486 research outputs found
The Statistics of Supersonic Isothermal Turbulence
We present results of large-scale three-dimensional simulations of supersonic
Euler turbulence with the piecewise parabolic method and multiple grid
resolutions up to 2048^3 points. Our numerical experiments describe
non-magnetized driven turbulent flows with an isothermal equation of state and
an rms Mach number of 6. We discuss numerical resolution issues and demonstrate
convergence, in a statistical sense, of the inertial range dynamics in
simulations on grids larger than 512^3 points. The simulations allowed us to
measure the absolute velocity scaling exponents for the first time. The
inertial range velocity scaling in this strongly compressible regime deviates
substantially from the incompressible Kolmogorov laws. The slope of the
velocity power spectrum, for instance, is -1.95 compared to -5/3 in the
incompressible case. The exponent of the third-order velocity structure
function is 1.28, while in incompressible turbulence it is known to be unity.
We propose a natural extension of Kolmogorov's phenomenology that takes into
account compressibility by mixing the velocity and density statistics and
preserves the Kolmogorov scaling of the power spectrum and structure functions
of the density-weighted velocity v=\rho^{1/3}u. The low-order statistics of v
appear to be invariant with respect to changes in the Mach number. For
instance, at Mach 6 the slope of the power spectrum of v is -1.69, and the
exponent of the third-order structure function of v is unity. We also directly
measure the mass dimension of the "fractal" density distribution in the
inertial subrange, D_m = 2.4, which is similar to the observed fractal
dimension of molecular clouds and agrees well with the cascade phenomenology.Comment: 15 pages, 19 figures, ApJ v665, n2, 200
Multiscale statistical analysis of coronal solar activity
Multi-filter images from the solar corona are used to obtain temperature maps
which are analyzed using techniques based on proper orthogonal decomposition
(POD) in order to extract dynamical and structural information at various
scales. Exploring active regions before and after a solar flare and comparing
them with quiet regions we show that the multiscale behavior presents distinct
statistical properties for each case that can be used to characterize the level
of activity in a region. Information about the nature of heat transport is also
be extracted from the analysis.Comment: 24 pages, 18 figure
Multi-D magnetohydrodynamic modelling of pulsar wind nebulae: recent progress and open questions
In the last decade, the relativistic magnetohydrodynamic (MHD) modelling of
pulsar wind nebulae, and of the Crab nebula in particular, has been highly
successful, with many of the observed dynamical and emission properties
reproduced down to the finest detail. Here, we critically discuss the results
of some of the most recent studies: namely the investigation of the origin of
the radio emitting particles and the quest for the acceleration sites of
particles of different energies along the termination shock, by using wisps
motion as a diagnostic tool; the study of the magnetic dissipation process in
high magnetization nebulae by means of new long-term three-dimensional
simulations of the pulsar wind nebula evolution; the investigation of the
relativistic tearing instability in thinning current sheets, leading to fast
reconnection events that might be at the origin of the Crab nebula gamma-ray
flares.Comment: 30 pages, 12 figure
Tensor Approximation for Multidimensional and Multivariate Data
Tensor decomposition methods and multilinear algebra are powerful tools to cope with challenges around multidimensional and multivariate data in computer graphics, image processing and data visualization, in particular with respect to compact representation and processing of increasingly large-scale data sets. Initially proposed as an extension of the concept of matrix rank for 3 and more dimensions, tensor decomposition methods have found applications in a remarkably wide range of disciplines. We briefly review the main concepts of tensor decompositions and their application to multidimensional visual data. Furthermore, we will include a first outlook on porting these techniques to multivariate data such as vector and tensor fields
Lagrangian ADER-WENO Finite Volume Schemes on Unstructured Triangular Meshes Based On Genuinely Multidimensional HLL Riemann Solvers
In this paper we use the genuinely multidimensional HLL Riemann solvers
recently developed by Balsara et al. to construct a new class of
computationally efficient high order Lagrangian ADER-WENO one-step ALE finite
volume schemes on unstructured triangular meshes. A nonlinear WENO
reconstruction operator allows the algorithm to achieve high order of accuracy
in space, while high order of accuracy in time is obtained by the use of an
ADER time-stepping technique based on a local space-time Galerkin predictor.
