In situ observation of three-dimensional anisotropies and scalings of space plasma turbulence at kinetic scales

2021 ◽  
Author(s):  
Tieyan Wang ◽  
Jiansen He ◽  
Olga Alexandrova ◽  
Malcolm Dunlop ◽  
Denise Perrone
Keyword(s):  
Three Dimensional ◽  
Wave Model ◽  
Structure Functions ◽  
Alfven Wave ◽  
Wave Number ◽  
Order Structure ◽  
In Situ Observation ◽  
Scale Invariant ◽  
Anisotropic Scaling ◽  
Background Magnetic Field

<p>The energy distribution at wave number space is known to be anisotropic in space plasmas. At kinetic scales, the standard Kinetic Alfven Wave model predicts anisotropy scaling of k<sub>par</sub> ∝ k<sub>perp</sub><sup>(1/3)</sup>, whereas the latest models considering the intermittency, or tearing instabilities, predict scalings such as k<sub>par</sub> ∝ k<sub>perp</sub><sup>(2/3)</sup> and k<sub>par</sub> ∝ k<sub>perp</sub><sup>(3/3)</sup>. Recent numerical simulations also payed considerable attention to this issue. Based on a unified analysis of five-point structure functions of the turbulence in three kinetic simulations, Cerri et al. 2019 obtained a converging result of l<sub>par</sub> ∝ l<sub>perp</sub><sup>(3/3)</sup>. To enrich our knowledge of the anisotropic scaling relation from an observational point of view, we conducted a statistical survey for the turbulence measured by MMS in the magnetosheath. For the 349 intervals with burst mode data, abundant evidence of 3D anisotropy at the sub-proton scale (1-100 km) is revealed by five-point second order structure functions. In particular, the eddies are mostly elongated along background magnetic field <strong>B<sub>0</sub></strong> and shortened in the two perpendicular directions. The ratio between eddies’ parallel and perpendicular lengths features a trend of rise then fall toward small scales, whereas the anisotropy in the perpendicular plane appears scale invariant. Moreover, over 30% of the events exhibit scaling relations close to l<sub>par</sub> ∝ l<sub>perp</sub><sup>(2/3)</sup>. In order to explain such signature, additional factors such as intermittency caused by different coherent structures may be required in addition to the critical balance premise.</p>

THE MULTIFRACTAL SCALING OF CLOUD RADIANCES FROM 1M TO 1KM

Fractals ◽  
2002 ◽  
Vol 10 (03) ◽  
pp. 253-264 ◽  
Author(s):  
D. SACHS ◽  
S. LOVEJOY ◽  
D. SCHERTZER
Keyword(s):  
Entire Range ◽  
Atmospheric Dynamics ◽  
Wave Number ◽  
Two Dimensional ◽  
Scale Invariant ◽  
Spectral Exponent ◽  
Scaling Properties ◽  
Anisotropic Scaling ◽  
Multifractal Scaling ◽  
Cloud Thickness

The cloud radiances and atmospheric dynamics are strongly nonlinearly coupled, the observed scaling of the former from 1 km to planetary scales is prima facae evidence for scale invariant dynamics. In contrast, the scaling properties of radiances at scales <1 km have not been well studied (contradictory claims have been made) and if a characteristic vertical cloud thickness existed, it could break the scaling of the horizontal radiances. In order to settle this issue, we use ground-based photography to study the cloud radiance field through the range scales where breaks in scaling have been reported (30 m to 500 m). Over the entire range 1 m to 1 km the two-dimensional (2D) energy spectrum (E(k)) of 38 clouds was found to accurately follow the scaling form E(k)≈ k-β where k is a wave number and β is the spectral exponent. This indirectly shows that there is no characteristic vertical cloud thickness, and that "radiative smoothing" of cloud structures occurs at all scales. We also quantitatively characterize the type of (multifractal) scaling showing that the main difference between transmitted and reflected radiance fields is the (scale-by-scale) non-conservation parameter H. These findings lend support to the unified scaling model of the atmosphere which postulates a single anisotropic scaling regime from planetary down to dissipation scales.

