886 research outputs found
Anomalous and dimensional scaling in anisotropic turbulence
We present a numerical study of anisotropic statistical fluctuations in
homogeneous turbulent flows. We give an argument to predict the dimensional
scaling exponents, (p+j)/3, for the projections of p-th order structure
function in the j-th sector of the rotational group. We show that measured
exponents are anomalous, showing a clear deviation from the dimensional
prediction. Dimensional scaling is subleading and it is recovered only after a
random reshuffling of all velocity phases, in the stationary ensemble. This
supports the idea that anomalous scaling is the result of a genuine inertial
evolution, independent of large-scale behavior.Comment: 4 pages, 3 figure
Anisotropic Homogeneous Turbulence: hierarchy and intermittency of scaling exponents in the anisotropic sectors
We present the first measurements of anisotropic statistical fluctuations in
perfectly homogeneous turbulent flows. We address both problems of
intermittency in anisotropic sectors and hierarchical ordering of anisotropies
on a direct numerical simulation of a three dimensional random Kolmogorov flow.
We achieved an homogeneous and anisotropic statistical ensemble by randomly
shifting the forcing phases. We observe high intermittency as a function of the
order of the velocity correlation within each fixed anisotropic sector and a
hierarchical organization of scaling exponents at fixed order of the velocity
correlation at changing the anisotropic sector.Comment: 6 pages, 3 eps figure
Scaling Exponents in Anisotropic Hydrodynamic Turbulence
In anisotropic turbulence the correlation functions are decomposed in the
irreducible representations of the SO(3) symmetry group (with different
"angular momenta" ). For different values of the second order
correlation function is characterized by different scaling exponents
. In this paper we compute these scaling exponents in a Direct
Interaction Approximation (DIA). By linearizing the DIA equations in small
anisotropy we set up a linear operator and find its zero-modes in the inertial
interval of scales. Thus the scaling exponents in each -sector follow
from solvability condition, and are not determined by dimensional analysis. The
main result of our calculation is that the scaling exponents
form a strictly increasing spectrum at least until , guaranteeing that
the effects of anisotropy decay as power laws when the scale of observation
diminishes. The results of our calculations are compared to available
experiments and simulations.Comment: 10 pages, 4 figures, PRE submitted. Fixed problems with figure
The Scaling Structure of the Velocity Statistics in Atmospheric Boundary Layer
The statistical objects characterizing turbulence in real turbulent flows
differ from those of the ideal homogeneous isotropic model.They
containcontributions from various 2d and 3d aspects, and from the superposition
ofinhomogeneous and anisotropic contributions. We employ the recently
introduceddecomposition of statistical tensor objects into irreducible
representations of theSO(3) symmetry group (characterized by and
indices), to disentangle someof these contributions, separating the universal
and the asymptotic from the specific aspects of the flow. The different
contributions transform differently under rotations and so form a complete
basis in which to represent the tensor objects under study. The experimental
data arerecorded with hot-wire probes placed at various heights in the
atmospheric surfacelayer. Time series data from single probes and from pairs of
probes are analyzed to compute the amplitudes and exponents of different
contributions to the second order statistical objects characterized by ,
and . The analysis shows the need to make a careful distinction
between long-lived quasi 2d turbulent motions (close to the ground) and
relatively short-lived 3d motions. We demonstrate that the leading scaling
exponents in the three leading sectors () appear to be different
butuniversal, independent of the positions of the probe, and the large
scaleproperties. The measured values of the exponent are , and .
We present theoretical arguments for the values of these exponents usingthe
Clebsch representation of the Euler equations; neglecting anomalous
corrections, the values obtained are 2/3, 1 and 4/3 respectively.Comment: PRE, submitted. RevTex, 38 pages, 8 figures included . Online (HTML)
version of this paper is avaliable at http://lvov.weizmann.ac.il
Dynamics of threads and polymers in turbulence: power-law distributions and synchronization
We study the behavior of threads and polymers in a turbulent flow. These
objects have finite spatial extension, so the flow along them differs slightly.