The multidimensional HLL and HLLC Riemann solvers operate at each vertex of the
grid, considering the entire Voronoi neighborhood of each node and allows for
larger time steps than conventional one-dimensional Riemann solvers. The
results produced by the multidimensional Riemann solver are then used twice in
our one-step ALE algorithm: first, as a node solver that assigns a unique
velocity vector to each vertex, in order to preserve the continuity of the
computational mesh; second, as a building block for genuinely multidimensional
numerical flux evaluation that allows the scheme to run with larger time steps
compared to conventional finite volume schemes that use classical
one-dimensional Riemann solvers in normal direction. A rezoning step may be
necessary in order to overcome element overlapping or crossing-over. We apply
the method presented in this article to two systems of hyperbolic conservation
laws, namely the Euler equations of compressible gas dynamics and the equations
of ideal classical magneto-hydrodynamics (MHD). Convergence studies up to
fourth order of accuracy in space and time have been carried out. Several
numerical test problems have been solved to validate the new approach
Cascades and transitions in turbulent flows
Turbulence is characterized by the non-linear cascades of energy and other
inviscid invariants across a huge range of scales, from where they are injected
to where they are dissipated. Recently, new experimental, numerical and
theoretical works have revealed that many turbulent configurations deviate from
the ideal 3D/2D isotropic cases characterized by the presence of a strictly
direct/inverse energy cascade, respectively. We review recent works from a
unified point of view and we present a classification of all known transfer
mechanisms. Beside the classical cases of direct and inverse cascades, the
different scenarios include: split cascades to small and large scales
simultaneously, multiple/dual cascades of different quantities, bi-directional
cascades where direct and inverse transfers of the same invariant coexist in
the same scale-range and finally equilibrium states where no cascades are
present, including the case when a condensate is formed. We classify all
transitions as the control parameters are changed and we analyse when and why
different configurations are observed. Our discussion is based on a set of
paradigmatic applications: helical turbulence, rotating and/or stratified
flows, MHD and passive/active scalars where the transfer properties are altered
as one changes the embedding dimensions, the thickness of the domain or other
relevant control parameters, as the Reynolds, Rossby, Froude, Peclet, or Alfven
numbers. We discuss the presence of anomalous scaling laws in connection with
the intermittent nature of the energy dissipation in configuration space. An
overview is also provided concerning cascades in other applications such as
bounded flows, quantum, relativistic and compressible turbulence, and active
matter, together with implications for turbulent modelling. Finally, we present
a series of open problems and challenges that future work needs to address.Comment: accepted for publication on Physics Reports 201
Ideal evolution of MHD turbulence when imposing Taylor-Green symmetries
We investigate the ideal and incompressible magnetohydrodynamic (MHD)
equations in three space dimensions for the development of potentially singular
structures. The methodology consists in implementing the four-fold symmetries
of the Taylor-Green vortex generalized to MHD, leading to substantial computer
time and memory savings at a given resolution; we also use a re-gridding method
that allows for lower-resolution runs at early times, with no loss of spectral
accuracy. One magnetic configuration is examined at an equivalent resolution of
points, and three different configurations on grids of
points. At the highest resolution, two different current and vorticity sheet
systems are found to collide, producing two successive accelerations in the
development of small scales. At the latest time, a convergence of magnetic
field lines to the location of maximum current is probably leading locally to a
strong bending and directional variability of such lines. A novel analytical
method, based on sharp analysis inequalities, is used to assess the validity of
the finite-time singularity scenario. This method allows one to rule out
spurious singularities by evaluating the rate at which the logarithmic
decrement of the analyticity-strip method goes to zero. The result is that the
finite-time singularity scenario cannot be ruled out, and the singularity time
could be somewhere between and More robust conclusions will
require higher resolution runs and grid-point interpolation measurements of
maximum current and vorticity.Comment: 18 pages, 13 figures, 2 tables; submitted to Physical Review
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