5,619 research outputs found
Imprints of expansion onto the local anisotropy of solar wind turbulence
We study the anisotropy of II-order structure functions defined in a frame
attached to the local mean field in three-dimensional (3D) direct numerical
simulations of magnetohydrodynamic turbulence, including or not the solar wind
expansion. We simulate spacecraft flybys through the numerical domain by taking
increments along the radial (wind) direction that forms an angle of with
the ambient magnetic field. We find that only when expansion is taken into
account, do the synthetic observations match the 3D anisotropy observed in the
solar wind, including the change of anisotropy with scales. Our simulations
also show that the anisotropy changes dramatically when considering increments
oblique to the radial directions. Both results can be understood by noting that
expansion reduces the radial component of the magnetic field at all scales,
thus confining fluctuations in the plane perpendicular to the radial. Expansion
is thus shown to affect not only the (global) spectral anisotropy, but also the
local anisotropy of second-order structure functions by influencing the
distribution of the local mean field, which enters this higher-order
statistics.Comment: 5 pages, 5 figures, accepted in ApJ
Alfv\'en-dynamo balance and magnetic excess in MHD turbulence
3D Magnetohydrodynamic (MHD) turbulent flows with initially magnetic and
kinetic energies at equipartition spontaneously develop a magnetic excess (or
residual energy), as well in numerical simulations and in the solar wind.
Closure equations obtained in 1983 describe the residual spectrum as being
produced by a dynamo source proportional to the total energy spectrum, balanced
by a linear Alfv\'en damping term. A good agreement was found in 2005 with
incompressible simulations; however, recent solar wind measurements disagree
with these results. The previous dynamo-Alfv\'en theory is generalized to a
family of models, leading to simple relations between residual and total energy
spectra. We want to assess these models in detail against MHD simulations and
solar wind data. The family of models is tested against compressible decaying
MHD simulations with low Mach number, low cross-helicity, zero mean magnetic
field, without or with expansion terms (EBM or expanding box model). A single
dynamo-Alfv\'en model is found to describe correctly both solar wind scalings
and compressible simulations without or with expansion. It is equivalent to the
1983-2005 closure equation but with critical balance of nonlinear turnover and
linear Alfv\'en times, while the dynamo source term remains unchanged. The
discrepancy with previous incompressible simulations is elucidated. The model
predicts a linear relation between the spectral slopes of total and residual
energies . Examining the solar wind data as in
\cite{2013ApJ...770..125C}, our relation is found to be valid whatever the
cross-helicity, even better so at high cross-helicity, with the total energy
slope varying from to .Comment: 7 pages, 7 figures, accepted for publication in A&
Three-dimensional Iroshnikov-Kraichnan turbulence in a mean magnetic field
Forced, weak MHD turbulence with guide field is shown to adopt different
regimes, depending on the magnetic excess of the large forced scales. When the
magnetic excess is large enough, the classical perpendicular cascade with
scaling is obtained, while when equipartition is imposed, an isotropic
scaling appears in all directions with respect to the mean field
(\cite{2010PhRvE..82b6406G} or GM10). We show here that the scaling of
the GM10 regime is not ruled by a small-scale cross-helicity cascade, and
propose that it is a 3D extension of a perpendicular weak Iroshnikov-Kraichnan
(IK) cascade. We analyze in detail the structure functions in real space and
show that they closely follow the critical balance relation both in the local
frame and the global frame: we show that there is no contradiction between this
and the isotropic scaling of the spectra. We propose a scenario
explaining the spectral structure of the GM10 regime, that starts with a
perpendicular weak IK cascade and extends to 3D by using quasi-resonant
couplings. The quasi-resonance condition happens to reduce the energy flux in
the same way as is done in the weak perpendicular cascade, so leading to a
scaling in all directions. We discuss the possible applications of these
findings to solar wind turbulence.Comment: Major re-write of manuscrip
Solar wind turbulence from MHD to sub-ion scales: high-resolution hybrid simulations
We present results from a high-resolution and large-scale hybrid (fluid
electrons and particle-in-cell protons) two-dimensional numerical simulation of
decaying turbulence. Two distinct spectral regions (separated by a smooth break
at proton scales) develop with clear power-law scaling, each one occupying
about a decade in wave numbers. The simulation results exhibit simultaneously
several properties of the observed solar wind fluctuations: spectral indices of
the magnetic, kinetic, and residual energy spectra in the magneto-hydrodynamic
