61 research outputs found
The Generation of Magnetic Fields Through Driven Turbulence
We have tested the ability of driven turbulence to generate magnetic field
structure from a weak uniform field using three dimensional numerical
simulations of incompressible turbulence. We used a pseudo-spectral code with a
numerical resolution of up to collocation points. We find that the
magnetic fields are amplified through field line stretching at a rate
proportional to the difference between the velocity and the magnetic field
strength times a constant. Equipartition between the kinetic and magnetic
energy densities occurs at a scale somewhat smaller than the kinetic energy
peak. Above the equipartition scale the velocity structure is, as expected,
nearly isotropic. The magnetic field structure at these scales is uncertain,
but the field correlation function is very weak. At the equipartition scale the
magnetic fields show only a moderate degree of anisotropy, so that the typical
radius of curvature of field lines is comparable to the typical perpendicular
scale for field reversal. In other words, there are few field reversals within
eddies at the equipartition scale, and no fine-grained series of reversals at
smaller scales. At scales below the equipartition scale, both velocity and
magnetic structures are anisotropic; the eddies are stretched along the local
magnetic field lines, and the magnetic energy dominates the kinetic energy on
the same scale by a factor which increases at higher wavenumbers. We do not
show a scale-free inertial range, but the power spectra are a function of
resolution and/or the imposed viscosity and resistivity. Our results are
consistent with the emergence of a scale-free inertial range at higher Reynolds
numbers.Comment: 14 pages (8 NEW figures), ApJ, in press (July 20, 2000?
Radio-wave propagation through a medium containing electron-density fluctuations described by an anisotropic Goldreich-Sridhar spectrum
We study the propagation of radio waves through a medium possessing density
fluctuations that are elongated along the ambient magnetic field and described
by an anisotropic Goldreich-Sridhar power spectrum. We derive general formulas
for the wave phase structure function, visibility, angular broadening,
diffraction-pattern length scales, and scintillation time scale for arbitrary
distributions of turbulence along the line of sight, and specialize these
formulas to idealized cases.Comment: 25 pages, 3 figures, submitted to Ap
Simulating Supersonic Turbulence in Magnetized Molecular Clouds
We present results of large-scale three-dimensional simulations of weakly
magnetized supersonic turbulence at grid resolutions up to 1024^3 cells. Our
numerical experiments are carried out with the Piecewise Parabolic Method on a
Local Stencil and assume an isothermal equation of state. The turbulence is
driven by a large-scale isotropic solenoidal force in a periodic computational
domain and fully develops in a few flow crossing times. We then evolve the flow
for a number of flow crossing times and analyze various statistical properties
of the saturated turbulent state. We show that the energy transfer rate in the
inertial range of scales is surprisingly close to a constant, indicating that
Kolmogorov's phenomenology for incompressible turbulence can be extended to
magnetized supersonic flows. We also discuss numerical dissipation effects and
convergence of different turbulence diagnostics as grid resolution refines from
256^3 to 1024^3 cells.Comment: 10 pages, 3 figures, to appear in the proceedings of the DOE/SciDAC
2009 conferenc
Perpendicular Ion Heating by Low-Frequency Alfven-Wave Turbulence in the Solar Wind
We consider ion heating by turbulent Alfven waves (AWs) and kinetic Alfven
waves (KAWs) with perpendicular wavelengths comparable to the ion gyroradius
and frequencies smaller than the ion cyclotron frequency. When the turbulence
amplitude exceeds a certain threshold, an ion's orbit becomes chaotic. The ion
then interacts stochastically with the time-varying electrostatic potential,
and the ion's energy undergoes a random walk. Using phenomenological arguments,
we derive an analytic expression for the rates at which different ion species
are heated, which we test by simulating test particles interacting with a
spectrum of randomly phased AWs and KAWs. We find that the stochastic heating
rate depends sensitively on the quantity epsilon = dv/vperp, where vperp is the
component of the ion velocity perpendicular to the background magnetic field
B0, and dv (dB) is the rms amplitude of the velocity (magnetic-field)
fluctuations at the gyroradius scale. In the case of thermal protons, when
epsilon << eps1, where eps1 is a constant, a proton's magnetic moment is nearly
conserved and stochastic heating is extremely weak. However, when epsilon >
