163 research outputs found
Inertial range turbulence in kinetic plasmas
The transfer of turbulent energy through an inertial range from the driving
scale to dissipative scales in a kinetic plasma followed by the conversion of
this energy into heat is a fundamental plasma physics process. A theoretical
foundation for the study of this process is constructed, but the details of the
kinetic cascade are not well understood. Several important properties are
identified: (a) the conservation of a generalized energy by the cascade; (b)
the need for collisions to increase entropy and realize irreversible plasma
heating; and (c) the key role played by the entropy cascade--a dual cascade of
energy to small scales in both physical and velocity space--to convert
ultimately the turbulent energy into heat. A strategy for nonlinear numerical
simulations of kinetic turbulence is outlined. Initial numerical results are
consistent with the operation of the entropy cascade. Inertial range turbulence
arises in a broad range of space and astrophysical plasmas and may play an
important role in the thermalization of fusion energy in burning plasmas.Comment: 11 pages, 2 figures, submitted to Physics of Plasmas, DPP Meeting
Special Issu
Evidence of Critical Balance in Kinetic Alfven Wave Turbulence Simulations
A numerical simulation of kinetic plasma turbulence is performed to assess
the applicability of critical balance to kinetic, dissipation scale turbulence.
The analysis is performed in the frequency domain to obviate complications
inherent in performing a local analysis of turbulence. A theoretical model of
dissipation scale critical balance is constructed and compared to simulation
results, and excellent agreement is found. This result constitutes the first
evidence of critical balance in a kinetic turbulence simulation and provides
evidence of an anisotropic turbulence cascade extending into the dissipation
range. We also perform an Eulerian frequency analysis of the simulation data
and compare it to the results of a previous study of magnetohydrodynamic
turbulence simulations.Comment: 10 pages, 9 figures, accepted for publication in Physics of Plasma
On the two-dimensional state in driven magnetohydrodynamic turbulence
The dynamics of the two-dimensional (2D) state in driven tridimensional (3D)
incompressible magnetohydrodynamic turbulence is investigated through
high-resolution direct numerical simulations and in the presence of an external
magnetic field at various intensities. For such a flow the 2D state (or slow
mode) and the 3D modes correspond respectively to spectral fluctuations in the
plan and in the area . It is shown that if
initially the 2D state is set to zero it becomes non negligible in few turnover
times particularly when the external magnetic field is strong. The maintenance
of a large scale driving leads to a break for the energy spectra of 3D modes;
when the driving is stopped the previous break is removed and a decay phase
emerges with alfv\'enic fluctuations. For a strong external magnetic field the
energy at large perpendicular scales lies mainly in the 2D state and in all
situations a pinning effect is observed at small scales.Comment: 11 pages, 11 figure
Is nonhelical hydromagnetic turbulence peaked at small scales?
Nonhelical hydromagnetic turbulence without an imposed magnetic field is
considered in the case where the magnetic Prandtl number is unity. The magnetic
field is entirely due to dynamo action. The magnetic energy spectrum peaks at a
wavenumber of about 5 times the minimum wavenumber in the domain, and not at
the resistive scale, as has previously been argued. Throughout the inertial
range the spectral magnetic energy exceeds the kinetic energy by a factor of
about 2.5, and both spectra are approximately parallel. At first glance, the
total energy spectrum seems to be close to k^{-3/2}, but there is a strong
bottleneck effect and it is suggested that the asymptotic spectrum is k^{-5/3}.
This is supported by the value of the second order structure function exponent
that is found to be \zeta_2=0.70, suggesting a k^{-1.70} spectrum.Comment: 6 pages, 6 figure
A numerical study of the alpha model for two-dimensional magnetohydrodynamic turbulent flows
We explore some consequences of the ``alpha model,'' also called the
``Lagrangian-averaged'' model, for two-dimensional incompressible
magnetohydrodynamic (MHD) turbulence. This model is an extension of the
smoothing procedure in fluid dynamics which filters velocity fields locally
while leaving their associated vorticities unsmoothed, and has proved useful
for high Reynolds number turbulence computations. We consider several known
effects (selective decay, dynamic alignment, inverse cascades, and the
probability distribution functions of fluctuating turbulent quantities) in
magnetofluid turbulence and compare the results of numerical solutions of the
primitive MHD equations with their alpha-model counterparts' performance for
the same flows, in regimes where available resolution is adequate to explore
both. The hope is to justify the use of the alpha model in regimes that lie
outside currently available resolution, as will be the case in particular in
three-dimensional geometry or for magnetic Prandtl numbers differing
significantly from unity. We focus our investigation, using direct numerical
simulations with a standard and fully parallelized pseudo-spectral method and
periodic boundary conditions in two space dimensions, on the role that such a
modeling of the small scales using the Lagrangian-averaged framework plays in
the large-scale dynamics of MHD turbulence. Several flows are examined, and for
all of them one can conclude that the statistical properties of the large-scale
spectra are recovered, whereas small-scale detailed phase information (such as
e.g. the location of structures) is lost.Comment: 22 pages, 20 figure
Strong Imbalanced Turbulence
We consider stationary, forced, imbalanced, or cross-helical MHD Alfvenic
turbulence where the waves traveling in one direction have higher amplitudes
than the opposite waves. This paper is dedicated to so-called strong
turbulence, which cannot be treated perturbatively. Our main result is that the
anisotropy of the weak waves is stronger than the anisotropy of a strong waves.
