222 research outputs found
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
Manifestation of anisotropy persistence in the hierarchies of MHD scaling exponents
The first example of a turbulent system where the failure of the hypothesis
of small-scale isotropy restoration is detectable both in the `flattening' of
the inertial-range scaling exponent hierarchy, and in the behavior of odd-order
dimensionless ratios, e.g., skewness and hyperskewness, is presented.
Specifically, within the kinematic approximation in magnetohydrodynamical
turbulence, we show that for compressible flows, the isotropic contribution to
the scaling of magnetic correlation functions and the first anisotropic ones
may become practically indistinguishable. Moreover, skewness factor now
diverges as the P\'eclet number goes to infinity, a further indication of
small-scale anisotropy.Comment: 4 pages Latex, 1 figur
Anomalous exponents in the rapid-change model of the passive scalar advection in the order
Field theoretic renormalization group is applied to the Kraichnan model of a
passive scalar advected by the Gaussian velocity field with the covariance
. Inertial-range
anomalous exponents, related to the scaling dimensions of tensor composite
operators built of the scalar gradients, are calculated to the order
of the expansion. The nature and the convergence of
the expansion in the models of turbulence is are briefly discussed.Comment: 4 pages; REVTeX source with 3 postscript figure
A model for alignment between microscopic rods and vorticity
Numerical simulations show that microscopic rod-like bodies suspended in a
turbulent flow tend to align with the vorticity vector, rather than with the
dominant eignevector of the strain-rate tensor. This paper investigates an
analytically solvable limit of a model for alignment in a random velocity field
with isotropic statistics. The vorticity varies very slowly and the isotropic
random flow is equivalent to a pure strain with statistics which are
axisymmetric about the direction of the vorticity. We analyse the alignment in
a weakly fluctuating uniaxial strain field, as a function of the product of the
strain relaxation time and the angular velocity about
the vorticity axis. We find that when , the rods are
predominantly either perpendicular or parallel to the vorticity
Persistence of small-scale anisotropies and anomalous scaling in a model of magnetohydrodynamics turbulence
The problem of anomalous scaling in magnetohydrodynamics turbulence is
considered within the framework of the kinematic approximation, in the presence
of a large-scale background magnetic field. The velocity field is Gaussian,
-correlated in time, and scales with a positive exponent .
Explicit inertial-range expressions for the magnetic correlation functions are
obtained; they are represented by superpositions of power laws with
non-universal amplitudes and universal (independent of the anisotropy and
forcing) anomalous exponents. The complete set of anomalous exponents for the
pair correlation function is found non-perturbatively, in any space dimension
, using the zero-mode technique. For higher-order correlation functions, the
anomalous exponents are calculated to using the renormalization group.
The exponents exhibit a hierarchy related to the degree of anisotropy; the
leading contributions to the even correlation functions are given by the
exponents from the isotropic shell, in agreement with the idea of restored
small-scale isotropy. Conversely, the small-scale anisotropy reveals itself in
the odd correlation functions : the skewness factor is slowly decreasing going
down to small scales and higher odd dimensionless ratios (hyperskewness etc.)
dramatically increase, thus diverging in the limit.Comment: 25 pages Latex, 1 Figur
Energy flux fluctuations in a finite volume of turbulent flow
The flux of turbulent kinetic energy from large to small spatial scales is
measured in a small domain B of varying size R. The probability distribution
function of the flux is obtained using a time-local version of Kolmogorov's
four-fifths law. The measurements, made at a moderate Reynolds number, show
frequent events where the flux is backscattered from small to large scales,
their frequency increasing as R is decreased. The observations are corroborated
by a numerical simulation based on the motion of many particles and on an
explicit form of the eddy damping.Comment: 10 Pages, 5 figures, 1 tabl
Pressure and intermittency in passive vector turbulence
We investigate the scaling properties a model of passive vector turbulence
with pressure and in the presence of a large-scale anisotropy. The leading
scaling exponents of the structure functions are proven to be anomalous. The
anisotropic exponents are organized in hierarchical families growing without
bound with the degree of anisotropy. Nonlocality produces poles in the
inertial-range dynamics corresponding to the dimensional scaling solution. The
increase with the P\'{e}clet number of hyperskewness and higher odd-dimensional
ratios signals the persistence of anisotropy effects also in the inertial
range.Comment: 4 pages, 1 figur
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
Anomalous scaling of a passive scalar in the presence of strong anisotropy
Field theoretic renormalization group and the operator product expansion are
applied to a model of a passive scalar field, advected by the Gaussian strongly
anisotropic velocity field. Inertial-range anomalous scaling behavior is
established, and explicit asymptotic expressions for the n-th order structure
functions of scalar field are obtained; they are represented by superpositions
of power laws with nonuniversal (dependent on the anisotropy parameters)
anomalous exponents. In the limit of vanishing anisotropy, the exponents are
associated with tensor composite operators built of the scalar gradients, and
exhibit a kind of hierarchy related to the degree of anisotropy: the less is
the rank, the less is the dimension and, consequently, the more important is
the contribution to the inertial-range behavior. The leading terms of the even
(odd) structure functions are given by the scalar (vector) operators. For the
finite anisotropy, the exponents cannot be associated with individual operators
(which are essentially ``mixed'' in renormalization), but the aforementioned
hierarchy survives for all the cases studied. The second-order structure
function is studied in more detail using the renormalization group and
zero-mode techniques.Comment: REVTEX file with EPS figure
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