eps1, the proton heating rate exceeds the cascade power that would be present
in strong balanced KAW turbulence with the same value of dv, and
magnetic-moment conservation is violated. For the random-phase waves in our
test-particle simulations, eps1 is approximately 0.2. For protons in low-beta
plasmas, epsilon is approximately dB/B0 divided by the square root of beta, and
epsilon can exceed eps1 even when dB/B0 << eps1. At comparable temperatures,
alpha particles and minor ions have larger values of epsilon than protons and
are heated more efficiently as a result. We discuss the implications of our
results for ion heating in coronal holes and the solar wind.Comment: 14 pages, 5 figures, submitted to Ap
Systematics of the magnetic-Prandtl-number dependence of homogeneous, isotropic magnetohydrodynamic turbulence
We present the results of our detailed pseudospectral direct numerical
simulation (DNS) studies, with up to collocation points, of
incompressible, magnetohydrodynamic (MHD) turbulence in three dimensions,
without a mean magnetic field. Our study concentrates on the dependence of
various statistical properties of both decaying and statistically steady MHD
turbulence on the magnetic Prandtl number over a large range,
namely, . We obtain data for a wide variety of
statistical measures such as probability distribution functions (PDFs) of
moduli of the vorticity and current density, the energy dissipation rates, and
velocity and magnetic-field increments, energy and other spectra, velocity and
magnetic-field structure functions, which we use to characterise intermittency,
isosurfaces of quantities such as the moduli of the vorticity and current, and
joint PDFs such as those of fluid and magnetic dissipation rates. Our
systematic study uncovers interesting results that have not been noted
hitherto. In particular, we find a crossover from larger intermittency in the
magnetic field than in the velocity field, at large , to smaller
intermittency in the magnetic field than in the velocity field, at low . Furthermore, a comparison of our results for decaying MHD turbulence
and its forced, statistically steady analogue suggests that we have strong
universality in the sense that, for a fixed value of , multiscaling
exponent ratios agree, at least within our errorbars, for both decaying and
statistically steady homogeneous, isotropic MHD turbulence.Comment: 49 pages,33 figure
Statistical features of rapidly rotating decaying turbulence: Enstrophy and energy spectra and coherent structures
In this paper we investigate the properties of rapidly rotating decaying
turbulence using numerical simulations and phenomenological modelling. We find
that as the turbulent flow evolves in time, the Rossby number decreases to
, and the flow becomes quasi-two-dimensional with strong coherent
columnar structures arising due to the inverse cascade of energy. We establish
that a major fraction of energy is confined in Fourier modes and
that correspond to the largest columnar structure in the flow. For
wavenumbers () greater than the enstrophy dissipation wavenumber (),
our phenomenological arguments and numerical study show that the enstrophy flux
and spectrum of a horizontal cross-section perpendicular to the axis of
rotation are given by and
respectively; for this 2D flow,
is the enstrophy dissipation rate, and is a constant.
Using these results, we propose a new form for the energy spectrum of rapidly
rotating decaying turbulence:
. This model of the energy
spectrum is based on wavenumber-dependent enstrophy flux, and it deviates
significantly from power law energy spectrum reported earlier
Colloquium: Nonlinear collective interactions in quantum plasmas with degenerate electron fluids
The current understanding of some important nonlinear collective processes in
quantum plasmas with degenerate electrons is presented. After reviewing the
basic properties of quantum plasmas, we present model equations (e.g. the
quantum hydrodynamic and effective nonlinear Schr\"odinger-Poisson equations)
that describe collective nonlinear phenomena at nanoscales. The effects of the
electron degeneracy arise due to Heisenberg's uncertainty principle and Pauli's
exclusion principle for overlapping electron wavefunctions that result in
tunneling of electrons and the electron degeneracy pressure. Since electrons
are Fermions (spin-1/2), there also appears an electron spin current and a spin
force acting on electrons due to the Bohr magnetization. The quantum effects
produce new aspects of electrostatic (ES) and electromagnetic (EM) waves in a
quantum plasma that are summarized in here. Furthermore, we discuss nonlinear
features of ES ion waves and electron plasma oscillations (ESOs), as well as
the trapping of intense EM waves in quantum electron density cavities.
