768 research outputs found
Arbitrary-order Hilbert spectral analysis for time series possessing scaling statistics: a comparison study with detrended fluctuation analysis and wavelet leaders
In this paper we present an extended version of Hilbert-Huang transform,
namely arbitrary-order Hilbert spectral analysis, to characterize the
scale-invariant properties of a time series directly in an amplitude-frequency
space. We first show numerically that due to a nonlinear distortion,
traditional methods require high-order harmonic components to represent
nonlinear processes, except for the Hilbert-based method. This will lead to an
artificial energy flux from the low-frequency (large scale) to the
high-frequency (small scale) part. Thus the power law, if it exists, is
contaminated. We then compare the Hilbert method with structure functions (SF),
detrended fluctuation analysis (DFA), and wavelet leader (WL) by analyzing
fractional Brownian motion and synthesized multifractal time series. For the
former simulation, we find that all methods provide comparable results. For the
latter simulation, we perform simulations with an intermittent parameter {\mu}
= 0.15. We find that the SF underestimates scaling exponent when q > 3. The
Hilbert method provides a slight underestimation when q > 5. However, both DFA
and WL overestimate the scaling exponents when q > 5. It seems that Hilbert and
DFA methods provide better singularity spectra than SF and WL. We finally apply
all methods to a passive scalar (temperature) data obtained from a jet
experiment with a Taylor's microscale Reynolds number Relambda \simeq 250. Due
to the presence of strong ramp-cliff structures, the SF fails to detect the
power law behavior. For the traditional method, the ramp-cliff structure causes
a serious artificial energy flux from the low-frequency (large scale) to the
high-frequency (small scale) part. Thus DFA and WL underestimate the scaling
exponents. However, the Hilbert method provides scaling exponents
{\xi}{\theta}(q) quite close to the one for longitudinal velocity.Comment: 13 pages, 10 figure
Sub-Kolmogorov-Scale Fluctuations in Fluid Turbulence
We relate the intermittent fluctuations of velocity gradients in turbulence
to a whole range of local dissipation scales generalizing the picture of a
single mean dissipation length. The statistical distribution of these local
dissipation scales as a function of Reynolds number is determined in numerical
simulations of forced homogeneous isotropic turbulence with a spectral
resolution never applied before which exceeds the standard one by at least a
factor of eight. The core of the scale distribution agrees well with a
theoretical prediction. Increasing Reynolds number causes the generation of
ever finer local dissipation scales. This is in line with a less steep decay of
the large-wavenumber energy spectra in the dissipation range. The energy
spectrum for the highest accessible Taylor microscale Reynolds number
R_lambda=107 does not show a bottleneck.Comment: 8 pages, 5 figures (Figs. 1 and 3 in reduced quality
Accurate estimation of third-order moments from turbulence measurements
Politano and Pouquet's law, a generalization of Kolmogorov's four-fifths law
to incompressible MHD, makes it possible to measure the energy cascade rate in
incompressible MHD turbulence by means of third-order moments. In
hydrodynamics, accurate measurement of third-order moments requires large
amounts of data because the probability distributions of velocity-differences
are nearly symmetric and the third-order moments are relatively small.