The corresponding drag forces produce a finite average stretching and the
thread is stretched most of the time. Nevertheless, the probability of
shrinking fluctuations is significant and is known to decay only as a
power-law. We show that the exponent of the power law is a universal number
independent of the statistics of the flow. For polymers the coil-stretch
transition exists: the flow must have a sufficiently large Lyapunov exponent to
overcome the elastic resistance and stretch the polymer from the coiled state
it takes otherwise. The probability of shrinking from the stretched state above
the transition again obeys a power law but with a non-universal exponent. We
show that well above the transition the exponent becomes universal and derive
the corresponding expression. Furthermore, we demonstrate synchronization: the
end-to-end distances of threads or polymers above the transition are
synchronized by the flow and become identical. Thus, the transition from
Newtonian to non-Newtonian behavior in dilute polymer solutions can be seen as
an ordering transition.Comment: 13 pages, version accepted to Journal of Statistical Mechanic
Universal long-time properties of Lagrangian statistics in the Batchelor regime and their application to the passive scalar problem
We consider transport of dynamically passive quantities in the Batchelor
regime of smooth in space velocity field. For the case of arbitrary temporal
correlations of the velocity we formulate the statistics of relevant
characteristics of Lagrangian motion. This allows to generalize many results
obtained previously for the delta-correlated in time strain, thus answering the
question of universality of these results.Comment: 11 pages, revtex; added references, typos correcte
Polymer transport in random flow
The dynamics of polymers in a random smooth flow is investigated in the
framework of the Hookean dumbbell model. The analytical expression of the
time-dependent probability density function of polymer elongation is derived
explicitly for a Gaussian, rapidly changing flow. When polymers are in the
coiled state the pdf reaches a stationary state characterized by power-law
tails both for small and large arguments compared to the equilibrium length.
The characteristic relaxation time is computed as a function of the Weissenberg
number. In the stretched state the pdf is unstationary and exhibits
multiscaling. Numerical simulations for the two-dimensional Navier-Stokes flow
confirm the relevance of theoretical results obtained for the delta-correlated
model.Comment: 28 pages, 6 figure
Magnetic field correlations in a random flow with strong steady shear
We analyze magnetic kinematic dynamo in a conducting fluid where the
stationary shear flow is accompanied by relatively weak random velocity
fluctuations. The diffusionless and diffusion regimes are described. The growth
rates of the magnetic field moments are related to the statistical
characteristics of the flow describing divergence of the Lagrangian
trajectories. The magnetic field correlation functions are examined, we
establish their growth rates and scaling behavior. General assertions are
illustrated by explicit solution of the model where the velocity field is
short-correlated in time
Independent Component Analysis of Spatiotemporal Chaos
Two types of spatiotemporal chaos exhibited by ensembles of coupled nonlinear
oscillators are analyzed using independent component analysis (ICA). For
diffusively coupled complex Ginzburg-Landau oscillators that exhibit smooth
amplitude patterns, ICA extracts localized one-humped basis vectors that
reflect the characteristic hole structures of the system, and for nonlocally
coupled complex Ginzburg-Landau oscillators with fractal amplitude patterns,
ICA extracts localized basis vectors with characteristic gap structures.
Statistics of the decomposed signals also provide insight into the complex
dynamics of the spatiotemporal chaos.Comment: 5 pages, 6 figures, JPSJ Vol 74, No.
Generation of Large-Scale Vorticity in a Homogeneous Turbulence with a Mean Velocity Shear
An effect of a mean velocity shear on a turbulence and on the effective force
which is determined by the gradient of Reynolds stresses is studied. Generation
of a mean vorticity in a homogeneous incompressible turbulent flow with an
imposed mean velocity shear due to an excitation of a large-scale instability
is found. The instability is caused by a combined effect of the large-scale
shear motions (''skew-induced" deflection of equilibrium mean vorticity) and
''Reynolds stress-induced" generation of perturbations of mean vorticity.
Spatial characteristics, such as the minimum size of the growing perturbations
and the size of perturbations with the maximum growth rate, are determined.
This instability and the dynamics of the mean vorticity are associated with the
Prandtl's turbulent secondary flows. This instability is similar to the
mean-field magnetic dynamo instability. Astrophysical applications of the
obtained results are discussed.Comment: 8 pages, 3 figures, REVTEX4, submitted to Phys. Rev.
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