scholarly journals Phenomenologies of intermittent Hall MHD turbulence

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Mimi Dai
Keyword(s):  
Hall Effect ◽  
Scaling Laws ◽  
Structure Functions ◽  
Energy Spectra ◽  
Mhd Turbulence ◽  
Hall Mhd

<p style='text-indent:20px;'>We introduce the concept of intermittency dimension for the magnetohydrodynamics (MHD) to quantify the intermittency effect. With dependence on the intermittency dimension, we derive phenomenological laws for intermittent MHD turbulence with and without the Hall effect. In particular, scaling laws of dissipation wavenumber, energy spectra and structure functions are predicted. Moreover, we are able to provide estimates for energy spectra and structure functions which are consistent with the predicted scalings.</p>

scholarly journals Scaling laws in Hall-inertial range turbulence

2019 ◽  
Author(s):  
Yasuhito Narita ◽  
Wolfgang Baumjohann ◽  
Rudolf A. Treumann
Keyword(s):  
Magnetic Field ◽  
Electric Field ◽  
Scaling Laws ◽  
Magnetic Energy ◽  
Spatial Scales ◽  
Electric Energy ◽  
Power Spectra ◽  
Inertial Range ◽  
Energy Spectra ◽  
Mhd Turbulence

Abstract. There is an increasing amount of observational evidence in space plasma for the breakdown of inertial-range spectra of magnetohydrodynamic (MHD) turbulence on spatial scales smaller than the ion inertial length. Magnetic energy spectra often exhibit a steepening, which is reminiscent of dissipation of turbulence energy, for example in wave-particle interactions. Electric energy spectra, on the other hand, tend to be flatter than those of MHD turbulence, which is indicative of a dispersive process converting magnetic into electric energy in electromagnetic wave excitation. Here we develop a model of the scaling laws and the power spectra for the Hall-inertial range in plasma turbulence. A phenomenological approach is taken. The Hall electric field attains an electrostatic component when the wave vectors are perpendicular to the mean magnetic field. The power spectra of Hall-turbulence are steep for the magnetic field with slope of −7/3 for compressible magnetic turbulence, they are flatter for the Hall electric field with slope −1/3. Our model for the Hall-turbulence serves as a likely candidate to explain the steepening of the magnetic energy spectra in the solar wind neither as indication of the dissipation range nor the dispersive range but as the Hall-inertial range. Our model also reproduces the shape of energy spectra in Kelvin-Helmholtz turbulence observed at the Earth magnetopause.

scholarly journals Scaling laws in Hall inertial-range turbulence

2019 ◽  
Vol 37 (5) ◽  
pp. 825-834 ◽  
Author(s):  
Yasuhito Narita ◽  
Wolfgang Baumjohann ◽  
Rudolf A. Treumann
Keyword(s):  
Magnetic Field ◽  
Electric Field ◽  
Scaling Laws ◽  
Magnetic Energy ◽  
Electric Energy ◽  
Power Spectra ◽  
Inertial Range ◽  
Energy Spectra ◽  
Mhd Turbulence ◽  
The Magnetic Field

Abstract. There is an increasing amount of observational evidence in space plasmas for the breakdown of inertial-range spectra of magnetohydrodynamic (MHD) turbulence on spatial scales smaller than the ion-inertial length. Magnetic energy spectra often exhibit a steepening, which is reminiscent of dissipation of turbulence energy, for example in wave–particle interactions. Electric energy spectra, on the other hand, tend to be flatter than those of MHD turbulence, which is indicative of a dispersive process converting magnetic into electric energy in electromagnetic wave excitation. Here we develop a model of the scaling laws and the power spectra for the Hall inertial range in plasma turbulence. In the present paper we consider a two-dimensional geometry with no wave vector component parallel to the magnetic field as is appropriate in Hall MHD. A phenomenological approach is taken. The Hall electric field attains an electrostatic component when the wave vectors are perpendicular to the mean magnetic field. The power spectra of Hall turbulence are steep for the magnetic field with a slope of -7/3 for compressible magnetic turbulence; they are flatter for the Hall electric field with a slope of -1/3. Our model for the Hall turbulence gives a possible explanation for the steepening of the magnetic energy spectra in the solar wind as an indication of neither the dissipation range nor the dispersive range but as the Hall inertial range. Our model also reproduces the shape of energy spectra in Kelvin–Helmholtz turbulence observed at the Earth's magnetopause.

