627 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
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
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
Mean value coordinates–based caricature and expression synthesis
We present a novel method for caricature synthesis based on mean value coordinates (MVC). Our method can be applied to any single frontal face image to learn a specified caricature face pair for frontal and 3D caricature synthesis. This technique only requires one or a small number of exemplar pairs and a natural frontal face image training set, while the system can transfer the style of the exemplar pair across individuals. Further exaggeration can be fulfilled in a controllable way. Our method is further applied to facial expression transfer, interpolation, and exaggeration, which are applications of expression editing. Additionally, we have extended our approach to 3D caricature synthesis based on the 3D version of MVC. With experiments we demonstrate that the transferred expressions are credible and the resulting caricatures can be characterized and recognized
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
Derivative moments in turbulent shear flows
We propose a generalized perspective on the behavior of high-order derivative
moments in turbulent shear flows by taking account of the roles of small-scale
intermittency and mean shear, in addition to the Reynolds number. Two
asymptotic regimes are discussed with respect to shear effects. By these means,
some existing disagreements on the Reynolds number dependence of derivative
moments can be explained. That odd-order moments of transverse velocity
derivatives tend not vanish as expected from elementary scaling considerations
does not necessarily imply that small-scale anisotropy persists at all Reynolds
numbers.Comment: 11 pages, 7 Postscript figure
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
Computing Topology Preservation of RBF Transformations for Landmark-Based Image Registration
In image registration, a proper transformation should be topology preserving.
Especially for landmark-based image registration, if the displacement of one
landmark is larger enough than those of neighbourhood landmarks, topology
violation will be occurred. This paper aim to analyse the topology preservation
of some Radial Basis Functions (RBFs) which are used to model deformations in
image registration. Mat\'{e}rn functions are quite common in the statistic
literature (see, e.g. \cite{Matern86,Stein99}). In this paper, we use them to
solve the landmark-based image registration problem. We present the topology
preservation properties of RBFs in one landmark and four landmarks model
respectively. Numerical results of three kinds of Mat\'{e}rn transformations
are compared with results of Gaussian, Wendland's, and Wu's functions
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
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