553 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
Disentangling Scaling Properties in Anisotropic and Inhomogeneous Turbulence
We address scaling in inhomogeneous and anisotropic turbulent flows by
decomposing structure functions into their irreducible representation of the
SO(3) symmetry group which are designated by indices. Employing
simulations of channel flows with Re we demonstrate that
different components characterized by different display different scaling
exponents, but for a given these remain the same at different distances
from the wall. The exponent agrees extremely well with high Re
measurements of the scaling exponents, demonstrating the vitality of the SO(3)
decomposition.Comment: 4 page
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
Statistical conservation laws in turbulent transport
We address the statistical theory of fields that are transported by a
turbulent velocity field, both in forced and in unforced (decaying)
experiments. We propose that with very few provisos on the transporting
velocity field, correlation functions of the transported field in the forced
case are dominated by statistically preserved structures. In decaying
experiments (without forcing the transported fields) we identify infinitely
many statistical constants of the motion, which are obtained by projecting the
decaying correlation functions on the statistically preserved functions. We
exemplify these ideas and provide numerical evidence using a simple model of
turbulent transport. This example is chosen for its lack of Lagrangian
structure, to stress the generality of the ideas
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