103 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 turbulent spectrum at plasma kinetic scales
The description of the turbulent spectrum of magnetic fluctuations in the
solar wind in the kinetic range of scales is not yet completely established.
Here, we perform a statistical study of 100 spectra measured by the STAFF
instrument on the Cluster mission, which allows to resolve turbulent
fluctuations from ion scales down to a fraction of electron scales, i.e. from
km to m. We show that for
(that corresponds approximately to the frequency in the spacecraft frame Hz), all the observed spectra can be described by a general law
, where is
the wave-vector component normal to the background magnetic field and
the electron Larmor radius. This exponential tail found in the solar wind seems
compatible with the Landau damping of magnetic fluctuations onto electrons.Comment: published in APJ, 15 of November 2012 (with reduced "Discussion"
section
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
Spectral energy dynamics in magnetohydrodynamic turbulence
Spectral direct numerical simulations of incompressible MHD turbulence at a
resolution of up to collocation points are presented for a
statistically isotropic system as well as for a setup with an imposed strong
mean magnetic field. The spectra of residual energy,
, and total energy,
, are observed to scale self-similarly in
the inertial range as ,
(isotropic case) and ,
(anisotropic case, perpendicular to the mean
field direction). A model of dynamic equilibrium between kinetic and magnetic
energy, based on the corresponding evolution equations of the eddy-damped
quasi-normal Markovian (EDQNM) closure approximation, explains the findings.
The assumed interplay of turbulent dynamo and Alfv\'en effect yields
which is confirmed by the simulations.Comment: accepted for publication by PR
Coupling the solar dynamo and the corona: wind properties, mass and momentum losses during an activity cycle
We study the connections between the sun's convection zone and the evolution
of the solar wind and corona. We let the magnetic fields generated by a 2.5D
axisymmetric kinematic dynamo code (STELEM) evolve in a 2.5D axisymmetric
coronal isothermal MHD code (DIP). The computations cover an 11 year activity
cycle. The solar wind's asymptotic velocity varies in latitude and in time in
good agreement with the available observations. The magnetic polarity reversal
happens at different paces at different coronal heights. Overall sun's mass
loss rate, momentum flux and magnetic braking torque vary considerably
throughout the cycle. This cyclic modulation is determined by the latitudinal
distribution of the sources of open flux and solar wind and the geometry of the
Alfv\'en surface. Wind sources and braking torque application zones also vary
accordingly
Statistical anisotropy of magnetohydrodynamic turbulence
Direct numerical simulations of decaying and forced magnetohydrodynamic (MHD)
turbulence without and with mean magnetic field are analyzed by higher-order
two-point statistics. The turbulence exhibits statistical anisotropy with
respect to the direction of the local magnetic field even in the case of global
isotropy. A mean magnetic field reduces the parallel-field dynamics while in
the perpendicular direction a gradual transition towards two-dimensional MHD
turbulence is observed with inertial-range scaling of the
perpendicular energy spectrum. An intermittency model based on the Log-Poisson
approach, , is able to describe the observed
structure function scalings.Comment: 4 pages, 3 figures. To appear in Phys.Rev.
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