Inverse cascade in simulated MHD turbulence driven by small scale source of magnetic helicity

2016 ◽  
Vol 52 (1) ◽  
pp. 261-268
Author(s):  
R. Stepanov ◽  
◽  
V. Titov ◽  
◽  
Keyword(s):  
Magnetic Helicity ◽  
Small Scale ◽  
Mhd Turbulence ◽  
Inverse Cascade

Strong MHD helical turbulence and the nonlinear dynamo effect

1976 ◽  
Vol 77 (2) ◽  
pp. 321-354 ◽  
Author(s):  
A. Pouquet ◽  
U. Frisch ◽  
J. Léorat
Keyword(s):  
Large Scale ◽  
Magnetic Energy ◽  
Three Dimensional ◽  
Power Laws ◽  
Inertial Range ◽  
Small Scale ◽  
Mhd Turbulence ◽  
Inverse Cascade ◽  
Small Scales ◽  
Dynamo Effect

To understand the turbulent generation of large-scale magnetic fields and to advance beyond purely kinematic approaches to the dynamo effect like that introduced by Steenbeck, Krause & Radler (1966)’ a new nonlinear theory is developed for three-dimensional, homogeneous, isotropic, incompressible MHD turbulence with helicity, i.e. not statistically invariant under plane reflexions. For this, techniques introduced for ordinary turbulence in recent years by Kraichnan (1971 a)’ Orszag (1970, 1976) and others are generalized to MHD; in particular we make use of the eddy-damped quasi-normal Markovian approximation. The resulting closed equations for the evolution of the kinetic and magnetic energy and helicity spectra are studied both theoretically and numerically in situations with high Reynolds number and unit magnetic Prandtl number.Interactions between widely separated scales are much more important than for non-magnetic turbulence. Large-scale magnetic energy brings to equipartition small-scale kinetic and magnetic excitation (energy or helicity) by the ‘Alfvén effect’; the small-scale ‘residual’ helicity, which is the difference between a purely kinetic and a purely magnetic helical term, induces growth of large-scale magnetic energy and helicity by the ‘helicity effect’. In the absence of helicity an inertial range occurs with a cascade of energy to small scales; to lowest order it is a −3/2 power law with equipartition of kinetic and magnetic energy spectra as in Kraichnan (1965) but there are −2 corrections (and possibly higher ones) leading to a slight excess of magnetic energy. When kinetic energy is continuously injected, an initial seed of magnetic field will grow to approximate equipartition, at least in the small scales. If in addition kinetic helicity is injected, an inverse cascade of magnetic helicity is obtained leading to the appearance of magnetic energy and helicity in ever-increasing scales (in fact, limited by the size of the system). This inverse cascade, predicted by Frischet al.(1975), results from a competition between the helicity and Alféh effects and yields an inertial range with approximately — 1 and — 2 power laws for magnetic energy and helicity. When kinetic helicity is injected at the scale linjand the rate$\tilde{\epsilon}^V$(per unit mass), the time of build-up of magnetic energy with scaleL[Gt ] linjis$t \approx L(|\tilde{\epsilon}^V|l^2_{\rm inj})^{-1/3}.$

scholarly journals Helical mode interactions and spectral transfer processes in magnetohydrodynamic turbulence

2016 ◽  
Vol 791 ◽  
pp. 61-96 ◽  
Author(s):  
Moritz Linkmann ◽  
Arjun Berera ◽  
Mairi McKay ◽  
Julia Jäger
Keyword(s):  
Energy Transfer ◽  
Magnetic Fields ◽  
Magnetic Helicity ◽  
Asymmetric Effect ◽  
Mhd Turbulence ◽  
Dynamo Action ◽  
Reverse Transfer ◽  
Transfer Processes ◽  
Inverse Cascade ◽  
Mode Interactions

