scholarly journals Third-moment descriptions of the interplanetary turbulent cascade, intermittency and back transfer

Author(s):  
Jesse T. Coburn ◽  
Miriam A. Forman ◽  
Charles W. Smith ◽  
Bernard J. Vasquez ◽  
Julia E. Stawarz

We review some aspects of solar wind turbulence with an emphasis on the ability of the turbulence to account for the observed heating of the solar wind. Particular attention is paid to the use of structure functions in computing energy cascade rates and their general agreement with the measured thermal proton heating. We then examine the use of 1 h data samples that are comparable in length to the correlation length for the fluctuations to obtain insights into local inertial range dynamics and find evidence for intermittency in the computed energy cascade rates. When the magnetic energy dominates the kinetic energy, there is evidence of anti-correlation in the cascade of energy associated with the outward- and inward-propagating components that we can only partially explain.

2012 ◽  
Vol 703 ◽  
pp. 238-254 ◽  
Author(s):  
Luke A. K. Blackbourn ◽  
Chuong V. Tran

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.


2009 ◽  
Vol 16 (1) ◽  
pp. 99-110 ◽  
Author(s):  
J. J. Podesta ◽  
M. A. Forman ◽  
C. W. Smith ◽  
D. C. Elton ◽  
Y. Malécot ◽  
...  

Abstract. Politano and Pouquet's law, a generalization of Kolmogorov's four-fifths law to incompressible MHD, makes it possible to measure the energy cascade rate in incompressible MHD turbulence by means of third-order moments. In hydrodynamics, accurate measurement of third-order moments requires large amounts of data because the probability distributions of velocity-differences are nearly symmetric and the third-order moments are relatively small. Measurements of the energy cascade rate in solar wind turbulence have recently been performed for the first time, but without careful consideration of the accuracy or statistical uncertainty of the required third-order moments. This paper investigates the statistical convergence of third-order moments as a function of the sample size N. It is shown that the accuracy of the third-moment <(δ v||)3> depends on the number of correlation lengths spanned by the data set and a method of estimating the statistical uncertainty of the third-moment is developed. The technique is illustrated using both wind tunnel data and solar wind data.


2009 ◽  
Vol 27 (8) ◽  
pp. 3019-3025 ◽  
Author(s):  
K. T. Osman ◽  
T. S. Horbury

Abstract. Measurements by the four Cluster spacecraft in the solar wind are used to determine quantitatively the field-aligned anisotropy of magnetohydrodynamic inertial range turbulence power levels and spectral indexes. We find, using time-lagged second order structure functions, that the spectral index is near 2 around the field-parallel direction, which is consistent with a "critical balance" turbulent cascade. Solar wind fluctuations are found to be anisotropic with power mainly in wavevectors perpendicular to the mean field, where the spectral index is around 5/3.


2007 ◽  
Vol 25 (8) ◽  
pp. 1913-1927 ◽  
Author(s):  
R. Bruno ◽  
R. D'Amicis ◽  
B. Bavassano ◽  
V. Carbone ◽  
L. Sorriso-Valvo

Abstract. This study focuses on the role that magnetically dominated fluctuations have within the solar wind MHD turbulence. It is well known that, as the wind expands, magnetic energy starts to dominate over kinetic energy but we lack of a statistical study apt to estimate the relevance of these fluctuations depending on wind speed, radial distance from the sun and heliographic latitude. Our results suggest that this kind of fluctuations can be interpreted as non-propagating structures, advected by the wind during its expansion. In particular, observations performed in the ecliptic revealed a clear radial dependence of these magnetic structures within fast wind, but not within slow wind. At short heliocentric distances (~0.3 AU) the turbulent population is largely dominated by Alfvénic fluctuations characterized by high values of normalized cross-helicity and a remarkable level of energy equipartition. However, as the wind expands, a new-born population, characterized by lower values of Alfvénicity and a clear imbalance in favor of magnetic energy becomes visible and clearly distinguishable from the Alfvénic population largely characterized by an outward sense of propagation. We estimate that more than 20% of all the analyzed intervals of hourly scale within fast wind are characterized by normalized cross-helicity close to zero and magnetic energy largely dominating over kinetic energy. Most of these advected magnetic structures result to be non-compressive and might represent the crossing of the border between adjacent flux tubes forming, as suggested in literature, the advected background structure of the interplanetary magnetic field. On the other hand, their features are also well fitted by the Magnetic Field Directional Turnings paradigm as proposed in literature.


2001 ◽  
Vol 19 (7) ◽  
pp. 681-686 ◽  
Author(s):  
B. P. Pandey ◽  
G. S. Lakhina

Abstract. The energetics of driven magnetic reconnections induced by the deformation of the magnetopause boundary due to the solar wind-magnetosphere interaction are studied. The bursty type reconnection ensues due to the forcing of the magnetopause boundary by the solar wind. For typical plasma parameters in the inner central plasma sheet (ICPS), the magnetic energy release during the reconnection is estimated and it is found that the available free energy is comparable to the observed kinetic energy of typical bursty bulk flows. It implies that the part of the free energy goes into the heating of the ICPS particles, whereas the rest goes into its acceleration. The accelerated particle manifests itself as bursty flows.Key words. Magnetospheric physics (magnetotail; storms and substorms)


2007 ◽  
Vol 112 (A7) ◽  
pp. n/a-n/a ◽  
Author(s):  
Bernard J. Vasquez ◽  
Charles W. Smith ◽  
Kathleen Hamilton ◽  
Benjamin T. MacBride ◽  
Robert J. Leamon

2020 ◽  
Vol 58 (6) ◽  
pp. 478-486
Author(s):  
L. S. Rakhmanova ◽  
M. O. Riazantseva ◽  
G. N. Zastenker ◽  
Yu. I. Yermolaev ◽  
I. G. Lodkina

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