Small-scale behavior of Hall magnetohydrodynamic turbulence

Stawarz, J. E.; Pouquet, A.

doi:10.1103/physreve.92.063102

Cited by 14 publications

(16 citation statements)

References 80 publications

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“…As f approaches f c i , U e ,⊥ and U i ,⊥ diverge with U e ,⊥ becoming shallower similar to E ⊥ , which is consistent with ions decoupling at these frequencies while the electrons remain frozen to the field. U i ,⊥ also becomes steeper than B ⊥ in this range consistent with simulations [e.g., Franci et al , ; Stawarz and Pouquet , ]. The divergence of U i ,⊥ and U e ,⊥ spectra begins at k ⊥ ρ i <1 and may be consistent with the ion inertial length, which is located at k ⊥ ρ i ≈0.65.…”

Section: Discussionsupporting

confidence: 85%

Observations of turbulence in a Kelvin‐Helmholtz event on 8 September 2015 by the Magnetospheric Multiscale mission

et al. 2016

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Spatial and high‐time‐resolution properties of the velocities, magnetic field, and 3‐D electric field within plasma turbulence are examined observationally using data from the Magnetospheric Multiscale mission. Observations from a Kelvin‐Helmholtz instability (KHI) on the Earth's magnetopause are examined, which both provides a series of repeatable intervals to analyze, giving better statistics, and provides a first look at the properties of turbulence in the KHI. For the first time direct observations of both the high‐frequency ion and electron velocity spectra are examined, showing differing ion and electron behavior at kinetic scales. Temporal spectra exhibit power law behavior with changes in slope near the ion gyrofrequency and lower hybrid frequency. The work provides the first observational evidence for turbulent intermittency and anisotropy consistent with quasi two‐dimensional turbulence in association with the KHI. The behavior of kinetic‐scale intermittency is found to have differences from previous studies of solar wind turbulence, leading to novel insights on the turbulent dynamics in the KHI.

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Section: Discussionsupporting

confidence: 85%

Observations of turbulence in a Kelvin‐Helmholtz event on 8 September 2015 by the Magnetospheric Multiscale mission

et al. 2016

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“…The magnetic field is expressed in Alfvén velocity units, P is the pressure, and J = ∇ × B the current density; ν and η are the kinematic viscosity and magnetic diffusivity, and ν ′ and η ′ are hyperviscosity and hyperdiffusivity coefficients associated with bi‐Laplacian terms. Their respective roles on the formation of small‐scale current sheets are discussed in detail in Stawarz & Pouquet (; see also Figure , for which we took ν = η , ν ′ = 0 = η ′ . )…”

Section: Coupling To a Magnetic Fieldmentioning

confidence: 99%

Helicity Dynamics, Inverse, and Bidirectional Cascades in Fluid and Magnetohydrodynamic Turbulence: A Brief Review

Pouquet

Rosenberg

Stawarz

et al. 2019

Earth and Space Science

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We briefly review helicity dynamics, inverse and bidirectional cascades in fluid and magnetohydrodynamic (MHD) turbulence, with an emphasis on the latter. The energy of a turbulent system, an invariant in the nondissipative case, is transferred to small scales through nonlinear mode coupling. Fifty years ago, it was realized that, for a two‐dimensional fluid, energy cascades instead to larger scales and so does magnetic excitation in MHD. However, evidence obtained recently indicates that, in fact, for a range of governing parameters, there are systems for which their ideal invariants can be transferred, with constant fluxes, to both the large scales and the small scales, as for MHD or rotating stratified flows, in the latter case including quasi‐geostrophic forcing. Such bidirectional, split, cascades directly affect the rate at which mixing and dissipation occur in these flows in which nonlinear eddies interact with fast waves with anisotropic dispersion laws, due, for example, to imposed rotation, stratification, or uniform magnetic fields. The directions of cascades can be obtained in some cases through the use of phenomenological arguments, one of which we derive here following classical lines in the case of the inverse magnetic helicity cascade in electron MHD. With more highly resolved data sets stemming from large laboratory experiments, high‐performance computing, and in situ satellite observations, machine learning tools are bringing novel perspectives to turbulence research. Such algorithms help devise new explicit subgrid‐scale parameterizations, which in turn may lead to enhanced physical insight, including in the future in the case of these new bidirectional cascades.

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“…Thus, the dynamical interactions between small and helicity spectra are constrained by a relation stemming from their conservation, providing a lack of uniqueness in power-law steady-state solutions (see [62] for the case of the cross-correlation between the velocity and magnetic field in MHD). Finally, in [63], it was shown that, for the small-scale behavior of Hall MHD in the decaying case, magnetic energy becomes dominant at sub-ionic scales, with narrow and intense current structures in which one observes a strong alignment between the current and the magnetic field (leading to force-free fields), as well as a narrow electric field auto-correlation function. On the other hand, the large-scale behavior of Hall-MHD, close to the ion inertial scale, has been much less investigated.…”

Section: Introductionmentioning

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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Small-scale behavior of Hall magnetohydrodynamic turbulence

Cited by 14 publications

References 80 publications

Observations of turbulence in a Kelvin‐Helmholtz event on 8 September 2015 by the Magnetospheric Multiscale mission

Observations of turbulence in a Kelvin‐Helmholtz event on 8 September 2015 by the Magnetospheric Multiscale mission

Helicity Dynamics, Inverse, and Bidirectional Cascades in Fluid and Magnetohydrodynamic Turbulence: A Brief Review

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

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