1,570 research outputs found
Information theory analysis of cascading process in a synthetic model of fluid turbulence
The use of transfer entropy has proven to be helpful in detecting which is the verse of dynamical driving in the interaction of two processes, X and Y . In this paper, we present a different normalization for the transfer entropy, which is capable of better detecting the information transfer direction. This new normalized transfer entropy is applied to the detection of the verse of energy flux transfer in a synthetic model of fluid turbulence, namely the Gledzer–Ohkitana–Yamada shell model. Indeed, this is a fully well-known model able to model the fully developed turbulence in the Fourier space, which is characterized by an energy cascade towards the small scales (large wavenumbers k), so that the application of the information-theory analysis to its outcome tests the reliability of the analysis tool rather than exploring the model physics. As a result, the presence of a direct cascade along the scales in the shell model and the locality of the interactions in the space of wavenumbers come out as expected, indicating the validity of this data analysis tool. In this context, the use of a normalized version of transfer entropy, able to account for the difference of the intrinsic randomness of the interacting processes, appears to perform better, being able to discriminate the wrong conclusions to which the “traditional” transfer entropy would drive
Damping of MHD turbulence in partially ionized gas and the observed difference of velocities of neutrals and ions
Theoretical and observational studies on the turbulence of the interstellar
medium developed fast in the past decades. The theory of supersonic magnetized
turbulence, as well as the understanding of projection effects of observed
quantities, are still in progress. In this work we explore the characterization
of the turbulent cascade and its damping from observational spectral line
profiles. We address the difference of ion and neutral velocities by clarifying
the nature of the turbulence damping in the partially ionized. We provide
theoretical arguments in favor of the explanation of the larger Doppler
broadening of lines arising from neutral species compared to ions as arising
from the turbulence damping of ions at larger scales. Also, we compute a number
of MHD numerical simulations for different turbulent regimes and explicit
turbulent damping, and compare both the 3-dimensional distributions of velocity
and the synthetic line profile distributions. From the numerical simulations,
we place constraints on the precision with which one can measure the 3D
dispersion depending on the turbulence sonic Mach number. We show that no
universal correspondence between the 3D velocity dispersions measured in the
turbulent volume and minima of the 2D velocity dispersions available through
observations exist. For instance, for subsonic turbulence the correspondence is
poor at scales much smaller than the turbulence injection scale, while for
supersonic turbulence the correspondence is poor for the scales comparable with
the injection scale. We provide a physical explanation of the existence of such
a 2D-3D correspondence and discuss the uncertainties in evaluating the damping
scale of ions that can be obtained from observations. However, we show that the
statistics of velocity dispersion from observed line profiles can provide the
spectral index and the energy transfer rate of turbulence. Also, comparing two
similar simulations with different viscous coefficients it was possible to
constrain the turbulent cut-off scale. This may especially prove useful since
it is believed that ambipolar diffusion may be one of the dominant dissipative
mechanism in star-forming regions. In this case, the determination of the
ambipolar diffusion scale may be used as a complementary method for the
determination of magnetic field intensity in collapsing cores. We discuss the
implications of our findings in terms of a new approach to magnetic field
measurement proposed by Li & Houde (2008).Comment: ApJ accepte
Linewidth Differences of Neutrals and Ions Induced by MHD Turbulence
We address the problem of the difference of line widths of neutrals and ions
observed from molecular clouds and explore whether this difference can arise
from the effects of magnetohydrodynamic (MHD) turbulence acting on partially
ionized gas. Among the three fundamental modes of MHD turbulence, we find fast
modes do not contribute to linewidth differences, whereas slow modes can have
an effect on different line widths for certain parameters. We focus on
Alfv\'{e}nic component because they contain most of the turbulent energy, and
consider the damping of this component taking into account both neutral-ion
collisions and neutral viscosity. We consider different regimes of turbulence
corresponding to different media magnetizations and turbulent drivings. In the
case of super-Alfv\'{e}nic turbulence, when the damping scale of Alfv\'{e}nic
turbulence is below , where is the injection scale of anisotropic
GS95-type turbulence, the linewidth difference does not depend on the magnetic
field strength. While for other turbulent regimes, the dependence is present.