We propose that critical balance, which was originally conceived as a causality
argument, has to be amended by what we call a propagation argument. This
revised formulation of critical balance is able to handle the imbalanced case
and reduces to old formulation in the balanced case. We also provide
phenomenological model of energy cascading and discuss possibility of
self-similar solutions in a realistic setup of driven turbulence.Comment: this is shorter, 5 page version of what is to appear in ApJ 682, Aug.
1, 200
Numerical simulations of strong incompressible magnetohydrodynamic turbulence
Magnetised plasma turbulence pervades the universe and is likely to play an
important role in a variety of astrophysical settings. Magnetohydrodynamics
(MHD) provides the simplest theoretical framework in which phenomenological
models for the turbulent dynamics can be built. Numerical simulations of MHD
turbulence are widely used to guide and test the theoretical predictions;
however, simulating MHD turbulence and accurately measuring its scaling
properties is far from straightforward. Computational power limits the
calculations to moderate Reynolds numbers and often simplifying assumptions are
made in order that a wider range of scales can be accessed. After describing
the theoretical predictions and the numerical approaches that are often
employed in studying strong incompressible MHD turbulence, we present the
findings of a series of high-resolution direct numerical simulations. We
discuss the effects that insufficiencies in the computational approach can have
on the solution and its physical interpretation
Suppression of small scale dynamo action by an imposed magnetic field
Non-helical hydromagnetic turbulence with an externally imposed magnetic
field is investigated using direct numerical simulations. It is shown that the
imposed magnetic field lowers the spectral magnetic energy in the inertial
range. This is explained by a suppression of the small scale dynamo. At large
scales, however, the spectral magnetic energy increases with increasing imposed
field strength for moderately strong fields, and decreases only slightly for
even stronger fields. The presence of Alfven waves is explicitly confirmed by
monitoring the evolution of magnetic field and velocity at one point. The
frequency omega agrees with vA k1, where vA is the Alfven speed and k1 is the
smallest wavenumber in the box.Comment: Final version (7 pages
On the Nature of Incompressible Magnetohydrodynamic Turbulence
A novel model of incompressible magnetohydrodynamic turbulence in the
presence of a strong external magnetic field is proposed for explanation of
recent numerical results. According to the proposed model, in the presence of
the strong external magnetic field, incompressible magnetohydrodynamic
turbulence becomes nonlocal in the sense that low frequency modes cause
decorrelation of interacting high frequency modes from the inertial interval.
It is shown that the obtained nonlocal spectrum of the inertial range of
incompressible magnetohydrodynamic turbulence represents an anisotropic
analogue of Kraichnan's nonlocal spectrum of hydrodynamic turbulence. Based on
the analysis performed in the framework of the weak coupling approximation,
which represents one of the equivalent formulations of the direct interaction
approximation, it is shown that incompressible magnetohydrodynamic turbulence
could be both local and nonlocal and therefore anisotropic analogues of both
the Kolmogorov and Kraichnan spectra are realizable in incompressible
magnetohydrodynamic turbulence.Comment: Physics of Plasmas (Accepted). A small chapter added about 2D MHD
turbulenc
On spectral scaling laws for incompressible anisotropic MHD turbulence
A heuristic model is given for anisotropic magnetohydrodynamics (MHD)
turbulence in the presence of a uniform external magnetic field B_0 {\bf {\hat
e}_{\pa}}. The model is valid for both moderate and strong and is able
to describe both the strong and weak wave turbulence regimes as well as the
transition between them. The main ingredient of the model is the assumption of
constant ratio at all scales between \add{the} linear wave period and \add{the}
nonlinear turnover timescale. Contrary to the model of critical balance
introduced by Goldreich and Sridhar [P. Goldreich and S. Sridhar, ApJ {\bf
438}, 763 (1995)], it is not assumed in addition that this ratio be equal to
unity at all scales which allows us to use the Iroshnikov-Kraichnan
phenomenology. It is then possible to recover the widely observed anisotropic
scaling law \kpa \propto \kpe^{2/3} between parallel and perpendicular
wavenumbers (with reference to B_0 {\bf {\hat e}_{\pa}}) and to obtain the
universal prediction, , for the total energy spectrum
E(\kpe,\kpa) \sim \kpe^{-\alpha} \kpa^{-\beta}. In particular, with such a
prediction the weak Alfv\'en wave turbulence constant-flux solution is
recovered and, for the first time, a possible explanation to its precursor
found numerically by Galtier et al [S. Galtier et al., J. Plasma Phys. {\bf
63}, 447 (2000)] is given
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