  
Large Class ◽  
Fourth Order ◽  
Landau Gauge ◽  
Third Order ◽  
Yang Mills ◽  
Free Theory ◽  
Non Linear ◽  
Functional Measure ◽  
Non Local ◽  
Jacobi Determinant

Abstract Supersymmetric Yang-Mills theories can be characterized by a non-local and non-linear transformation of the bosonic fields (Nicolai map) mapping the interacting functional measure to that of a free theory, such that the Jacobi determinant of the transformation equals the product of the fermionic determinants obtained by integrating out the gauginos and ghosts at least on the gauge hypersurface. While this transformation has been known so far only for the Landau gauge and to third order in the Yang-Mills coupling, we here extend the construction to a large class of (possibly non-linear and non-local) gauges, and exhibit the conditions for all statements to remain valid off the gauge hypersurface. Finally, we present explicit results to second order in the axial gauge and to fourth order in the Landau gauge.

scholarly journals Flux expulsion with dynamics

2016 ◽  
Vol 791 ◽  
pp. 568-588 ◽  
Author(s):  
Andrew D. Gilbert ◽  
Joanne Mason ◽  
Steven M. Tobias
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Lorentz Force ◽  
Differential Rotation ◽  
Time Scale ◽  
Scaling Laws ◽  
Dynamical Regime ◽  
Kinematic Evolution ◽  
Flux Expulsion ◽  
The Magnetic Field

In the process of flux expulsion, a magnetic field is expelled from a region of closed streamlines on a $TR_{m}^{1/3}$ time scale, for magnetic Reynolds number $R_{m}\gg 1$ ($T$ being the turnover time of the flow). This classic result applies in the kinematic regime where the flow field is specified independently of the magnetic field. A weak magnetic ‘core’ is left at the centre of a closed region of streamlines, and this decays exponentially on the $TR_{m}^{1/2}$ time scale. The present paper extends these results to the dynamical regime, where there is competition between the process of flux expulsion and the Lorentz force, which suppresses the differential rotation. This competition is studied using a quasi-linear model in which the flow is constrained to be axisymmetric. The magnetic Prandtl number $R_{m}/R_{e}$ is taken to be small, with $R_{m}$ large, and a range of initial field strengths $b_{0}$ is considered. Two scaling laws are proposed and confirmed numerically. For initial magnetic fields below the threshold $b_{core}=O(UR_{m}^{-1/3})$, flux expulsion operates despite the Lorentz force, cutting through field lines to result in the formation of a central core of magnetic field. Here $U$ is a velocity scale of the flow and magnetic fields are measured in Alfvén units. For larger initial fields the Lorentz force is dominant and the flow creates Alfvén waves that propagate away. The second threshold is $b_{dynam}=O(UR_{m}^{-3/4})$, below which the field follows the kinematic evolution and decays rapidly. Between these two thresholds the magnetic field is strong enough to suppress differential rotation, leaving a magnetically controlled core spinning in solid body motion, which then decays slowly on a time scale of order $TR_{m}$.

scholarly journals Cancellation exponents and multifractal scaling laws in the solar wind magnetohydrodynamic turbulence

1996 ◽  
Vol 14 (8) ◽  
pp. 777-785 ◽  
Author(s):  
V. Carbone ◽  
R. Bruno
Keyword(s):  
Solar Wind ◽  
Velocity Field ◽  
Scaling Laws ◽  
Interplanetary Medium ◽  
Low Frequency ◽  
Scaling Exponent ◽  
Magnetohydrodynamic Turbulence ◽  
Low Speed ◽  
Multifractal Scaling

Abstract. Some signed measures in turbulence are found to be sign-singular, that is their sign reverses continuously on arbitrary finer scales with a reduction of the cancellation between positive and negative contributions. The strength of the singularity is characterized by a scaling exponent κ, the cancellation exponent. In the present study by using some turbulent samples of the velocity field obtained from spacecraft measurements in the interplanetary medium, we show that sign-singularity is present everywhere in low-frequency turbulent samples. The cancellation exponent can be related to the characteristic scaling laws of turbulence. Differences in the values of κ, calculated in both high- and low-speed streams, allow us to outline some physical differences in the samples with different velocities.

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