Turbulent cascade in the solar wind on ion scales

2020 ◽  
Author(s):  
Petr Hellinger ◽  
Andrea Verdini ◽  
Simone Landi ◽  
Luca Franci ◽  
Emanuele Papini ◽  
...  
Keyword(s):  
Solar Wind ◽  
Numerical Simulations ◽  
Hall Effect ◽  
Power Spectra ◽  
Two Dimensional ◽  
Mhd Turbulence ◽  
Ion Heating ◽  
Simulation Results ◽  
Hall Mhd ◽  
Turbulent Cascade

&lt;p&gt;Magnetic power spectra in the solar wind typically exhibit a transition, steepening, on characteristic ion scales. This transition is not yet fully understood. Two basic phenomena are usually suspected: Hall physics and dissipation. We investigate properties of this transition using numerical simulations.&amp;#160; We analyze results of two-dimensional hybrid simulations using a compressible version of von K&amp;#225;rm&amp;#225;n-Howarth equation for statistically homogeneous Hall MHD turbulence and compare these results to the predictions for the incompressible Hall MHD. The simulation results indicate that the transition between large, MHD and sub-ion scales is related to a combination of the Hall effect and ion heating/energization.&lt;/p&gt;

scholarly journals Scaling and Similarity of the Anisotropic Coherent Eddies in Near-Surface Atmospheric Turbulence

2018 ◽  
Vol 75 (3) ◽  
pp. 943-964 ◽  
Author(s):  
Khaled Ghannam ◽  
Gabriel G. Katul ◽  
Elie Bou-Zeid ◽  
Tobias Gerken ◽  
Marcelo Chamecki
Keyword(s):  
Scaling Laws ◽  
Velocity Structure ◽  
Scaling Law ◽  
Longitudinal Velocity ◽  
Structure Functions ◽  
Length Scale ◽  
Near Surface ◽  
Vegetation Canopies ◽  
Velocity Spectra ◽  
Attached Eddies

Abstract The low-wavenumber regime of the spectrum of turbulence commensurate with Townsend’s “attached” eddies is investigated here for the near-neutral atmospheric surface layer (ASL) and the roughness sublayer (RSL) above vegetation canopies. The central thesis corroborates the significance of the imbalance between local production and dissipation of turbulence kinetic energy (TKE) and canopy shear in challenging the classical distance-from-the-wall scaling of canonical turbulent boundary layers. Using five experimental datasets (two vegetation canopy RSL flows, two ASL flows, and one open-channel experiment), this paper explores (i) the existence of a low-wavenumber k−1 scaling law in the (wind) velocity spectra or, equivalently, a logarithmic scaling ln(r) in the velocity structure functions; (ii) phenomenological aspects of these anisotropic scales as a departure from homogeneous and isotropic scales; and (iii) the collapse of experimental data when plotted with different similarity coordinates. The results show that the extent of the k−1 and/or ln(r) scaling for the longitudinal velocity is shorter in the RSL above canopies than in the ASL because of smaller scale separation in the former. Conversely, these scaling laws are absent in the vertical velocity spectra except at large distances from the wall. The analysis reveals that the statistics of the velocity differences Δu and Δw approach a Gaussian-like behavior at large scales and that these eddies are responsible for momentum/energy production corroborated by large positive (negative) excursions in Δu accompanied by negative (positive) ones in Δw. A length scale based on TKE dissipation collapses the velocity structure functions at different heights better than the inertial length scale.

scholarly journals Solar wind low-frequency magnetohydrodynamic turbulence: extended self-similarity and scaling laws

1996 ◽  
Vol 3 (4) ◽  
pp. 247-261 ◽  
Author(s):  
V. Carbone ◽  
P. Veltri ◽  
R. Bruno
Keyword(s):  
Solar Wind ◽  
Scaling Laws ◽  
Velocity Structure ◽  
Fluid Flows ◽  
Structure Functions ◽  
Point Of View ◽  
Self Similarity ◽  
Extended Self ◽  
Scaling Exponents ◽  
Magnetohydrodynamic Turbulence

