Chiral exact relations for helicities in Hall magnetohydrodynamic turbulence

Banerjee, Supratik; Galtier, Sébastien

doi:10.1103/physreve.93.033120

Cited by 25 publications

(42 citation statements)

References 66 publications

(90 reference statements)

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“…In the HMHD limit with  d 0 e , we have verified that our result is in exact agreement with the expression of Banerjee and Galtier [70].…”

Section: Mean Helicity Flux Ratessupporting

confidence: 90%

“…Hence, we sum up this preliminary analysis by observing that  + can undergo both forward and inverse cascades as predicted by Banerjee and Galtier [70]. We have also verified that our XMHD spectra, in the HMHD limit, are equal to the ones obtained earlier by Servidio et al [109].…”

Section: Absolute Equilibrium Statessupporting

confidence: 89%

“…In our analysis, we are interested in the flux rate of the generalized helicities (15) within the framework of XMHD that are injected at some length scale. By following the steps outlined in Banerjee and Galtier [70], we first introduce the symmetric two-point correlation function…”

Section: Mean Helicity Flux Ratesmentioning

confidence: 99%

“…We follow this up by using some of these aspects to gain a better understanding XMHD turbulence. In section 3, we generalize the results of Banerjee and Galtier [70] on helicity flux transfer rates to include electron inertia, and we also briefly raise the issue of the directional nature of the cascades. This matter is addressed in more detail in section 4, where we predict that the inverse cascade of magnetic helicity operates in the HMHD regime, but is absent when we consider the inertial MHD (IMHD) range that is valid at sub-electron skin depth scales.…”

Section: Introductionmentioning

confidence: 99%

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On the structure and statistical theory of turbulence of extended magnetohydrodynamics

2017

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Recent progress regarding the noncanonical Hamiltonian formulation of extended magnetohydrodynamics (XMHD), a model with Hall drift and electron inertia, is summarized. The advantages of the Hamiltonian approach are invoked to study some general properties of XMHD turbulence, and to compare them against their ideal MHD counterparts. For instance, the helicity flux transfer rates for XMHD are computed, and Liouville's theorem for this model is also verified. The latter is used, in conjunction with the absolute equilibrium states, to arrive at the spectra for the invariants, and to determine the direction of the cascades, e.g., generalizations of the well-known ideal MHD inverse cascade of magnetic helicity. After a similar analysis is conducted for XMHD by inspecting second order structure functions and absolute equilibrium states, a couple of interesting results emerge. When cross helicity is taken to be ignorable, the inverse cascade of injected magnetic helicity also occurs in the Hall MHD range-this is shown to be consistent with previous results in the literature. In contrast, in the inertial MHD range, viz at scales smaller than the electron skin depth, all spectral quantities are expected to undergo direct cascading. The consequences and relevance of our results in space and astrophysical plasmas are also briefly discussed.

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“…In the HMHD limit with  d 0 e , we have verified that our result is in exact agreement with the expression of Banerjee and Galtier [70].…”

Section: Mean Helicity Flux Ratessupporting

confidence: 90%

Section: Absolute Equilibrium Statessupporting

confidence: 89%

Section: Mean Helicity Flux Ratesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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On the structure and statistical theory of turbulence of extended magnetohydrodynamics

2017

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“…This change of invariants from the MHD case may imply as well a change in the dynamics of the flow (see, e.g., [80]). Note that in the expression of H G,M appear polarized waves (right and left, respectively); namely, H G can be written as [81]; H G is also called ion helicity in [82]. When MHD flows in the Solar Wind are strongly correlated, accelerated particles are more prominent [83]; this is likely due to the role played by H C in the so-called exact laws for MHD [84] (see [38] for an observation of such laws, and see below, equation (6) for the helical case in Hall MHD).…”

Section: B the Ideal Casementioning

confidence: 99%

Coupling Large Eddies and Waves in Turbulence: Case Study of Magnetic Helicity at the Ion Inertial Scale

2020

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In turbulence, for neutral or conducting fluids, a large ratio of scales is excited because of the possible occurrence of inverse cascades to large, global scales together with direct cascades to small, dissipative scales, as observed in the atmosphere and oceans, or in the solar environment. In this context, using direct numerical simulations with forcing, we analyze scale dynamics in the presence of magnetic fields with a generalized Ohm's law including a Hall current. The ion inertial length H serves as the control parameter at fixed Reynolds number. Both the magnetic and generalized helicity -invariants in the ideal case -grow linearly with time, as expected from classical arguments. The cross-correlation between the velocity and magnetic field grows as well, more so in relative terms for a stronger Hall current. We find that the helical growth rates vary exponentially with H , provided the ion inertial scale resides within the inverse cascade range. These exponential variations are recovered phenomenologically using simple scaling arguments. They are directly linked to the wavenumber power-law dependence of generalized and magnetic helicity, ∼ k −2 , in their inverse ranges. This illustrates and confirms the important role of the interplay between large and small scales in the dynamics of turbulent flows. arXiv:2001.11625v1 [physics.flu-dyn] 31 Jan 2020 and large scales play an essential role in estimating the efficiency of mixing in such flows [28][29][30], and it is found to vary linearly with the control parameter, namely the Froude number [31,32]. B. The case of space plasmasSimilar phenomena are observed as well for turbulent flows in the presence of magnetic fields. Such fields, together with charged particles, are abundant in the cosmos. At large scales, the magnetohydrodynamic (MHD) approximation, in which the displacement current is neglected in Maxwell's equations, is adequate, and observations of the Solar Wind, dating back to the Voyager spacecraft, confirmed the physical description of a medium governed by the interactions of turbulent, nonlinear eddies and Alfvén waves (see, e.g., for recent reviews, [33-36] and references therein). Turbulence is also found to play a central role in shaping these media [37][38][39].However, as the direct turbulent cascade of energy approaches smaller scales, plasma effects and dispersive waves come into effect, appearing for example through a generalized Ohm's law whose expression depends on the degree of ionization of the medium, which itself can differ greatly from the solar wind to the interstellar gas. Current spacecraft technologies allow for the resolution of much smaller temporal and spatial scales than what was available previously, and one can now reach the ion inertial length, H , and perhaps the electron inertial length (see for definitions the next section, and e.g. [40]). Other types of waves, kinetic Alfvén waves or whistler waves for example, come into play between the ion and electron scales, and the distribution of energy among modes is altered...

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An efficient Hermite-Galerkin spectral scheme for three-dimensional incompressible Hall-magnetohydrodynamic system on infinite domain

Guo,

Mei,

Jiang

2024

Journal of Computational Physics

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Chiral exact relations for helicities in Hall magnetohydrodynamic turbulence

Cited by 25 publications

References 66 publications

On the structure and statistical theory of turbulence of extended magnetohydrodynamics

On the structure and statistical theory of turbulence of extended magnetohydrodynamics

Coupling Large Eddies and Waves in Turbulence: Case Study of Magnetic Helicity at the Ion Inertial Scale

An efficient Hermite-Galerkin spectral scheme for three-dimensional incompressible Hall-magnetohydrodynamic system on infinite domain

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