Spectral transfer processes in homogeneous magnetohydrodynamic (MHD) turbulence are investigated analytically by decomposition of the velocity and magnetic fields in Fourier space into helical modes. Steady solutions of the dynamical system which governs the evolution of the helical modes are determined, and a stability analysis of these solutions is carried out. The interpretation of the analysis is that unstable solutions lead to energy transfer between the interacting modes while stable solutions do not. From this, a dependence of possible interscale energy and helicity transfers on the helicities of the interacting modes is derived. As expected from the inverse cascade of magnetic helicity in 3-D MHD turbulence, mode interactions with like helicities lead to transfer of energy and magnetic helicity to smaller wavenumbers. However, some interactions of modes with unlike helicities also contribute to an inverse energy transfer. As such, an inverse energy cascade for non-helical magnetic fields is shown to be possible. Furthermore, it is found that high values of the cross-helicity may have an asymmetric effect on forward and reverse transfer of energy, where forward transfer is more quenched in regions of high cross-helicity than reverse transfer. This conforms with recent observations of solar wind turbulence. For specific helical interactions the relation to dynamo action is established. The present analysis provides new theoretical insights into physical processes where inverse cascade and dynamo action are involved, such as the evolution of cosmological and astrophysical magnetic fields and laboratory plasmas.

scholarly journals Inverse cascade of hybrid helicity in BΩ -MHD turbulence

2019 ◽  
Vol 4 (7) ◽  
Author(s):  
Mélissa D. Menu ◽  
Sébastien Galtier ◽  
Ludovic Petitdemange
Keyword(s):  
Mhd Turbulence ◽  
Inverse Cascade

Non-Gaussian probability distributions of solar wind fluctuations

1994 ◽  
Vol 12 (12) ◽  
pp. 1127-1138 ◽  
Author(s):  
E. Marsch ◽  
C. Y. Tu
Keyword(s):  
Solar Wind ◽  
Probability Distributions ◽  
Time Lag ◽  
Small Scale ◽  
Time Lags ◽  
Mhd Turbulence ◽  
Theoretical Concepts ◽  
Fluid Turbulence ◽  
Long Time ◽  
Non Gaussian

Abstract. The probability distributions of field differences ∆x(τ)=x(t+τ)-x(t), where the variable x(t) may denote any solar wind scalar field or vector field component at time t, have been calculated from time series of Helios data obtained in 1976 at heliocentric distances near 0.3 AU. It is found that for comparatively long time lag τ, ranging from a few hours to 1 day, the differences are normally distributed according to a Gaussian. For shorter time lags, of less than ten minutes, significant changes in shape are observed. The distributions are often spikier and narrower than the equivalent Gaussian distribution with the same standard deviation, and they are enhanced for large, reduced for intermediate and enhanced for very small values of ∆x. This result is in accordance with fluid observations and numerical simulations. Hence statistical properties are dominated at small scale τ by large fluctuation amplitudes that are sparsely distributed, which is direct evidence for spatial intermittency of the fluctuations. This is in agreement with results from earlier analyses of the structure functions of ∆x. The non-Gaussian features are differently developed for the various types of fluctuations. The relevance of these observations to the interpretation and understanding of the nature of solar wind magnetohydrodynamic (MHD) turbulence is pointed out, and contact is made with existing theoretical concepts of intermittency in fluid turbulence.

scholarly journals MHD turbulence

2019 ◽  
Vol 5 (1) ◽  
Author(s):  
Andrey Beresnyak
Keyword(s):  
Numerical Experiments ◽  
Turbulence Models ◽  
Mhd Equations ◽  
Turbulence Theory ◽  
Current Status ◽  
Small Scale ◽  
Mhd Turbulence ◽  
Wave Modes

AbstractWe review the current status of research in MHD turbulence theory and numerical experiments and their applications to astrophysics and solar science. We introduce general tools for studying turbulence, basic turbulence models, MHD equations and their wave modes. Subsequently, we cover the theories and numerics of Alfvénic turbulence, imbalanced turbulence, small-scale dynamos and models and numerics for supersonic MHD turbulence.

scholarly journals Solar cycle changes in the geo-effectiveness of small-scale solar wind turbulence measured by Wind and ACE at 1 AU

2007 ◽  
Vol 25 (5) ◽  
pp. 1183-1197 ◽  
Author(s):  
M. L. Parkinson ◽  
R. C. Healey ◽  
P. L. Dyson
Keyword(s):  
Solar Wind ◽  
Solar Cycle ◽  
Solar Minimum ◽  
Large Scale ◽  
Small Scale ◽  
Scaling Exponent ◽  
Mhd Turbulence ◽  
Scaling Exponents ◽  
Solar Wind Turbulence ◽  
Wind Turbulence