Abstract. In this paper we review some of the work done in investigating the scaling properties of Magnetohydrodynamic turbulence, by using velocity fluctuations measurements performed in the interplanetary space plasma by the Helios spacecraft. The set of scaling exponents ξq for the q-th order velocity structure functions, have been determined by using the Extended Self-Similarity hypothesis. We have found that the q-th order velocity structure function, when plotted vs. the 4-th order structure function, displays a range of self-similarity which extends over all the lengths covered by measurements, thus allowing for a very good determination of ξq. Moreover the results seem to show that the scaling exponents are the same regardless the various observation periods considered. The obtained scaling exponents have been compared with the results of some intermittency models for Kraichnan's turbulence, derived in the framework of infinitely divisible fragmentation processes, showing the good agreement between these models and our observations. Finally, on the basis of the actually available data sets, we show that scaling laws in Solar Wind turbulence seem to be different from turbulent scaling laws in the ordinary fluid flows. This is true for high-order velocity structure functions, while low-order velocity structure functions show the same scaling laws. Since our measurements involve length scales which extend over many order of magnitude where dissipation is practically absent, our results show that Solar Wind turbulence can be regarded as a testing bench for the investigation of general scaling behaviour in turbulent flows. In particular our results strongly support the point of view which attributes a key role to the inertial range dynamics in determining the intermittency characteristics in fluid flows, in contrast with the point of view which attributes intermittency to a finite Reynolds number effect.

scholarly journals Coronal Heating, Weak MHD Turbulence, and Scaling Laws

2007 ◽  
Vol 657 (1) ◽  
pp. L47-L51 ◽  
Author(s):  
A. F. Rappazzo ◽  
M. Velli ◽  
G. Einaudi ◽  
R. B. Dahlburg
Keyword(s):  
Scaling Laws ◽  
Coronal Heating ◽  
Mhd Turbulence

scholarly journals On inertial-range scaling laws

1996 ◽  
Vol 306 ◽  
pp. 167-181 ◽  
Author(s):  
John C. Bowman
Keyword(s):  
Steady State ◽  
High Resolution ◽  
Scaling Laws ◽  
State Energy ◽  
Three Dimensional ◽  
Inertial Range ◽  
Energy Spectra ◽  
Two Dimensional ◽  
Unified Framework ◽  
Asymptotic Nature

Inertial-range scaling laws for two- and three-dimensional turbulence are re-examined within a unified framework. A new correction to Kolmogorov's k−5/3 scaling is derived for the energy inertial range. A related modification is found to Kraichnan's logarithmically corrected two-dimensional enstrophy-range law that removes its unexpected divergence at the injection wavenumber. The significance of these corrections is illustrated with steady-state energy spectra from recent high-resolution closure computations. Implications for conventional numerical simulations are discussed. These results underscore the asymptotic nature of inertial-range scaling laws.

scholarly journals Properties of Hall-MHD Turbulence at Sub-Ion Scales: Spectral Transfer Analysis

Atmosphere ◽  
2021 ◽  
Vol 12 (12) ◽  
pp. 1632
Author(s):  
Emanuele Papini ◽  
Petr Hellinger ◽  
Andrea Verdini ◽  
Simone Landi ◽  
Luca Franci ◽  
...  
Keyword(s):  
Numerical Simulations ◽  
Transfer Rate ◽  
Space Plasma ◽  
Theoretical Models ◽  
Magnetic Fluctuations ◽  
Energy Transfer Rate ◽  
Mhd Turbulence ◽  
Developed Turbulence ◽  
First Time ◽  
Hall Mhd

We present results of a multiscale study of Hall-magnetohydrodynamic (MHD) turbulence, carried out on a dataset of compressible nonlinear 2D Hall-MHD numerical simulations of decaying Alfvénic turbulence. For the first time, we identify two distinct regimes of fully developed turbulence. In the first one, the power spectrum of the turbulent magnetic fluctuations at sub-ion scales exhibits a power law with a slope of ∼−2.9, typically observed both in solar wind and in magnetosheath turbulence. The second regime, instead, shows a slope of −7/3, in agreement with classical theoretical models of Hall-MHD turbulence. A spectral-transfer analysis reveals that the latter regime occurs when the energy transfer rate at sub-ion scales is dominated by the Hall term, whereas in the former regime, the governing process is the dissipation (and the system exhibits large intermittency). Results of this work are relevant to the space plasma community, as they may potentially reconcile predictions from theoretical models with results from numerical simulations and spacecraft observations.

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