scholarly journals Multi-spacecraft measurement of anisotropic power levels and scaling in solar wind turbulence

2009 ◽  
Vol 27 (8) ◽  
pp. 3019-3025 ◽  
Author(s):  
K. T. Osman ◽  
T. S. Horbury
Keyword(s):  
Solar Wind ◽  
Spectral Index ◽  
Mean Field ◽  
Structure Functions ◽  
Inertial Range ◽  
Order Structure ◽  
Parallel Direction ◽  
The Mean ◽  
Time Lagged ◽  
Turbulent Cascade

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.

scholarly journals Observation of an inertial-range energy cascade within a reconnection jet in the Earth’s magnetotail

2020 ◽  
Vol 500 (1) ◽  
pp. L6-L10
Author(s):  
Riddhi Bandyopadhyay ◽  
Alexandros Chasapis ◽  
D J Gershman ◽  
B L Giles ◽  
C T Russell ◽  
...  
Keyword(s):  
Broad Band ◽  
Structure Functions ◽  
Inertial Range ◽  
Order Structure ◽  
Linear Scaling ◽  
Tail Region ◽  
Scale Invariant ◽  
Third Order ◽  
Velocity Spectra ◽  
Turbulent Cascade

ABSTRACT The Earth’s magnetotail region provides a unique environment for the study of plasma turbulence. We investigate the turbulence developed in an exhaust produced by magnetic reconnection in the terrestrial magnetotail region. Magnetic and velocity spectra show broad-band fluctuations corresponding to the inertial range, with Kolmorogov scaling of −5/3, indicative of a well-developed turbulent cascade. We examine the mixed, third-order structure functions, and obtain a linear scaling in the inertial range. This linear scaling of the third-order structure functions implies a scale-invariant cascade of energy through the inertial range. A Politano–Pouquet third-order analysis gives an estimate of the incompressive energy transfer rate of ${\sim}10^{7}~\mathrm{J\, kg^{-1}\, s^{-1}}$. This is four orders of magnitude higher than the values typically measured in the 1-au solar wind, suggesting that the turbulence cascade plays an important role as a pathway of energy dissipation during reconnection events in the tail region.

scholarly journals Structure function measurements of the intermittent MHD turbulent cascade

1997 ◽  
Vol 4 (3) ◽  
pp. 185-199 ◽  
Author(s):  
T. S. Horbury ◽  
A. Balogh
Keyword(s):  
Energy Transfer ◽  
High Speed ◽  
Solar Wind Plasma ◽  
Turbulent Energy ◽  
Structure Functions ◽  
Order Structure ◽  
Data Sets ◽  
Magnetic Field Data ◽  
Spacecraft Data ◽  
Turbulent Cascade

Abstract. The intertmittent nature of turbulence within solar wind plasma has been demonstrated by several studies of spacecraft data. Using magnetic field data taken in high speed flows at high heliographic latitudes by the Ulysses probe, the character of fluctuations within the inertia] range is discussed. Structure functions are used extensively. A simple consideration of errors associated with calculations of high moment structure functions is shown to be useful as a practical estimate of the reliability of such calculations. For data sets of around 300 000 points, structure functions of moments above 5 are rarely reliable on the basis of this test, highlighting the importance of considering uncertainties in such calculations. When unreliable results are excluded, it is shown that inertial range polar fluctuations are well described by a multifractal model of turbulent energy transfer. Detailed consideration of the scaling of high order structure functions suggests energy transfer consistent with a "Kolmogorov" cascade.

scholarly journals Anisotropy in solar wind plasma turbulence

2015 ◽  
Vol 373 (2041) ◽  
pp. 20140152 ◽  
Author(s):  
S. Oughton ◽  
W. H. Matthaeus ◽  
M. Wan ◽  
K. T. Osman
Keyword(s):  
Solar Wind ◽  
Initial Conditions ◽  
Energy Levels ◽  
Mean Field ◽  
Solar Wind Plasma ◽  
Inertial Range ◽  
Field Energy ◽  
Range Theory ◽  
Fluctuation Energy ◽  
Dissipation Range

