281 research outputs found
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
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
Universality and saturation of intermittency in passive scalar turbulence
The statistical properties of a scalar field advected by the non-intermittent
Navier-Stokes flow arising from a two-dimensional inverse energy cascade are
investigated. The universality properties of the scalar field are directly
probed by comparing the results obtained with two different types of injection
mechanisms. Scaling properties are shown to be universal, even though
anisotropies injected at large scales persist down to the smallest scales and
local isotropy is not fully restored. Scalar statistics is strongly
intermittent and scaling exponents saturate to a constant for sufficiently high
orders. This is observed also for the advection by a velocity field rapidly
changing in time, pointing to the genericity of the phenomenon. The persistence
of anisotropies and the saturation are both statistical signatures of the
ramp-and-cliff structures observed in the scalar field.Comment: 4 pages, 8 figure
Correlation functions in isotropic and anisotropic turbulence: the role of the symmetry group
The theory of fully developed turbulence is usually considered in an
idealized homogeneous and isotropic state. Real turbulent flows exhibit the
effects of anisotropic forcing. The analysis of correlation functions and
structure functions in isotropic and anisotropic situations is facilitated and
made rational when performed in terms of the irreducible representations of the
relevant symmetry group which is the group of all rotations SO(3). In this
paper we firstly consider the needed general theory and explain why we expect
different (universal) scaling exponents in the different sectors of the
symmetry group. We exemplify the theory context of isotropic turbulence (for
third order tensorial structure functions) and in weakly anisotropic turbulence
(for the second order structure function). The utility of the resulting
expressions for the analysis of experimental data is demonstrated in the
context of high Reynolds number measurements of turbulence in the atmosphere.Comment: 35 pages, REVTEX, 1 figure, Phys. Rev. E, submitte
Inhomogeneous Anisotropic Passive Scalars
We investigate the behaviour of the two-point correlation function in the
context of passive scalars for non homogeneous, non isotropic forcing
ensembles. Exact analytical computations can be carried out in the framework of
the Kraichnan model for each anisotropic sector. It is shown how the
homogeneous solution is recovered at separations smaller than an intrinsic
typical lengthscale induced by inhomogeneities, and how the different Fourier
modes in the centre-of-mass variable recombine themselves to give a ``beating''
(superposition of power laws) described by Bessel functions. The pure power-law
behaviour is restored even if the inhomogeneous excitation takes place at very
small scales.Comment: 14 pages, 5 figure
Anomalous scaling, nonlocality and anisotropy in a model of the passively advected vector field
A model of the passive vector quantity advected by a Gaussian
time-decorrelated self-similar velocity field is studied; the effects of
pressure and large-scale anisotropy are discussed. The inertial-range behavior
of the pair correlation function is described by an infinite family of scaling
exponents, which satisfy exact transcendental equations derived explicitly in d
dimensions. The exponents are organized in a hierarchical order according to
their degree of anisotropy, with the spectrum unbounded from above and the
leading exponent coming from the isotropic sector. For the higher-order
structure functions, the anomalous scaling behavior is a consequence of the
existence in the corresponding operator product expansions of ``dangerous''
composite operators, whose negative critical dimensions determine the
exponents. A close formal resemblance of the model with the stirred NS equation
reveals itself in the mixing of operators. Using the RG, the anomalous
exponents are calculated in the one-loop approximation for the even structure
functions up to the twelfth order.Comment: 37 pages, 4 figures, REVTe
Dynamical equations for high-order structure functions, and a comparison of a mean field theory with experiments in three-dimensional turbulence
Two recent publications [V. Yakhot, Phys. Rev. E {\bf 63}, 026307, (2001) and
R.J. Hill, J. Fluid Mech. {\bf 434}, 379, (2001)] derive, through two different
approaches that have the Navier-Stokes equations as the common starting point,
a set of steady-state dynamic equations for structure functions of arbitrary
order in hydrodynamic turbulence. These equations are not closed. Yakhot
proposed a "mean field theory" to close the equations for locally isotropic
turbulence, and obtained scaling exponents of structure functions and an
expression for the tails of the probability density function of transverse
velocity increments. At high Reynolds numbers, we present some relevant
experimental data on pressure and dissipation terms that are needed to provide
closure, as well as on aspects predicted by the theory. Comparison between the
theory and the data shows varying levels of agreement, and reveals gaps
inherent to the implementation of the theory.Comment: 16 pages, 23 figure
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
Scaling, renormalization and statistical conservation laws in the Kraichnan model of turbulent advection
We present a systematic way to compute the scaling exponents of the structure
functions of the Kraichnan model of turbulent advection in a series of powers
of , adimensional coupling constant measuring the degree of roughness of
the advecting velocity field. We also investigate the relation between standard
and renormalization group improved perturbation theory. The aim is to shed
light on the relation between renormalization group methods and the statistical
conservation laws of the Kraichnan model, also known as zero modes.Comment: Latex (11pt) 43 pages, 22 figures (Feynman diagrams). The reader
interested in the technical details of the calculations presented in the
paper may want to visit:
http://www.math.helsinki.fi/mathphys/paolo_files/passive_scalar/passcal.htm
Statistical geometry in scalar turbulence
A general link between geometry and intermittency in passive scalar
turbulence is established. Intermittency is qualitatively traced back to events
where tracer particles stay for anomalousy long times in degenerate geometries
characterized by strong clustering. The quantitative counterpart is the
existence of special functions of particle configurations which are
statistically invariant under the flow. These are the statistical integrals of
motion controlling the scalar statistics at small scales and responsible for
the breaking of scale invariance associated to intermittency.Comment: 4 pages, 5 figure
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