On Exact Laws in Incompressible Hall Magnetohydrodynamic Turbulence

Ferrand, R.; Galtier, Sébastien; Sahraoui, Fouad; Meyrand, Romain; Andrés, Nahuel; Banerjee, Supratik

doi:10.3847/1538-4357/ab2be9

Cited by 49 publications

(61 citation statements)

References 65 publications

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“…for ∆t 1 s, compatible with the spectral break visible near 1 Hz in Figure 1), where a different type of cascade may take place [4, 71,84]. However, the scaling in this range should be studied in the framework of ion plasma physics, for example by including the Hall-MHD corrections to the Politano-Pouquet law [46,55]. This is left for future study.…”

Section: Resultsmentioning

confidence: 87%

“…The Politano-Pouquet law describes the scaling of the small imbalance between positive and negative energy flux in the turbulent cascade, and is associated with the scaledependent intrinsic asymmetry (skewness) of the turbulent fluctuations [1,41]. The linear scaling (1) was robustly observed in numerical simulations [44][45][46], in the solar wind plasma [47][48][49][50][51], and in the terrestrial magnetosheath [52][53][54]. In order to attempt a description of the local energy flux from space data time series, the law (1) can be revisited without computing the average, thus giving a time series of the heuristic proxy of the local energy transfer rates (LET) at a given scale ∆t, which can be estimated by computing the quantity:…”

Section: A a Proxy Of The Local Energy Transfer In Turbulencementioning

confidence: 98%

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Sign Singularity of the Local Energy Transfer in Space Plasma Turbulence

et al. 2019

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2In weakly collisional space plasmas, the turbulent cascade provides most of the energy that is dissipated at small scales by various kinetic processes. Understanding the characteristics of such dissipative mechanisms requires the accurate knowledge of the fluctuations that make energy available for conversion at small scales, as different dissipation processes are triggered by fluctuations of a different nature. The scaling properties of different energy channels are estimated here using a proxy of the local energy transfer, based on the third-order moment scaling law for magnetohydrodynamic turbulence. In particular, the sign-singularity analysis was used to explore the scaling properties of the alternating positive-negative energy fluxes, thus providing information on the structure and topology of such fluxes for each of the different type of fluctuations. The results show the highly complex geometrical nature of the flux, and that the local contributions associated with energy and cross-helicity nonlinear transfer have similar scaling properties. Consequently, the fractal properties of current and vorticity structures are similar to those of the Alfvénic fluctuations. PACS numbers: 94.05.-a, 94.05.Lk, 95.30.Qd

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Section: Resultsmentioning

confidence: 87%

Section: A a Proxy Of The Local Energy Transfer In Turbulencementioning

confidence: 98%

Sign Singularity of the Local Energy Transfer in Space Plasma Turbulence

et al. 2019

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“…This is because these laws allow one to better understand the turbulence dynamics, to evidence turbulence inertial range in numerical and experimental data and to estimate the energy cascade rate in turbulent flows. The original idea developed by Kolmogorov (1941) for Navier-Stokes equations was generalized to plasmas described within various theoretical frameworks: incompressible MHD (IMHD) (Politano and Pouquet 1998) (hereafter PP98), incompressible Hall-MHD (IHMHD) (Galtier 2006b;Banerjee and Galtier 2017;Hellinger et al 2018;Ferrand et al 2019), compressible MHD (CMHD) (Banerjee and Galtier 2013) (hereafter BG13) (see also the new derivation of the same law using the classical variables , and instead of the Elsässer variables in Andrés and Sahraoui (2017)), compressible Hall-MHD (Andrés et al 2018a) and incompressible twofluid model (Andrés et al 2016). The PP98 model has been widely applied to in situ measurements in the SW to estimate the amount of the energy that is cascaded from large-to-small scale where it is expected to be dissipated into plasma heating (Smith et al 2006;Sorriso-Valvo et al 2007;MacBride et al 2008;Marino et al 2008;Carbone et al 2009;Stawarz et al 2009;Coburn et al 2014;Banerjee et al 2016).…”

Section: Energy Cascade Rate Of Compressible Isothermal Mhd Turbulencementioning

confidence: 99%

Magnetohydrodynamic and kinetic scale turbulence in the near-Earth space plasmas: a (short) biased review

Sahraoui

Hadid

Huang

2020

Rev. Mod. Plasma Phys.

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The near-Earth space is a unique laboratory to explore turbulence and energy dissipation processes in magnetized plasmas thanks to the availability of high-quality data from various orbiting spacecraft, such as Wind, Stereo, Cluster, Themis, and the more recent one, the NASA Magnetospheric Multiscale (MMS) mission. In comparison with the solar wind, plasma turbulence in the magnetosheath remains far less explored, possibly because of the complexity of the magnetosheath dynamics that challenges any "realistic" theoretical modeling of turbulence in it. This complexity is due to different reasons such as the confinement of the magnetosheath plasma between two dynamical boundaries, namely the bow shock and the magnetopause; the high variability of the SW pressure that "shakes" and compresses continuously the magnetosheath plasma; and the presence of large-density fluctuations and temperature anisotropies that generate various instabilities and plasma modes. In this paper, we will review some results that we have obtained in recent years on plasma turbulence in the SW and the magnetosheath, both at the magnetohydrodynamics (MHD) and the sub-ion (kinetic) scales, using the state-of-the-art theoretical models and in situ spacecraft observations. We will focus on three major features of the plasma turbulence, namely its nature and scaling laws, the role of small-scale coherent structures in plasma heating, and the role of density fluctuations in enhancing the turbulent energy cascade rate. The latter is estimated using (analytical) exact laws derived for compressible MHD theories applied to in situ observations from the Cluster and Themis spacecraft. Finally, we will discuss some current trends in space plasmas turbulence research and future space missions dedicated to this topic that are currently being prepared within the community.

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“…H. Matthaeus et al, 1999;MacBride et al, 2008;Benzi et al, 1993;Grossmann et al, 1997;, the exact relation provides a precise computation of the amount of energy per unit time and volume (or heating rate) as a function of the velocity and magnetic correlation functions. The MHD exact relation and its connection with the nonlinear energy cascade rate has been numerically validated for both incompressible and compressible MHD turbulence , and has been generalized to include sub-ion scale effects Hadid et al, 2018;Hellinger et al, 2018;Ferrand et al, 2019;Banerjee & Andrés, 2020). Estimations of the energy cascade rate in the inertial range of solar wind turbulence have been previously computed at 1 Astronomical Unit (AU) (see, Marino et al, 2008;Coburn et al, 2014;Coburn et al, 2015;Banerjee et al, 2016;Hadid et al, 2017) and more recently at ∼ 0.2 AU (Bandyopadhyay et al, 2020;Chen et al, 2020).…”

Section: Introductionmentioning

confidence: 99%