Structure transitions induced by the Hall term in homogeneous and isotropic magnetohydrodynamic turbulence

Miura, Hideaki; Araki, Keisuke

doi:10.1063/1.4890857

Cited by 27 publications

(37 citation statements)

References 40 publications

(50 reference statements)

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“…As for the fully-developed turbulence of the HMHD systems, the effects of the Hall term on the properties of MHD turbulence have been attracted interests of many researchers from various viewpoints including the closure approach in the weak/wave turbulence framework [21], evaluation of turbulent energy transfer and dynamo action using direct numerical simulation (DNS) data [22], and coherent structure formation by DNS [23].…”

Section: Introductionmentioning

confidence: 99%

Differential-geometrical approach to the dynamics of dissipationless incompressible Hall magnetohydrodynamics: II. Geodesic formulation and Riemannian curvature analysis of hydrodynamic and magnetohydrodynamic stabilities

Araki

2017

J. Phys. A: Math. Theor.

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Abstract. In this study, the dynamics of a dissipationless incompressible Hall magnetohydrodynamic (HMHD) medium are formulated as geodesics on a direct product of two volume-preserving diffeomorphism groups. Formulations are given for the geodesic and Jacobi equations based on a linear connection with physically desirable properties, which agrees with the Levi-Civita connection. Derivations of the explicit normal-mode expressions for the Riemannian metric, Levi-Civita connection, and related formulae and equations are also provided using the generalized Elsässer variables (GEVs). Examinations of the stabilities of the hydrodynamic (HD, α = 0) and magnetohydrodynamic (MHD, α → 0) motions and the O(α) Hall-term effect in terms of the Jacobi equation and the Riemannian sectional curvature tensor are presented, where α represents the Hall-term strength parameter. It is very interesting that the sectional curvatures of the MHD and HMHD systems between two GEV modes were found to take both the positive (stable) and negative (unstable) values, while that of the HD system between two complex helical waves was observed to be negative definite. Moreover, for the MHD case, negative sectional curvatures were found to occur only when mode interaction was "local," i.e., the wavenumber moduli of the main flow (say p) and perturbation (say k) were relatively close to each other. However, in the nonlocal limit (k p or k p), the sectional curvatures were always positive. This result leads to the conjecture that the MHD interactions mainly excite wavy or non-growing motions; however, some local interactions cause dynamical instability that leads to chaotic or turbulent plasma motions. Additionally, it was found that the tendencies of the O(α) effects are opposite between the ion cyclotron and whistler modes. Comparison with the energy-Casimir method is also discussed using a remarkable constant of motion which relates the Riemannian curvature to the second variation of the Hamiltonian.

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Section: Introductionmentioning

confidence: 99%

Differential-geometrical approach to the dynamics of dissipationless incompressible Hall magnetohydrodynamics: II. Geodesic formulation and Riemannian curvature analysis of hydrodynamic and magnetohydrodynamic stabilities

Araki

2017

J. Phys. A: Math. Theor.

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“…[15][16][17][18][19][20][21][22][23][24]). A few direct numerical simulations, however, have been performed in Hall MHD turbulence to study either in a classical way the behavior of the velocity and magnetic field fluctuations [2,7,[25][26][27], or in a more sophisticated way by separating the fluctuations in terms of polarities (left and right) [28]. Shell models have also been used to investigate in particular the transition from standard to * Electronic address: supratik.banerjee@uni-koeln.de † Electronic address: sebastien.galtier@lpp.polytechnique.fr…”

Section: Introductionmentioning

confidence: 99%

Chiral exact relations for helicities in Hall magnetohydrodynamic turbulence

Banerjee

Galtier

2016

Phys. Rev. E

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Besides total energy, three-dimensional incompressible Hall magnetohydrodynamics (MHD) possesses two inviscid invariants which are the magnetic helicity and the generalized helicity. New exact relations are derived for homogeneous (non-isotropic) stationary Hall MHD turbulence (and also for its inertialess electron MHD limit) with non-zero helicities and in the asymptotic limit of large Reynolds numbers. The universal laws are written only in terms of mixed second-order structure functions, i.e. the scalar product of two different increments. It provides, therefore, a direct measurement of the dissipation rates for the corresponding invariant flux. This study shows that the generalized helicity cascade is strongly linked to the left polarized fluctuations while the magnetic helicity cascade is linked to the right polarized fluctuations.

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“…of runs iMHD-2, iHMHD-2, and iXMHD-2 at t 1 is shown. Being sustained by the energy input by the dynamo action, the energy level of E M (k, t) is higher than that of E K (k, t) almost at all k. It has been reported earlier that the Hall term brings about a new scaling law k −7/3 (sub-inertial scaling region) in the sub-ion scale k > k H = 1/ H , in addition to the primary scaling region of Kolmogorov's k −5/3 (or can be the Iroshnikov-Kraichnan k −1/2 )-law [20][21][22].…”

Section: Hall and Gyro-viscous Effects In The Fourier Spacementioning

confidence: 71%

Extended Magnetohydrodynamic Simulations of Decaying, Homogeneous, Approximately-Isotropic and Incompressible Turbulence

Miura

2019

Fluids

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Incompressible magnetohydrodynamic (MHD) turbulence under influences of the Hall and the gyro-viscous terms was studied by means of direct numerical simulations of freely decaying, homogeneous and approximately isotropic turbulence. Numerical results were compared among MHD, Hall MHD, and extended MHD models focusing on differences of Hall and extended MHD turbulence from MHD turbulence at a fully relaxed state. Magnetic and kinetic energies, energy spectra, energy transfer, vorticity and current structures were studied. The Hall and gyro-viscous terms change the energy transfer in the equations of motions to be forward-transfer-dominant while the magnetic energy transfer remains backward-transfer-dominant. The gyro-viscosity works as a kind of hyper-diffusivity, attenuating the kinetic energy spectrum sharply at a high wave-number region. However, this term also induces high-vorticity events more frequently than MHD turbulence, making the turbulent field more intermittent. Vortices and currents were found to be transformed from sheet to tubular structures under the influences of the Hall and/or the gyro-viscous terms. These observations highlight features of fluid-dynamic aspect of turbulence in sub-ion-scales where turbulence is governed by the ion skin depth and ion Larmor radius.

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Structure transitions induced by the Hall term in homogeneous and isotropic magnetohydrodynamic turbulence

Cited by 27 publications

References 40 publications

Differential-geometrical approach to the dynamics of dissipationless incompressible Hall magnetohydrodynamics: II. Geodesic formulation and Riemannian curvature analysis of hydrodynamic and magnetohydrodynamic stabilities

Differential-geometrical approach to the dynamics of dissipationless incompressible Hall magnetohydrodynamics: II. Geodesic formulation and Riemannian curvature analysis of hydrodynamic and magnetohydrodynamic stabilities

Chiral exact relations for helicities in Hall magnetohydrodynamic turbulence

Extended Magnetohydrodynamic Simulations of Decaying, Homogeneous, Approximately-Isotropic and Incompressible Turbulence

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