291 research outputs found
Scale dependence and cross-scale transfer of kinetic energy in compressible hydrodynamic turbulence at moderate Reynolds numbers
We investigate properties of the scale dependence and cross-scale transfer of
kinetic energy in compressible three-dimensional hydrodynamic turbulence, by
means of two direct numerical simulations of decaying turbulence with initial
Mach numbers M = 1/3 and M = 1, and with moderate Reynolds numbers, R_lambda ~
100. The turbulent dynamics is analyzed using compressible and incompressible
versions of the dynamic spectral transfer (ST) and the Karman-Howarth-Monin
(KHM) equations. We find that the nonlinear coupling leads to a flux of the
kinetic energy to small scales where it is dissipated; at the same time, the
reversible pressure-dilatation mechanism causes oscillatory exchanges between
the kinetic and internal energies with an average zero net energy transfer.
While the incompressible KHM and ST equations are not generally valid in the
simulations, their compressible counterparts are well satisfied and describe,
in a quantitatively similar way, the decay of the kinetic energy on large
scales, the cross-scale energy transfer/cascade, the pressure dilatation, and
the dissipation. There exists a simple relationship between the KHM and ST
results through the inverse proportionality between the wave vector k and the
spatial separation length l as k l ~ 3^1/2. For a given time the dissipation
and pressure-dilatation terms are strong on large scales in the KHM approach
whereas the ST terms become dominant on small scales; this is owing to the
complementary cumulative behavior of the two methods. The effect of pressure
dilatation is weak when averaged over a period of its oscillations and may lead
to a transfer of the kinetic energy from large to small scales without a net
exchange between the kinetic and internal energies. Our results suggest that
for large-enough systems there exists an inertial range for the kinetic energy
cascade ...Comment: 14 pages, 10 figure
Plasma turbulence and kinetic instabilities at ion scales in the expanding solar wind
The relationship between a decaying strong turbulence and kinetic instabilities in a slowly expanding plasma is investigated using two-dimensional (2D) hybrid expanding box simulations. We impose an initial ambient magnetic field perpendicular to the simulation box, and we start with a spectrum of large-scale, linearly polarized, random-phase Alfvénic fluctuations that have energy equipartition between kinetic and magnetic fluctuations and vanishing correlation between the two fields. A turbulent cascade rapidly develops; magnetic field fluctuations exhibit a power-law spectrum at large scales and a steeper spectrum at ion scales. The turbulent cascade leads to an overall anisotropic proton heating, protons are heated in the perpendicular direction, and, initially, also in the parallel direction. The imposed expansion leads to generation of a large parallel proton temperature anisotropy which is at later stages partly reduced by turbulence. The turbulent heating is not sufficient to overcome the expansion-driven perpendicular cooling and the system eventually drives the oblique firehose instability in a form of localized nonlinear wave packets which efficiently reduce the parallel temperature anisotropy. This work demonstrates that kinetic instabilities may coexist with strong plasma turbulence even in a constrained 2D regime
Magnetic field turbulence in the solar wind at sub-ion scales: in situ observations and numerical simulations
We investigate the transition of the solar wind turbulent cascade from MHD to
sub-ion range by means of a detail comparison between in situ observations and
hybrid numerical simulations. In particular we focus on the properties of the
magnetic field and its component anisotropy in Cluster measurements and hybrid
2D simulations. First, we address the angular distribution of wave-vectors in
the kinetic range between ion and electron scales by studying the variance
anisotropy of the magnetic field components. When taking into account the
single-direction sampling performed by spacecraft in the solar wind, the main
properties of the fluctuations observed in situ are also recovered in our
numerical description. This result confirms that solar wind turbulence in the
sub-ion range is characterized by a quasi-2D gyrotropic distribution of
k-vectors around the mean field. We then consider the magnetic compressibility
associated with the turbulent cascade and its evolution from large-MHD to
sub-ion scales. The ratio of field-aligned to perpendicular fluctuations,
typically low in the MHD inertial range, increases significantly when crossing
ion scales and its value in the sub-ion range is a function of the total plasma
beta only, as expected from theoretical predictions, with higher magnetic
compressibility for higher beta. Moreover, we observe that this increase has a
gradual trend from low to high beta values in the in situ data; this behaviour
is well captured by the numerical simulations. The level of magnetic field
compressibility that is observed in situ and in the simulations is in fairly
good agreement with theoretical predictions, especially at high beta,
suggesting that in the kinetic range explored the turbulence is supported by
low-frequency and highly-oblique fluctuations in pressure balance, like kinetic
Alfv\'en waves or other slowly evolving coherent structures.Comment: Manuscript submitted to Frontiers Astronomy and Space Sciences,
Research Topic: Improving the Understanding of Kinetic Processes in Solar
Wind and Magnetosphere: From CLUSTER to MM
von Karman-Howarth Equation for Hall Magnetohydrodynamics: Hybrid Simulations
A dynamical vectorial equation for homogeneous incompressible Hall-magnetohydrodynamic (MHD) turbulence together with the exact scaling law for third-order correlation tensors, analogous to that for the incompressible MHD, is rederived and applied to the results of two-dimensional hybrid simulations of plasma turbulence. At large (MHD) scales the simulations exhibit a clear inertial range where the MHD dynamic law is valid. In the sub-ion range the cascade continues via the Hall term, but the dynamic law derived in the framework of incompressible Hall-MHD equations is obtained only in a low plasma beta simulation. For a higher beta plasma the cascade rate decreases in the sub-ion range and the change becomes more pronounced as the plasma beta increases. This break in the cascade flux can be ascribed to nonthermal (kinetic) features or to others terms in the dynamical equation that are not included in the Hall-MHD incompressible approximation
Mirror Instability in the Turbulent Solar Wind
The relationship between a decaying strong turbulence and the mirror instability in a slowly expanding plasma is investigated using two-dimensional hybrid expanding box simulations. We impose an initial ambient magnetic field perpendicular to the simulation box, and we start with a spectrum of large-scale, linearly polarized, random-phase Alfvénic fluctuations that have energy equipartition between kinetic and magnetic fluctuations and a vanishing correlation between the two fields. A turbulent cascade rapidly develops, magnetic field fluctuations exhibit a Kolmogorov-like power-law spectrum at large scales and a steeper spectrum at sub-ion scales. The imposed expansion (taking a strictly transverse ambient magnetic field) leads to the generation of an important perpendicular proton temperature anisotropy that eventually drives the mirror instability. This instability generates large-amplitude, nonpropagating, compressible, pressure-balanced magnetic structures in a form of magnetic enhancements/humps that reduce the perpendicular temperature anisotropy
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