Energy cascade rate in isothermal compressible magnetohydrodynamic turbulence

The first complete estimation of the compressible energy cascade rate |εC| at magnetohydrodynamic (MHD) and sub-ion scales is obtained in the Earth's magnetosheath using Magnetospheric MultiScale (MMS) spacecraft data and an exact law derived recently for compressible Hall MHD turbulence. A multi-spacecraft technique is used to compute the velocity and magnetic gradients, and then all the correlation functions involved in the exact relation. It is shown that when the density fluctuations are relatively small, |εC| identifies well with its incompressible analogue |εI| at MHD scales but becomes much larger than |εI| at sub-ion scales. For larger density fluctuations, |εC| is larger than |εI| at every scale with a value significantly higher than for smaller density fluctuations. Our study reveals also that for both small and large density fluctuations, the non-flux terms remain always negligible with respect to the flux terms and that the major contribution to |εC| at sub-ion scales comes from the compressible Hall flux.Introduction. Turbulence is a universal phenomenon observed from quantum to astrophysical scales [see e.g., 1-3]. It is mainly characterized by a nonlinear transfer (or cascade) of energy from a source to a sink. In astrophysical plasmas, fully developed turbulence plays a major role in several physical processes such as accretion flows around massive objects, star formation, solar wind heating or energy transport in planetary magnetospheres [e.g., 4-7]. In particular, the Earth's magnetosheath (MS) -the region of the solar wind downstream of the bow shock [8] -provides a unique laboratory to investigate compressible plasma turbulence. Indeed, a key feature of the MS plasma is the high level of density fluctuations in it, which can reach up to 100% of the background density [9][10][11], in contrast to the solar wind where it is ∼ 20% [12,13]. Thanks to the high time resolution data provided by the Magnetospheric Multi-Scale (MMS) mission in the Earth's MS [14], we are now able for the first time to measure the compressible energy cascade rate ε C from the magnetohydrodynamic (MHD) inertial range down to the sub-ion scales.

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confidence: 83%

Energy Cascade Rate Measured in a Collisionless Space Plasma with MMS Data and Compressible Hall Magnetohydrodynamic Turbulence Theory

et al. 2019

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“…The data consists of three periodic cubes giving the three components of the magnetic field in each grid point. The values of ε Hall are obtained by averaging the mixed field increments of the different exact laws over all the points of the data cubes and spherically integrating them, using for the increment vectors a set of specific directions in space defined by 73 base vectors as described in Taylor et al (2003), and lengths going from a three points distance to half the size of the cubes (see also, Andrés et al 2018b). First of all, we want to check numerically the new law F19 and more precisely the analytical relation found between H and 4I A .…”

Section: Numerical Studymentioning

confidence: 99%

On Exact Laws in Incompressible Hall Magnetohydrodynamic Turbulence

Ferrand

Galtier

Sahraoui

et al. 2019

ApJ

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A comparison is made between several existing exact laws in incompressible Hall magnetohydrodynamic (IHMHD) turbulence in order to show their equivalence, despite stemming from different mathematical derivations. Using statistical homogeneity, we revisit the law proposed by Hellinger et al. (2018) and show that it can be written, after being corrected by a multiplicative factor, in a more compact form implying only flux terms expressed as increments of the turbulent fields. The Hall contribution of this law is tested and compared to other exact laws derived by Galtier (2008) and Banerjee & Galtier (2017) using direct numerical simulations (DNSs) of three-dimensional electron MHD (EMHD) turbulence with a moderate mean magnetic field. We show that the studied laws are equivalent in the inertial range, thereby offering several choices on the formulation to use depending on the needs. The expressions that depend explicitly on a mean (guide) field may lead to residual errors in estimating the energy cascade rate ; however, we demonstrate that this guide field can be removed from these laws after mathematical manipulation. Therefore, it is recommended to use an expression independent of the mean guide field to analyze numerical or in-situ spacecraft data. arXiv:1905.06110v1 [physics.flu-dyn]

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“…In the absence of detailed 3D spatio-temporal observations and/or experimental data, numerical simulations are often used to support the interpretation of observations or, in the case of turbulence research, have become one of the major drivers of scientific advances. This pertains, for example, to studying energy dissipation and turbulent energy cascades, (e.g., Yang et al 2016;Grete et al 2017;Andrs et al 2018) or to turbulence modeling (Clark et al 1979;Germano et al 1991;Chernyshov et al 2012;Grete et al 2016).…”

Section: Introductionmentioning

confidence: 99%

As a Matter of State: The Role of Thermodynamics in Magnetohydrodynamic Turbulence

Grete

O’Shea

Beckwith

2020

ApJ

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Turbulence simulations play a key role in advancing the general understanding of the physical properties turbulence and in interpreting astrophysical observations of turbulent plasmas. For the sake of simplicity, however, turbulence simulations are often conducted in the isothermal limit. Given that the majority of astrophysical systems are not governed by isothermal dynamics, we aim to quantify the impact of thermodynamics on the physics of turbulence, through varying adiabatic index, γ, combined with a range of optically thin cooling functions. In this paper, we present a suite of ideal magnetohydrodynamics simulations of thermally balanced stationary turbulence in the subsonic, super-Alfvénic, high β p (ratio of thermal to magnetic pressure) regime, where turbulent dissipation is balanced by two idealized cooling functions (approximating linear cooling and free-free emission) and examine the impact of the equation of state by considering cases that correspond to isothermal, monatomic and diatomic gases. We find a strong anticorrelation between thermal and magnetic pressure independent of thermodynamics, whereas the strong anticorrelation between density and magnetic field found in the isothermal case weakens with increasing γ. Similarly, with the linear relation between variations in density and thermal pressure with sonic Mach number becomes steeper with increasing γ. This suggests that there exists a degeneracy in these relations with respect to thermodynamics and Mach number in this regime, which is dominated by slow magnetosonic modes. These results have implications for attempts to infer (e.g.) Mach numbers from (e.g.) Faraday rotation measurements, without additional information regarding the thermodynamics of the plasma. However, our results suggest that this degeneracy can be broken by utilizing higher-order moments of observable distribution functions.

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Energy cascade rate in isothermal compressible magnetohydrodynamic turbulence

Cited by 42 publications

References 72 publications

Energy Cascade Rate Measured in a Collisionless Space Plasma with MMS Data and Compressible Hall Magnetohydrodynamic Turbulence Theory

Energy Cascade Rate Measured in a Collisionless Space Plasma with MMS Data and Compressible Hall Magnetohydrodynamic Turbulence Theory

On Exact Laws in Incompressible Hall Magnetohydrodynamic Turbulence

As a Matter of State: The Role of Thermodynamics in Magnetohydrodynamic Turbulence

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