Abstract. Multi-scale structure of the solar wind in the ecliptic at 1 AU undergoes significant evolution with the phase of the solar cycle. Wind spacecraft measurements during 1995 to 1998 and ACE spacecraft measurements during 1997 to 2005 were used to characterise the evolution of small-scale (~1 min to 2 h) fluctuations in the solar wind speed vsw, magnetic energy density B2, and solar wind ε parameter, in the context of large-scale (~1 day to years) variations. The large-scale variation in ε most resembled large-scale variations in B2. The probability density of large fluctuations in ε and B2 both had strong minima during 1995, a familiar signature of solar minimum. Generalized Structure Function (GSF) analysis was used to estimate inertial range scaling exponents aGSF and their evolution throughout 1995 to 2005. For the entire data set, the weighted average scaling exponent for small-scale fluctuations in vsw was aGSF=0.284±0.001, a value characteristic of intermittent MHD turbulence (>1/4), whereas the scaling exponents for corresponding fluctuations in B2 and ε were aGSF=0.395±0.001 and 0.334±0.001, respectively. These values are between the range expected for Gaussian fluctuations (1/2) and Kolmogorov turbulence (1/3). However, the scaling exponent for ε changed from a Gaussian-Kolmogorov value of 0.373±0.005 during 1997 (end of solar minimum) to an MHD turbulence value of 0.247±0.004 during 2003 (recurrent fast streams). Changes in the characteristics of solar wind turbulence may be reproducible from one solar cycle to the next.

scholarly journals Energetic particle parallel diffusion in a cascading wave turbulence in the foreshock region

2007 ◽  
Vol 14 (5) ◽  
pp. 587-601 ◽  
Author(s):  
F. Otsuka ◽  
Y. Omura ◽  
O. Verkhoglyadova
Keyword(s):  
Solar Wind ◽  
Pitch Angle ◽  
Homogeneous Model ◽  
Bow Shock ◽  
Isotropic Scattering ◽  
Wave Turbulence ◽  
Small Scale ◽  
Dimensional System ◽  
Inverse Cascade ◽  
Background Magnetic Field

Abstract. We study parallel (field-aligned) diffusion of energetic particles in the upstream of the bow shock with test particle simulations. We assume parallel shock geometry of the bow shock, and that MHD wave turbulence convected by the solar wind toward the shock is purely transverse in one-dimensional system with a constant background magnetic field. We use three turbulence models: a homogeneous turbulence, a regular cascade from a large scale to smaller scales, and an inverse cascade from a small scale to larger scales. For the homogeneous model the particle motions along the average field are Brownian motions due to random and isotropic scattering across 90 degree pitch angle. On the other hand, for the two cascade models particle motion is non-Brownian due to coherent and anisotropic pitch angle scattering for finite time scale. The mean free path λ|| calculated by the ensemble average of these particle motions exhibits dependence on the distance from the shock. It also depends on the parameters such as the thermal velocity of the particles, solar wind flow velocity, and a wave turbulence model. For the inverse cascade model, the dependence of λ|| at the shock on the thermal energy is consistent with the hybrid simulation done by Giacalone (2004), but the spatial dependence of λ|| is inconsistent with it.

scholarly journals Inverse Energy Cascade in Advanced MHD Turbulence (the RNG Method)

1993 ◽  
Vol 157 ◽  
pp. 255-261
Author(s):  
N. Kleeorin ◽  
I. Rogachevskii
Keyword(s):  
Magnetic Field ◽  
Large Scale ◽  
Magnetic Field Effect ◽  
Magnetic Reynolds Number ◽  
Energy Cascade ◽  
Small Scale ◽  
Magnetic Fluctuations ◽  
Mhd Turbulence ◽  
Inverse Energy Cascade ◽  
Large Scale Magnetic Field

The nonlinear (in terms of the large-scale magnetic field) effect of the modification of the magnetic force by an advanced small-scale magnetohydrodynamic (MHD) turbulence is considered. The phenomenon is due to the generation of magnetic fluctuations at the expense of hydrodynamic pulsations. It results in a decrease of the elasticity of the large-scale magnetic field.The renormalization group (RNG) method was employed for the investigation of the MHD turbulence at the large magnetic Reynolds number. It was found that the level of the magnetic fluctuations can exceed that obtained from the equipartition assumption due to the inverse energy cascade in advanced MHD turbulence.This effect can excite an instability of the large-scale magnetic field due to the energy transfer from the small-scale turbulent pulsations. This instability is an example of the inverse energy cascade in advanced MHD turbulence. It may act as a mechanism for the large-scale magnetic ropes formation in the solar convective zone and spiral galaxies.

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