Karman-Howarth-Monin equation for compressible Hall MHD  turbulence: 2D and 3D Hall MHD simulations

2021 ◽  
Author(s):  
Victor Montagud-Camps ◽  
Petr Hellinger ◽  
Andrea Verdini ◽  
Simone Landi ◽  
Emanuele Papini ◽  
...  
Keyword(s):  
Three Dimensional ◽  
Structure Functions ◽  
Real Space ◽  
Energy Cascade ◽  
Mhd Equations ◽  
Order Structure ◽  
Mhd Simulations ◽  
Turbulence Anisotropy ◽  
Basic Fluid ◽  
Hall Mhd

&lt;p&gt;Turbulence in the solar wind is developed along a vast range of scales, generally under weakly compressible and strong magnetic field plasma conditions. &lt;br&gt;The effects of weakly and moderate compressibility (Mach &amp;#8804;1) and turbulence anisotropy on the energy transfer rate are investigated at MHD and Hall MHD scales. For this purpose, the results of two and three-dimensional compressible Hall MHD simulations are analyzed using a new form of the Karman-Howarth-Monin (KHM) equations that accounts for compressible effects down to Hall MHD scales.&lt;br&gt;The KHM are dynamic equations directly derived from the basic fluid equations that describe the plasma, such as the Hall MHD equations. They provide a relation between the two-point cross-correlations in real space or II-order structure functions, the III-order structure functions and the energy cascade rate of turbulence. These relations depend upon turbulence anisotropy. The effects of compressibility and the Hall term on anisotropy and the estimation of the energy cascade rate via the KHM equations are discussed.&lt;/p&gt;

Third-order structure function relations for quasi-geostrophic turbulence

2007 ◽  
Vol 572 ◽  
pp. 255-260 ◽  
Author(s):  
ERIK LINDBORG
Keyword(s):  
Structure Function ◽  
Three Dimensional ◽  
Structure Functions ◽  
Order Structure ◽  
Third Order ◽  
Longitudinal Structure ◽  
The Third ◽  
Inverse Cascade ◽  
Geostrophic Turbulence ◽  
Potential Enstrophy

We derive two third-order structure function relations for quasi-geostrophic turbulence, one for the forward cascade of potential enstrophy and one for the inverse cascade of energy. These relations are the counterparts of Kolmovorov's (1941) four-fifths law for the third-order longitudinal structure functions of three-dimensional turbulence.

On the existence of transverse MHD oscillations in an inhomogeneous magnetoplasma

1990 ◽  
Vol 43 (1) ◽  
pp. 83-99 ◽  
Author(s):  
Andrew N. Wright
Keyword(s):  
Magnetic Field ◽  
Three Dimensional ◽  
Background Field ◽  
Alfven Wave ◽  
Field Perturbation ◽  
Independent Field ◽  
Background Magnetic Field ◽  
Field Geometry ◽  
Divergence Free ◽  
Field Lines

In a cold plasma with no compressional field perturbation the equations governing the two perpendicular components of magnetic-field perturbation decouple. These two equations depend only upon spatial derivatives along the background magnetic field, and give the impression of independent field-line motion in the two transverse directions. However, the perturbation magnetic field b must be divergence-free. It is not meaningful to ask if the field perturbation on an individual background line of force satisfies ∇. b = 0. To decide whether b is divergence-free, we need to know about its spatial variation, i.e. what the state of the neighbouring field lines is. In this paper we investigate two classes of solutions: first we allow the perturbation magnetic flux to satisfy ∇. b = 0 by threading across the background lines of force; the second solution closes b by allowing the perturbation flux to encircle the background field lines (torsional Alfvén waves). For both of these solutions we study the relationship between neighbouring field lines, and are able to derive a set of criteria that the background medium must satisfy. For both classes we find restrictions upon the background magnetic-field geometry - the first class also has a constraint upon the plasma density. The introduction of perfectly conducting massive boundaries is also considered, and a relation given that they must satisfy if the field perturbation is to remain transverse. The criteria are presented in such a manner that it is easy to test if a given medium will be able to support the solutions described above. For example, a three-dimensional dipolo geometry is able to carry oscillatory toroidal fields; but not purely poloidal ones or a torsional Alfvén wave.

scholarly journals Physics of kinetic Alfvén waves: a gyrokinetic theory approach