Measurements of the energy cascade rate in solar wind turbulence have recently
been performed for the first time, but without careful consideration of the
accuracy or statistical uncertainty of the required third-order moments. This
paper investigates the statistical convergence of third-order moments as a
function of the sample size N. It is shown that the accuracy of the
third-moment depends on the number of correlation lengths spanned by the data
set and a method of estimating the statistical uncertainty of the third-moment
is developed. The technique is illustrated using both wind tunnel data and
solar wind data.Comment: Submitted to: Nonlinear Processes in Geophysic
Low Temperature Gaseous Helium and very High Turbulence Experiments
Cryogenic gaseous helium gives access to extreme turbulent experimental conditions. The very high cooling helium flow rates available at CERN have been used to reach Reynolds numbers up to Re ~ 10**7 in a round jet experiment. First results are discussed
Probing quantum and classical turbulence analogy through global bifurcations in a von K\'arm\'an liquid Helium experiment
We report measurements of the dissipation in the Superfluid Helium high
REynold number von Karman flow (SHREK) experiment for different forcing
conditions, through a regime of global hysteretic bifurcation. Our
macroscopical measurements indicate no noticeable difference between the
classical fluid and the superfluid regimes, thereby providing evidence of the
same dissipative anomaly and response to asymmetry in fluid and superfluid
regime. %In the latter case, A detailed study of the variations of the
hysteretic cycle with Reynolds number supports the idea that (i) the stability
of the bifurcated states of classical turbulence in this closed flow is partly
governed by the dissipative scales and (ii) the normal and the superfluid
component at these temperatures (1.6K) are locked down to the dissipative
length scale.Comment: 5 pages, 5 figure
Probability Density Function of Longitudinal Velocity Increment in Homogeneous Turbulence
Two conditional averages for the longitudinal velocity increment u_r of the
simulated turbulence are calculated: h(u_r) is the average of the increment of
the longitudinal Laplacian velocity field with u_r fixed, while g(u_r) is the
corresponding one of the square of the difference of the gradient of the
velocity field. Based on the physical argument, we suggest the formulae for h
and g, which are quite satisfactorily fitted to the 512^3 DNS data. The
predicted PDF is characterized as
(1) the Gaussian distribution for the small amplitudes,
(2) the exponential distribution for the large ones, and (3) a prefactor
before the exponential function for the intermediate ones.Comment: 4 pages, 4 figures, using RevTeX3.
The 0.4-Mo Eclipsing Binary CU Cancri: Absolute Dimensions, Comparison with Evolutionary Models and Possible Evidence for a Circumstellar Dust Disk
Photometric observations in the R and I bands of the detached M-type
double-lined eclipsing binary CU Cnc have been acquired and analysed. The
photometric elements obtained from the analysis of the light curves have been
combined with an existing spectroscopic solution to yield high-precision
(errors<2%) absolute dimensions: M_A=0.4333+/-0.0017 Mo, M_B=0.3980+/-0.0014
Mo, R_A=0.4317+/-0.0052 Ro, and R_B=0.3908+/-0.0094 Ro. The mean effective
temperature of the system has been estimated to be Teff=3140+/-150 K by
comparing multi-band photometry with synthetic colors computed from model
atmospheres. Additionally, we have been able to obtain an estimate for the age
(~320 Myr) and chemical composition ([Fe/H]~0.0) of the binary system through
its membership of the Castor moving group. With all these observational
constraints, we have carried out a critical test of recent stellar models for
low-mass stars. The comparison reveals that most evolutionary models
underestimate the radius of the stars by as much as 10%, thus confirming the
trend observed by Torres & Ribas (2002) for YY Gem and V818 Tau. In the
mass-absolute magnitude diagram, CU Cnc is observed to be dimmer than other
stars of the same mass. After ruling out a number of different scenarios, the
apparent faintness of CU Cnc can be explained if its components are some 10%
cooler than similar-mass stars or if there is some source of circumstellar dust
absorption. The latter could be a tantalizing indirect evidence for a coplanar
(Vega-like) dusty disk around this relatively young M-type binary.Comment: 14 pages, 5 figures, 6 tables. Accepted for publication in A&A.
Tables 1 and 2 available in electronic form at the CDS after publicatio
Separation between coherent and turbulent fluctuations. What can we learn from the Empirical Mode Decomposition?
The performances of a new data processing technique, namely the Empirical
Mode Decomposition, are evaluated on a fully developed turbulent velocity
signal perturbed by a numerical forcing which mimics a long-period flapping.
First, we introduce a "resemblance" criterion to discriminate between the
polluted and the unpolluted modes extracted from the perturbed velocity signal
by means of the Empirical Mode Decomposition algorithm. A rejection procedure,
playing, somehow, the role of a high-pass filter, is then designed in order to
infer the original velocity signal from the perturbed one. The quality of this
recovering procedure is extensively evaluated in the case of a "mono-component"
perturbation (sine wave) by varying both the amplitude and the frequency of the
perturbation. An excellent agreement between the recovered and the reference
velocity signals is found, even though some discrepancies are observed when the
perturbation frequency overlaps the frequency range corresponding to the
energy-containing eddies as emphasized by both the energy spectrum and the
structure functions. Finally, our recovering procedure is successfully
performed on a time-dependent perturbation (linear chirp) covering a broad
range of frequencies.Comment: 23 pages, 13 figures, submitted to Experiments in Fluid
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