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

<p>Turbulence in the solar wind is developed along a vast range of scales, generally under weakly compressible and strong magnetic field plasma conditions. <br>The effects of weakly and moderate compressibility (Mach ≤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.<br>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.</p>

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.

scholarly journals Numerical simulations of Hall MHD small-scale dynamos

2009 ◽  
Vol 5 (H15) ◽  
pp. 436-437
Author(s):  
Daniel O. Gómez ◽  
Pablo D. Mininni ◽  
Pablo Dmitruk
Keyword(s):  
Numerical Simulations ◽  
Hall Effect ◽  
Three Dimensional ◽  
Theoretical Framework ◽  
Mhd Equations ◽  
Small Scale ◽  
Hall Parameter ◽  
Hall Mhd ◽  
Three Dimensional Simulations

AbstractMuch of the progress in our understanding of dynamo mechanisms, has been made within the theoretical framework of magnetohydrodynamics (MHD). However, for sufficiently diffuse media, the Hall effect eventually becomes non-negligible. We present results from three dimensional simulations of the Hall-MHD equations subjected to random non-helical forcing. We study the role of the Hall effect in the dynamo efficiency for different values of the Hall parameter, using a pseudospectral code to achieve exponentially fast convergence.

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.

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>

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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