202 research outputs found
Role of cross helicity in magnetohydrodynamic turbulence
Strong incompressible three-dimensional magnetohydrodynamic turbulence is
investigated by means of high resolution direct numerical simulations. The
simulations show that the configuration space is characterized by regions of
positive and negative cross-helicity, corresponding to highly aligned or
anti-aligned velocity and magnetic field fluctuations, even when the average
cross-helicity is zero. To elucidate the role of cross-helicity, the spectra
and structure of turbulence are obtained in imbalanced regions where
cross-helicity is non-zero. When averaged over regions of positive and negative
cross-helicity, the result is consistent with the simulations of balanced
turbulence. An analytical explanation for the obtained results is proposed.Comment: 4 pages, 4 figure
Weak and strong regimes of incompressible magnetohydrodynamic turbulence
It is shown that in the framework of the weak turbulence theory, the
autocorrelation and cascade timescales are always of the same order of
magnitude. This means that, contrary to the general belief, any model of
turbulence which implies a large number of collisions among wave packets for an
efficient energy cascade (such as the Iroshnikov-Kraichnan model) are not
compatible with the weak turbulence theory.Comment: Accepted to Phys. Plasma
The Lagrangian frequency spectrum as a diagnostic for magnetohydrodynamic turbulence dynamics
For the phenomenological description of magnetohydrodynamic turbulence
competing models exist, e.g. Boldyrev [Phys.Rev.Lett. \textbf{96}, 115002,
2006] and Gogoberidze [Phys.Plas. \textbf{14}, 022304, 2007], which predict the
same Eulerian inertial-range scaling of the turbulent energy spectrum although
they employ fundamentally different basic interaction mechanisms. {A relation
is found that links} the Lagrangian frequency spectrum {with} the
autocorrelation timescale of the turbulent fluctuations, ,
and the associated cascade timescale, . Thus, the
Lagrangian energy spectrum can serve to identify weak
() and strong
() interaction mechanisms providing
insight into the turbulent energy cascade. The new approach is illustrated by
results from direct numerical simulations of two- and three-dimensional
incompressible MHD turbulence.Comment: accepted for publication in PR
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
Energy spectra stemming from interactions of Alfven waves and turbulent eddies
We present a numerical analysis of an incompressible decaying
magnetohydrodynamic turbulence run on a grid of 1536^3 points. The Taylor
Reynolds number at the maximum of dissipation is ~1100, and the initial
condition is a superposition of large scale ABC flows and random noise at small
scales, with no uniform magnetic field. The initial kinetic and magnetic
energies are equal, with negligible correlation. The resulting energy spectrum
is a combination of two components, each moderately resolved. Isotropy obtains
in the large scales, with a spectral law compatible with the
Iroshnikov-Kraichnan theory stemming from the weakening of nonlinear
interactions due to Alfven waves; scaling of structure functions confirms the
non-Kolmogorovian nature of the flow in this range. At small scales, weak
turbulence emerges with a k_{\perp}^{-2} spectrum, the perpendicular direction
referring to the local quasi-uniform magnetic field.Comment: 4 pages, 4 figure
MHD Turbulence Revisited
Kraichnan (1965) proposed that MHD turbulence occurs as a result of
collisions between oppositely directed Alfv\'en wave packets. Recent work has
generated some controversy over the nature of non linear couplings between
colliding Alfv\'en waves. We find that the resolution to much of the confusion
lies in the existence of a new type of turbulence, intermediate turbulence, in
which the cascade of energy in the inertial range exhibits properties
intermediate between those of weak and strong turbulent cascades. Some
properties of intermediate MHD turbulence are: (i) in common with weak
turbulent cascades, wave packets belonging to the inertial range are long
lived; (ii) however, components of the strain tensor are so large that, similar
to the situation in strong turbulence, perturbation theory is not applicable;
(iii) the breakdown of perturbation theory results from the divergence of
neighboring field lines due to wave packets whose perturbations in velocity and
magnetic fields are localized, but whose perturbations in displacement are not;
(iv) 3--wave interactions dominate individual collisions between wave packets,
but interactions of all orders make comparable contributions to the
intermediate turbulent energy cascade; (v) successive collisions are correlated
since wave packets are distorted as they follow diverging field lines; (vi) in
common with the weak MHD cascade, there is no parallel cascade of energy, and
the cascade to small perpendicular scales strengthens as it reaches higher wave
numbers; (vii) For an appropriate weak excitation, there is a natural
progression from a weak, through an intermediate, to a strong cascade.Comment: 25 pages, to appear in The Astrophysical Journa
The Spectral Slope and Kolmogorov Constant of MHD turbulence
The spectral slope of strong MHD turbulence has recently been a matter of
controversy. While Goldreich-Sridhar model (1995) predicts Kolmogorov's -5/3
slope of turbulence, shallower slopes were often reported by numerical studies.
We argue that earlier numerics was affected by driving due to a diffuse
locality of energy transfer in MHD case. Our highest-resolution simulation
(3072^2x1024) has been able to reach the asymptotic -5/3 regime of the energy
slope. Additionally, we found that so-called dynamic alignment, proposed in the
model with -3/2 slope, saturates and therefore can not affect asymptotic slope.
The observation of the asymptotic regime allowed us to measure Kolmogorov
constant C_KA=3.2+-0.2 for purely Alfv\'enic turbulence and C_K=4.1+-0.3 for
full MHD turbulence. These values are much higher than the hydrodynamic value
of 1.64. The larger value of Kolmogorov constant is an indication of a fairly
inefficient energy transfer and, as we show in this Letter, is in theoretical
agreement with our observation of diffuse locality. We also explain what has
been missing in numerical studies that reported shallower slopes.Comment: 5 pages 3 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.
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