Imbalanced kinetic Alfvén wave turbulence: from weak turbulence theory to nonlinear diffusion models for the strong regime

Passot, T.; Sulem, P. L.

doi:10.1017/s0022377819000187

Cited by 29 publications

(47 citation statements)

References 92 publications

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“…Third is the range near the ion characteristic scales ∼ [0.1, 1] Hz that we call the transition range (it is often referred to as the dissipation range), where spectra can steepen significantly to ∼ f −4.5 (Goldstein et al 1994;Leamon et al 1998;Stawicki et al 2001;Smith et al 2006;Bruno et al 2014). The actual scaling and the physics in this zone is still an unsettled question, e.g., (Bruno et al 2014;Voitenko and De Keyser 2016;Kobayashi et al 2017;Passot and Sulem 2019). Fourth is the dispersive range far below the ion scale, ∼ [3, 30] Hz , with a scaling f and ∈ [−3.1, −2.3] Kiyani et al 2009;Alexandrova et al 2012;.…”

Section: Solar Wind 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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Section: Solar Wind 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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“…It has also been conjectured that H C can be measured in the solar convection zone [85]. Moreover, the cross-helicity in MHD is known to grow with time [86], and it has been shown to be of different signs in the large and small scales, with the so-called pinning effect at the dissipation scale [87] (see also [88]). This dichotomy is also present in the spatial structures of the flow [89], with large one-signed lobes of high relative correlation separated in the current sheets by fast oscillating structures [90].…”

Section: B the Ideal Casementioning

confidence: 99%

“…Today, this remains a disputed issue which may depend on the model that is used. A unifying framework, for a two-dimensional formulation of reduced MHD in the presence of a strong uniform magnetic field, from large (MHD) scales to scales below the ion inertial length, has been proposed in [88], with, in particular, a detailed analysis of the weak (wave) turbulence regime leading to integro-differential equations with various steady power-law solutions. Exact scaling laws in terms of structure functions can be derived for 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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“…In this case, the nonlinear diffusion equations are derived by taking the strongly local interactions limit of the kinetic equations; the latter equations being themselves derived in a systematical way. Recently, such a model has been proposed by Passot & Sulem (2019) for KAW turbulence (a model also valid for oblique whistler waves as explained in Galtier & Meyrand (2015)) neglecting the coupling to other types of waves. The derivation can be qualified as semi-analytical because the problem is fundamentally anisotropic and in the final step of the derivation the authors neglected the cascade along the uniform magnetic field to find an expression for the nonlinear diffusion equation.…”

Section: Model Of Kaw Turbulencementioning

confidence: 99%

Spectrum in Kinetic Alfvén Wave Turbulence: Implications for the Solar Wind

David

Galtier

2019

ApJL

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The nature of solar wind turbulence at large scale is rather well understood in the theoretical framework of magnetohydrodynamics. The situation is quite different at sub-proton scales where the magnetic energy spectrum measured by different spacecrafts does not fit with the classical turbulence predictions: a power law index close to −8/3 is generally reported which is far from the predictions of strong and wave turbulence, −7/3 and −5/2 respectively. This discrepancy is considered as a major problem for solar wind turbulence. Here, we show with a nonlinear diffusion model of weak kinetic Alfvén wave turbulence where the cascade is driven by local triadic interactions (Passot & Sulem 2019), that a magnetic spectrum with a power law index of −8/3 can emerge. This scaling corresponds to a self-similar solution of the second kind with a front propagation following the law k f ∼ (t * − t) −3/4 , with t < t * . This solution appears when we relax the implicit assumption of stationarity generally made in turbulence. The agreement between the theory and observations can be interpreted as an evidence of the non-stationarity of solar wind turbulence at sub-proton scales.

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Imbalanced kinetic Alfvén wave turbulence: from weak turbulence theory to nonlinear diffusion models for the strong regime

Cited by 29 publications

References 92 publications

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

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

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

Spectrum in Kinetic Alfvén Wave Turbulence: Implications for the Solar Wind

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