Specifically, simulation studies of the coupled nonlinear Schr\"odinger (NLS)
and Poisson equations reveal the formation and dynamics of localized ES
structures at nanoscales in a quantum plasma. We also discuss the effect of an
external magnetic field on the plasma wave spectra and develop quantum
magnetohydrodynamic (Q-MHD) equations. The results are useful for understanding
numerous collective phenomena in quantum plasmas, such as those in compact
astrophysical objects, in plasma-assisted nanotechnology, and in the
next-generation of intense laser-solid density plasma interaction experiments.Comment: 25 pages, 14 figures. To be published in Reviews of Modern Physic
Astrophysical turbulence modeling
The role of turbulence in various astrophysical settings is reviewed. Among
the differences to laboratory and atmospheric turbulence we highlight the
ubiquitous presence of magnetic fields that are generally produced and
maintained by dynamo action. The extreme temperature and density contrasts and
stratifications are emphasized in connection with turbulence in the
interstellar medium and in stars with outer convection zones, respectively. In
many cases turbulence plays an essential role in facilitating enhanced
transport of mass, momentum, energy, and magnetic fields in terms of the
corresponding coarse-grained mean fields. Those transport properties are
usually strongly modified by anisotropies and often completely new effects
emerge in such a description that have no correspondence in terms of the
original (non coarse-grained) fields.Comment: 88 pages, 26 figures, published in Reports on Progress in Physic
Theory and Applications of Non-Relativistic and Relativistic Turbulent Reconnection
Realistic astrophysical environments are turbulent due to the extremely high
Reynolds numbers. Therefore, the theories of reconnection intended for
describing astrophysical reconnection should not ignore the effects of
turbulence on magnetic reconnection. Turbulence is known to change the nature
of many physical processes dramatically and in this review we claim that
magnetic reconnection is not an exception. We stress that not only
astrophysical turbulence is ubiquitous, but also magnetic reconnection itself
induces turbulence. Thus turbulence must be accounted for in any realistic
astrophysical reconnection setup. We argue that due to the similarities of MHD
turbulence in relativistic and non-relativistic cases the theory of magnetic
reconnection developed for the non-relativistic case can be extended to the
relativistic case and we provide numerical simulations that support this
conjecture. We also provide quantitative comparisons of the theoretical
predictions and results of numerical experiments, including the situations when
turbulent reconnection is self-driven, i.e. the turbulence in the system is
generated by the reconnection process itself. We show how turbulent
reconnection entails the violation of magnetic flux freezing, the conclusion
that has really far reaching consequences for many realistically turbulent
astrophysical environments. In addition, we consider observational testing of
turbulent reconnection as well as numerous implications of the theory. The
former includes the Sun and solar wind reconnection, while the latter include
the process of reconnection diffusion induced by turbulent reconnection, the
acceleration of energetic particles, bursts of turbulent reconnection related
to black hole sources as well as gamma ray bursts. Finally, we explain why
turbulent reconnection cannot be explained by turbulent resistivity or derived
through the mean field approach.Comment: 66 pages, 24 figures, a chapter of the book "Magnetic Reconnection -
Concepts and Applications", editors W. Gonzalez, E. N. Parke
Simulations of small-scale turbulent dynamo
We report an extensive numerical study of the small-scale turbulent dynamo at
large magnetic Prandtl numbers Pm. A Pm scan is given for the model case of
low-Reynolds-number turbulence. We concentrate on three topics: magnetic-energy
spectra and saturation levels, the structure of the field lines, and the
field-strength distribution. The main results are (1) the folded structure
(direction reversals at the resistive scale, field lines curved at the scale of
the flow) persists from the kinematic to the nonlinear regime; (2) the field
distribution is self-similar and appears to be lognormal during the kinematic
regime and exponential in the saturated state; and (3) the bulk of the magnetic
energy is at the resistive scale in the kinematic regime and remains there
after saturation, although the spectrum becomes much shallower. We propose an
analytical model of saturation based on the idea of partial
two-dimensionalization of the velocity gradients with respect to the local
direction of the magnetic folds. The model-predicted spectra are in excellent
agreement with numerical results. Comparisons with large-Re, moderate-Pm runs
are carried out to confirm the relevance of these results. New features at
large Re are elongation of the folds in the nonlinear regime from the viscous
scale to the box scale and the presence of an intermediate nonlinear stage of
slower-than-exponential magnetic-energy growth accompanied by an increase of
the resistive scale and partial suppression of the kinetic-energy spectrum in
the inertial range. Numerical results for the saturated state do not support
scale-by-scale equipartition between magnetic and kinetic energies, with a
definite excess of magnetic energy at small scales. A physical picture of the
saturated state is proposed.Comment: aastex using emulateapj; 32 pages, final published version; a pdf
file (4Mb) of the paper containing better-quality versions of figs. 5, 8, 12,
15, 17 is available from http://www.damtp.cam.ac.uk/user/as629 or by email
upon request
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