(MHD) inertial range along with a flattening of the electric field spectrum, an
increase in magnetic compressibility, and a strong coupling of the cascade with
the density and the parallel component of the magnetic fluctuations at
sub-proton scales. Our findings support the interpretation that in the solar
wind large-scale MHD fluctuations naturally evolve beyond proton scales into a
turbulent regime that is governed by the generalized Ohm's law.Comment: 5 pages, 5 figures; introduction and conclusions changed, references
updated, accepted for publication in ApJ
Two-dimensional Hybrid Simulations of Kinetic Plasma Turbulence: Current and Vorticity vs Proton Temperature
Proton temperature anisotropies between the directions parallel and
perpendicular to the mean magnetic field are usually observed in the solar wind
plasma. Here, we employ a high-resolution hybrid particle-in-cell simulation in
order to investigate the relation between spatial properties of the proton
temperature and the peaks in the current density and in the flow vorticity. Our
results indicate that, although regions where the proton temperature is
enhanced and temperature anisotropies are larger correspond approximately to
regions where many thin current sheets form, no firm quantitative evidence
supports the idea of a direct causality between the two phenomena. On the other
hand, quite a clear correlation between the behavior of the proton temperature
and the out-of-plane vorticity is obtained.Comment: 4 pages, 2 figures, Proceedings of the Fourteenth International Solar
Wind Conferenc
High-resolution hybrid simulations of kinetic plasma turbulence at proton scales
We investigate properties of plasma turbulence from magneto-hydrodynamic
(MHD) to sub-ion scales by means of two-dimensional, high-resolution hybrid
particle-in-cell simulations. We impose an initial ambient magnetic field,
perpendicular to the simulation box, and we add a spectrum of large-scale
magnetic and kinetic fluctuations, with energy equipartition and vanishing
correlation. Once the turbulence is fully developed, we observe a MHD inertial
range, where the spectra of the perpendicular magnetic field and the
perpendicular proton bulk velocity fluctuations exhibit power-law scaling with
spectral indices of -5/3 and -3/2, respectively. This behavior is extended over
a full decade in wavevectors and is very stable in time. A transition is
observed around proton scales. At sub-ion scales, both spectra steepen, with
the former still following a power law with a spectral index of ~-3. A -2.8
slope is observed in the density and parallel magnetic fluctuations,
highlighting the presence of compressive effects at kinetic scales. The
spectrum of the perpendicular electric fluctuations follows that of the proton
bulk velocity at MHD scales, and flattens at small scales. All these features,
which we carefully tested against variations of many parameters, are in good
agreement with solar wind observations. The turbulent cascade leads to on
overall proton energization with similar heating rates in the parallel and
perpendicular directions. While the parallel proton heating is found to be
independent on the resistivity, the number of particles per cell and the
resolution employed, the perpendicular proton temperature strongly depends on
these parameters.Comment: 15 pages, 13 figures, submitted to Ap
Anisotropy of third-order structure functions in MHD turbulence
The measure of the third-order structure function, Y, is employed in the
solar wind to compute the cascade rate of turbulence. In the absence of a mean
field B0=0, Y is expected to be isotropic (radial) and independent of the
direction of increments, so its measure yields directly the cascade rate. For
turbulence with mean field, as in the solar wind, Y is expected to become more
two dimensional (2D), that is, to have larger perpendicular components, loosing
the above simple symmetry. To get the cascade rate one should compute the flux
of Y, which is not feasible with single-spacecraft data, thus measurements rely
upon assumptions about the unknown symmetry. We use direct numerical
simulations (DNS) of magneto-hydrodynamic (MHD) turbulence to characterize the
anisotropy of Y. We find that for strong guide field B0=5 the degree of
two-dimensionalization depends on the relative importance of shear and pseudo
polarizations (the two components of an Alfv\'en mode in incompressible MHD).
The anisotropy also shows up in the inertial range. The more Y is 2D, the more
the inertial range extent differs along parallel and perpendicular directions.
We finally test the two methods employed in observations and find that the
so-obtained cascade rate may depend on the angle between B0 and the direction
of increments. Both methods yield a vanishing cascade rate along the parallel
direction, contrary to observations, suggesting a weaker anisotropy of solar
wind turbulence compared to our DNS. This could be due to a weaker mean field
and/or to solar wind expansion.Comment: Some text editing and typos corrected, 13 pages, 6 figures, to be
published in Ap
- …