For instance, the difference between the squares of the neutral and ion
velocity dispersions in strong sub-Alfv\'{e}nic turbulence allows evaluation of
magnetic field. We discuss earlier findings on the neutral-ion linewidth
differences in the literature and compare the expressions for magnetic field we
obtain with those published earlier.Comment: 26 pages, 8 figure
Scaling of Information in Turbulence
We propose a new perspective on Turbulence using Information Theory. We
compute the entropy rate of a turbulent velocity signal and we particularly
focus on its dependence on the scale. We first report how the entropy rate is
able to describe the distribution of information amongst scales, and how one
can use it to isolate the injection, inertial and dissipative ranges, in
perfect agreement with the Batchelor model and with a fBM model. In a second
stage, we design a conditioning procedure in order to finely probe the
asymmetries in the statistics that are responsible for the energy cascade. Our
approach is very generic and can be applied to any multiscale complex system.Comment: in Europhysics Letters, 201
A three-dimensional wavelet based multifractal method : about the need of revisiting the multifractal description of turbulence dissipation data
We generalize the wavelet transform modulus maxima (WTMM) method to
multifractal analysis of 3D random fields. This method is calibrated on
synthetic 3D monofractal fractional Brownian fields and on 3D multifractal
singular cascade measures as well as their random function counterpart obtained
by fractional integration. Then we apply the 3D WTMM method to the dissipation
field issue from 3D isotropic turbulence simulations. We comment on the need to
revisiting previous box-counting analysis which have failed to estimate
correctly the corresponding multifractal spectra because of their intrinsic
inability to master non-conservative singular cascade measures.Comment: 5 pages, 3figures, submitted to Phys. Rev. Let
Evidence of Intermittent Cascades from Discrete Hierarchical Dissipation in Turbulence
We present the results of a search of log-periodic corrections to scaling in
the moments of the energy dissipation rate in experiments at high Reynolds
number (2500) of three-dimensional fully developed turbulence. A simple
dynamical representation of the Richardson-Kolmogorov cartoon of a cascade
shows that standard averaging techniques erase by their very construction the
possible existence of log-periodic corrections to scaling associated with a
discrete hierarchy. To remedy this drawback, we introduce a novel ``canonical''
averaging that we test extensively on synthetic examples constructed to mimick
the interplay between a weak log-periodic component and rather strong
multiplicative and phase noises. Our extensive tests confirm the remarkable
observation of statistically significant log-periodic corrections to scaling,
with a prefered scaling ratio for length scales compatible with the value gamma
= 2. A strong confirmation of this result is provided by the identification of
up to 5 harmonics of the fundamental log-periodic undulations, associated with
up to 5 levels of the underlying hierarchical dynamical structure. A natural
interpretation of our results is that the Richardson-Kolmogorov mental picture
of a cascade becomes a realistic description if one allows for intermittent
births and deaths of discrete cascades at varying scales.Comment: Latex document of 40 pages, including 18 eps figure
Quantifying and containing the curse of high resolution coronal imaging
Future missions such as Solar Orbiter (SO), InterHelioprobe, or Solar Probe
aim at approaching the Sun closer than ever before, with on board some high
resolution imagers (HRI) having a subsecond cadence and a pixel area of about
at the Sun during perihelion. In order to guarantee their scientific
success, it is necessary to evaluate if the photon counts available at these
resolution and cadence will provide a sufficient signal-to-noise ratio (SNR).
We perform a first step in this direction by analyzing and characterizing the
spatial intermittency of Quiet Sun images thanks to a multifractal analysis.
We identify the parameters that specify the scale-invariance behavior. This
identification allows next to select a family of multifractal processes, namely
the Compound Poisson Cascades, that can synthesize artificial images having
some of the scale-invariance properties observed on the recorded images.
The prevalence of self-similarity in Quiet Sun coronal images makes it
relevant to study the ratio between the SNR present at SoHO/EIT images and in
coarsened images. SoHO/EIT images thus play the role of 'high resolution'
images, whereas the 'low-resolution' coarsened images are rebinned so as to
simulate a smaller angular resolution and/or a larger distance to the Sun. For
a fixed difference in angular resolution and in Spacecraft-Sun distance, we
determine the proportion of pixels having a SNR preserved at high resolution
given a particular increase in effective area. If scale-invariance continues to
prevail at smaller scales, the conclusion reached with SoHO/EIT images can be
transposed to the situation where the resolution is increased from SoHO/EIT to
SO/HRI resolution at perihelion.Comment: 25 pages, 1 table, 7 figure
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