A review of spectral anisotropy and variance anisotropy for solar wind fluctuations is given, with the discussion covering inertial range and dissipation range scales. For the inertial range, theory, simulations and observations are more or less in accord, in that fluctuation energy is found to be primarily in modes with quasi-perpendicular wavevectors (relative to a suitably defined mean magnetic field), and also that most of the fluctuation energy is in the vector components transverse to the mean field. Energy transfer in the parallel direction and the energy levels in the parallel components are both relatively weak. In the dissipation range, observations indicate that variance anisotropy tends to decrease towards isotropic levels as the electron gyroradius is approached; spectral anisotropy results are mixed. Evidence for and against wave interpretations and turbulence interpretations of these features will be discussed. We also present new simulation results concerning evolution of variance anisotropy for different classes of initial conditions, each with typical background solar wind parameters.

scholarly journals Statistical Analysis of Magnetic Field Fluctuations in Coronal Mass Ejection-Driven Sheath Regions

2021 ◽  
Vol 7 ◽  
Author(s):  
E. K. J. Kilpua ◽  
S. W. Good ◽  
M. Ala-Lahti ◽  
A. Osmane ◽  
D. Fontaine ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Solar Wind ◽  
Statistical Analysis ◽  
Coronal Mass Ejection ◽  
Inertial Range ◽  
Spectral Indices ◽  
Shock Region ◽  
Field Fluctuations ◽  
The Mean ◽  
Mass Ejection

We report a statistical analysis of magnetic field fluctuations in 79 coronal mass ejection- (CME-) driven sheath regions that were observed in the near-Earth solar wind. Wind high-resolution magnetic field data were used to investigate 2 h regions adjacent to the shock and ejecta leading edge (Near-Shock and Near-LE regions, respectively), and the results were compared with a 2 h region upstream of the shock. The inertial-range spectral indices in the sheaths are found to be mostly steeper than the Kolmogorov −5/3 index and steeper than in the solar wind ahead. We did not find indications of an f−1 spectrum, implying that magnetic fluctuation properties in CME sheaths differ significantly from planetary magnetosheaths and that CME-driven shocks do not reset the solar wind turbulence, as appears to happen downstream of planetary bow shocks. However, our study suggests that new compressible fluctuations are generated in the sheath for a wide variety of shock/upstream conditions. Fluctuation properties particularly differed between the Near-Shock region and the solar wind ahead. A strong positive correlation in the mean magnetic compressibility was found between the upstream and downstream regions, but the compressibility values in the sheaths were similar to those in the slow solar wind (<0.2), regardless of the value in the preceding wind. However, we did not find clear correlations between the inertial-range spectral indices in the sheaths and shock/preceding solar wind properties, nor with the mean normalized fluctuation amplitudes. Correlations were also considerably lower in the Near-LE region than in the Near-Shock region. Intermittency was also considerably higher in the sheath than in the upstream wind according to several proxies, particularly so in the Near-Shock region. Fluctuations in the sheath exhibit larger rotations than upstream, implying the presence of strong current sheets in the sheath that can add to intermittency.

scholarly journals Shallow water wave turbulence

2019 ◽  
Vol 874 ◽  
pp. 1169-1196 ◽  
Author(s):  
Pierre Augier ◽  
Ashwin Vishnu Mohanan ◽  
Erik Lindborg
Keyword(s):  
Reynolds Number ◽  
Structure Function ◽  
Shallow Water ◽  
Water Wave ◽  
Structure Functions ◽  
Wave Turbulence ◽  
Order Structure ◽  
Third Order ◽  
Shallow Water Wave ◽  
The Mean

The dynamics of irrotational shallow water wave turbulence forced at large scales and dissipated at small scales is investigated. First, we derive the shallow water analogue of the ‘four-fifths law’ of Kolmogorov turbulence for a third-order structure function involving velocity and displacement increments. Using this relation and assuming that the flow is dominated by shocks, we develop a simple model predicting that the shock amplitude scales as $(\unicode[STIX]{x1D716}d)^{1/3}$, where $\unicode[STIX]{x1D716}$ is the mean dissipation rate and $d$ the mean distance between the shocks, and that the $p$th-order displacement and velocity structure functions scale as $(\unicode[STIX]{x1D716}d)^{p/3}r/d$, where $r$ is the separation. Then we carry out a series of forced simulations with resolutions up to $7680^{2}$, varying the Froude number, $F_{f}=(\unicode[STIX]{x1D716}L_{f})^{1/3}/c$, where $L_{f}$ is the forcing length scale and $c$ is the wave speed. In all simulations a stationary state is reached in which there is a constant spectral energy flux and equipartition between kinetic and potential energy in the constant flux range. The third-order structure function relation is satisfied with a high degree of accuracy. Mean energy is found to scale approximately as $E\sim \sqrt{\unicode[STIX]{x1D716}L_{f}c}$, and is also dependent on resolution, indicating that shallow water wave turbulence does not fit into the paradigm of a Richardson–Kolmogorov cascade. In all simulations shocks develop, displayed as long thin bands of negative divergence in flow visualisations. The mean distance between the shocks is found to scale as $d\sim F_{f}^{1/2}L_{f}$. Structure functions of second and higher order are found to scale in good agreement with the model. We conclude that in the weak limit, $F_{f}\rightarrow 0$, shocks will become denser and weaker and finally disappear for a finite Reynolds number. On the other hand, for a given $F_{f}$, no matter how small, shocks will prevail if the Reynolds number is sufficiently large.