2021 ◽  
Vol 5 (1) ◽  
Author(s):  
Liu Chen ◽  
Fulvio Zonca ◽  
Yu Lin
Keyword(s):  
Kinetic Theory ◽  
Short Wavelength ◽  
Spectral Feature ◽  
Transport Processes ◽  
Alfven Wave ◽  
Wave Number ◽  
Larmor Radius ◽  
Theory Approach ◽  
Background Magnetic Field ◽  
Linear And Nonlinear

AbstractThe transverse shear Alfvén wave (SAW) is a fundamental anisotropic electromagnetic oscillation in plasmas with a finite background magnetic field. In realistic plasmas with spatial inhomogeneities, SAW exhibits the interesting spectral feature of a continuous spectrum. That is, the SAW oscillation frequency varies in the non-uniform (radial) direction. This continuum spectral feature then naturally leads to the phase-mixing process; i.e., time asymptotically, the effective radial wave-number increases with time. Any initial perturbation of SAW structures will, thus, evolve eventually into short-wavelength structures; termed as kinetic Alfvén wave (KAW). Obviously, one needs to employ kinetic theory approach to properly describe the dynamics of KAW; including effects such as finite ion-Larmor radius (FILR) and/or wave–particle interactions. When KAW was first discovered and discussed in 1975–1976, it was before the introduction of the linear electromagnetic gyrokinetic theory (1978) and nonlinear electromagnetic gyrokinetic theory (1982). Kinetic treatments then often involved the complicated procedures of taking the low-frequency limit of the Vlasov kinetic theory and/or employing the drift-kinetic theory approach; forsaking, thus, the FILR effects. In recent years, the powerful nonlinear gyrokinetic theory has been employed to re-examine both the linear and nonlinear physics of KAWs. This brief review will cover results of linear and nonlinear analytical theories, simulations, as well as observational evidences. We emphasize, in particular, that due to the enhanced electron–ion de-coupling in the short-wavelength regime, KAWs possess significantly enhanced nonlinear coupling coefficients and, thereby, play important roles in the heating, acceleration, and transport processes of charged particles in magnetized plasmas.

Investigation of the influence of combustion-induced thermal expansion on two-point turbulence statistics using conditioned structure functions

2019 ◽  
Vol 867 ◽  
pp. 45-76 ◽  
Author(s):  
V. A. Sabelnikov ◽  
A. N. Lipatnikov ◽  
S. Nishiki ◽  
T. Hasegawa
Keyword(s):  
Thermal Expansion ◽  
Turbulent Flow ◽  
Turbulent Flows ◽  
Three Dimensional ◽  
Structure Functions ◽  
Single Step ◽  
Small Scale ◽  
Order Structure ◽  
Constant Density ◽  
Local Velocity

The second-order structure functions (SFs) of the velocity field, which characterize the velocity difference at two points, are widely used in research into non-reacting turbulent flows. In the present paper, the approach is extended in order to study the influence of combustion-induced thermal expansion on turbulent flow within a premixed flame brush. For this purpose, SFs conditioned to various combinations of mixture states at two different points (reactant–reactant, reactant–product, product–product, etc.) are introduced in the paper and a relevant exact transport equation is derived in the appendix. Subsequently, in order to demonstrate the capabilities of the newly developed approach for advancing the understanding of turbulent reacting flows, the conditioned SFs are extracted from three-dimensional (3-D) direct numerical simulation data obtained from two statistically 1-D planar, fully developed, weakly turbulent, premixed, single-step-chemistry flames characterized by significantly different (7.53 and 2.50) density ratios, with all other things being approximately equal. Obtained results show that the conditioned SFs differ significantly from standard mean SFs and convey a large amount of important information on various local phenomena that stem from the influence of combustion-induced thermal expansion on turbulent flow. In particular, the conditioned SFs not only (i) indicate a number of already known local phenomena discussed in the paper, but also (ii) reveal a less recognized phenomenon such as substantial influence of combustion-induced thermal expansion on turbulence in constant-density unburned reactants and even (iii) allow us to detect a new phenomenon such as the appearance of strong local velocity perturbations (shear layers) within flamelets. Moreover, SFs conditioned to heat-release zones indicate a highly anisotropic influence of combustion-induced thermal expansion on the evolution of small-scale two-point velocity differences within flamelets, with the effects being opposite (an increase or a decrease) for different components of the local velocity vector.

