1,143 research outputs found
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
Nonperturbative Spectrum of Anomalous Scaling Exponents in the Anisotropic Sectors of Passively Advected Magnetic Fields
We address the scaling behavior of the covariance of the magnetic field in
the three-dimensional kinematic dynamo problem when the boundary conditions
and/or the external forcing are not isotropic. The velocity field is gaussian
and -correlated in time, and its structure function scales with a
positive exponent . The covariance of the magnetic field is naturally
computed as a sum of contributions proportional to the irreducible
representations of the SO(3) symmetry group. The amplitudes are non-universal,
determined by boundary conditions. The scaling exponents are universal, forming
a discrete, strictly increasing spectrum indexed by the sectors of the symmetry
group. When the initial mean magnetic field is zero, no dynamo effect is found,
irrespective of the anisotropy of the forcing. The rate of isotropization with
decreasing scales is fully understood from these results.Comment: 22 pages, 2 figures. Submitted to PR
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
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
Isotropy vs anisotropy in small-scale turbulence
The decay of large-scale anisotropies in small-scale turbulent flow is
investigated. By introducing two different kinds of estimators we discuss the
relation between the presence of a hierarchy for the isotropic and the
anisotropic scaling exponents and the persistence of anisotropies. Direct
measurements from a channel flow numerical simulation are presented.Comment: 7 pages, 2 figure
Entanglement subvolume law for 2D frustration-free spin systems
Let be a frustration-free Hamiltonian describing a 2D grid of qudits with
local interactions, a unique ground state, and local spectral gap lower bounded
by a positive constant. For any bipartition defined by a vertical cut of length
running from top to bottom of the grid, we prove that the corresponding
entanglement entropy of the ground state of is upper bounded by
. For the special case of a 1D chain, our result provides a
new area law which improves upon prior work, in terms of the scaling with qudit
dimension and spectral gap. In addition, for any bipartition of the grid into a
rectangular region and its complement, we show that the entanglement
entropy is upper bounded as where
is the boundary of . This represents the first subvolume bound on
entanglement in frustration-free 2D systems. In contrast with previous work,
our bounds depend on the local (rather than global) spectral gap of the
Hamiltonian. We prove our results using a known method which bounds the
entanglement entropy of the ground state in terms of certain properties of an
approximate ground state projector (AGSP). To this end, we construct a new AGSP
which is based on a robust polynomial approximation of the AND function and we
show that it achieves an improved trade-off between approximation error and
entanglement
Statistics of pressure and of pressure-velocity correlations in isotropic turbulence
Some pressure and pressure-velocity correlation in a direct numerical
simulations of a three-dimensional turbulent flow at moderate Reynolds numbers
have been analyzed. We have identified a set of pressure-velocity correlations
which posseses a good scaling behaviour. Such a class of pressure-velocity
correlations are determined by looking at the energy-balance across any
sub-volume of the flow. According to our analysis, pressure scaling is
determined by the dimensional assumption that pressure behaves as a ``velocity
squared'', unless finite-Reynolds effects are overwhelming. The SO(3)
decompositions of pressure structure functions has also been applied in order
to investigate anisotropic effects on the pressure scaling.Comment: 21 pages, 8 figur
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