Applicability of Kolmogorov's and Monin's equations of turbulence

1997 ◽  
Vol 353 ◽  
pp. 67-81 ◽  
Author(s):  
REGINALD J. HILL
Keyword(s):  
Structure Function ◽  
Structure Functions ◽  
Inertial Range ◽  
Homogeneous Turbulence ◽  
Order Structure ◽  
Third Order ◽  
Local Isotropy ◽  
The Third ◽  
Moderate Reynolds Number ◽  
Wide Range

The equation relating second- and third-order velocity structure functions was presented by Kolmogorov; Monin attempted to derive that equation on the basis of local isotropy. Recently, concerns have been raised to the effect that Kolmogorov's equation and an ancillary incompressibility condition governing the third-order structure function were proven only on the restrictive basis of isotropy and that the statistic involving pressure that appears in the derivation of Kolmogorov's equation might not vanish on the basis of local isotropy. These concerns are resolved. In so doing, results are obtained for the second- and third-order statistics on the basis of local homogeneity without use of local isotropy. These results are applicable to future studies of the approach toward local isotropy. Accuracy of Kolmogorov's equation is shown to be more sensitive to anisotropy of the third-order structure function than to anisotropy of the second-order structure function. Kolmogorov's 4/5 law for the inertial range of the third-order structure function is obtained without use of the incompressibility conditions on the second- and third-order structure functions. A generalization of Kolmogorov's 4/5 law, which applies to the inertial range of locally homogeneous turbulence at very large Reynolds numbers, is shown to also apply to the energy-containing range for the more restrictive case of stationary, homogeneous turbulence. The variety of derivations of Kolmogorov's and Monin's equations leads to a wide range of applicability to experimental conditions, including, in some cases, turbulence of moderate Reynolds number.

scholarly journals THE EMC EFFECT AND HIGH MOMENTUM NUCLEONS IN NUCLEI

2013 ◽  
Vol 22 (07) ◽  
pp. 1330017 ◽  
Author(s):  
OR HEN ◽  
DOUGLAS W. HIGINBOTHAM ◽  
GERALD A. MILLER ◽  
ELI PIASETZKY ◽  
LAWRENCE B. WEINSTEIN
Keyword(s):  
Linear Relation ◽  
Short Range ◽  
Mean Field ◽  
Structure Functions ◽  
High Momentum ◽  
Convolution Model ◽  
Recent Developments ◽  
The Mean ◽  
Emc Effect ◽  
Short Range Correlations

Recent developments in understanding the influence of the nucleus on deep-inelastic structure functions, the EMC effect, are reviewed. A new data base which expresses ratios of structure functions in terms of the Bjorken variable xA = AQ2/(2MA q0) is presented. Information about two-nucleon short-range correlations (SRC) from experiments is also discussed and the remarkable linear relation between SRC and the EMC effect is reviewed. A convolution model that relates the underlying source of the EMC effect to modification of either the mean-field nucleons or SRC nucleons is presented. It is shown that both approaches are equally successful in describing the current EMC data.

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

2015 ◽  
Vol 373 (2041) ◽  
pp. 20140150 ◽  
Author(s):  
Jesse T. Coburn ◽  
Miriam A. Forman ◽  
Charles W. Smith ◽  
Bernard J. Vasquez ◽  
Julia E. Stawarz
Keyword(s):  
Solar Wind ◽  
Kinetic Energy ◽  
Correlation Length ◽  
Magnetic Energy ◽  
Inertial Range ◽  
Energy Cascade ◽  
Range Dynamics ◽  
Back Transfer ◽  
Third Moment ◽  
Turbulent Cascade

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.

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