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 Anisotropic scaling of remotely sensed drainage basins: the differential anisotropy scaling technique

2007 ◽  
Vol 14 (4) ◽  
pp. 337-350 ◽  
Author(s):  
A. Beaulieu ◽  
H. Gaonac'h ◽  
S. Lovejoy
Keyword(s):  
Loess Plateau ◽  
Drainage System ◽  
Wave Number ◽  
Drainage Basins ◽  
Scale Invariant ◽  
Scaling Technique ◽  
Higher Dimensional ◽  
Anisotropic Scaling ◽  
Rotation Parameters ◽  
Scaling Fields

Abstract. We investigate the statistical properties of dendritic drainage areas from diverse geological environments (Deception Canyon, Utah and the Loess Plateau, China) using narrow band visible ASTER satellite images. We show that from 240 m to 7680 m, the isotropic (angle integrated) energy spectra E(k) of all the fields closely follow a power law form: E(k)∝k−β where k is a wave number and β a scale invariant exponent. In spite of this good isotropic scaling, images with very similar β's and similar isotropic multifractal exponents have distinct textures; we suggest that the differences are primarily due to anisotropy, which is nevertheless scaling. We develop the new "Differential Anisotropy Scaling" technique to characterize this scale-by-scale (differential) anisotropy and we test it on simulated anisotropic scaling fields. The method gives useful characterizations of the scale by scale anisotropy irrespective of whether or not the analyzed field is scaling. When the anisotropy is not too strong, the parameters can be interpreted as scale invariant anisotropy exponents. Viewed as a method of estimating these exponents, it has the advantage of relying on two linear regressions rather than on complex higher dimensional nonlinear ones. When applied to dendritic drainage basins we find that they have distinct anisotropies characterized by differential anisotropy stretching and rotation parameters as well as by a distinct absolute anisotropy at the reference scale of 960 m. Our new method allows us to statistically distinguish, not only between two geologically different drainage basins (the China Loess Plateau and Utah Deception Canyon), but also between different regions of the same China drainage system.

On the deficiency of even-order structure functions as inertial-range diagnostics

2008 ◽  
Vol 602 ◽  
pp. 287-302 ◽  
Author(s):  
P. A. DAVIDSON ◽  
P.-Å. KROGSTAD
Keyword(s):  
Structure Function ◽  
Isotropic Turbulence ◽  
Three Dimensional ◽  
Physical Space ◽  
Reynolds Numbers ◽  
Structure Functions ◽  
Inertial Range ◽  
Second Order ◽  
Order Structure ◽  
Even Order

In the limit of vanishing viscosity, ν→0, Kolmogorov's two-thirds, 〈(Δυ)2〉~ε2/3r2/3, and five-thirds, E~ε2/3k−5/3, laws are formally equivalent. (Here 〈(Δυ)2〉 is the second-order structure function, ε the dissipation rate, r the separation in physical space, E the three-dimensional energy spectrum, and k the wavenumber.) However, for the Reynolds numbers encountered in terrestrial experiments, or numerical simulations, it is invariably easier to observe the five-thirds law. We ask why this should be. To this end, we create artificial fields of isotropic turbulence composed of a random sea of Gaussian eddies whose size and energy distribution can be controlled. We choose the energy of eddies of scale, s, to vary as s2/3, in accordance with Kolmogorov's 1941 law, and vary the range of scales, γ=smax/smin, in any one realization from γ=25 to γ=800. This is equivalent to varying the Reynolds number in an experiment from Rλ=60 to Rλ=600. We find that, while there is some evidence of a five-thirds law for γ>50; (Rλ>100), the two-thirds law only starts to become apparent when γ approaches 200 (Rλ~240). The reason for this discrepancy is that the second-order structure function is a poor filter, mixing information about energy and enstrophy, and from scales larger and smaller than r. In particular, in the inertial range, 〈(Δυ)2〉 takes the form of a mixed power law, a1 + a2r2 + a3r2/3, where a2r2 tracks the variation in enstrophy and a3r2/3 the variation in energy. These findings are shown to be consistent with experimental data where the ‘pollution’ of the r2/3 law by the enstrophy contribution, a2r2, is clearly evident. We show that higher-order structure functions (of even order) suffer from a similar deficiency.

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