8,919 research outputs found
Lagrangian and Eulerian velocity structure functions in hydrodynamic turbulence
The Lagrangian and Eulerian transversal velocity structure functions of fully
developed fluid turbulence are found basing on the Navier-Stokes equation. The
structure functions are shown to obey the scaling relations inside the inertial
range. The scaling exponents are calculated analytically without using
dimensional considerations. The obtained values are in a very good agreement
with recent numerical and experimental data.Comment: 4 pages, 1 figur
The Viscous Lengths in Hydrodynamic Turbulence are Anomalous Scaling Functions
It is shown that the idea that scaling behavior in turbulence is limited by
one outer length and one inner length is untenable. Every n'th order
correlation function of velocity differences \bbox{\cal
F}_n(\B.R_1,\B.R_2,\dots) exhibits its own cross-over length to
dissipative behavior as a function of, say, . This length depends on
{and on the remaining separations} . One result of this Letter
is that when all these separations are of the same order this length scales
like with
, with being
the scaling exponent of the 'th order structure function. We derive a class
of scaling relations including the ``bridge relation" for the scaling exponent
of dissipation fluctuations .Comment: PRL, Submitted. REVTeX, 4 pages, I fig. (not included) PS Source of
the paper with figure avalable at http://lvov.weizmann.ac.il/onlinelist.htm
Dynamics of Passive-Scalar Turbulence
We present the first study of the dynamic scaling or multiscaling of
passive-scalar and passive-vector turbulence. For the Kraichnan version of
passive-scalar and passive-vector turbulence we show analytically, in both
Eulerian and quasi-Lagrangian frameworks, that simple dynamic scaling is
obtained but with different dynamic exponents. By developing the multifractal
model we show that dynamic multiscaling occurs in passive-scalar turbulence
only if the advecting velocity field is itself multifractal. We substantiate
our results by detailed numerical simulations in shell models of passive-scalar
advection.Comment: published versio
Hybridization-related correction to the jellium model for fullerenes
We introduce a new type of correction for a more accurate description of
fullerenes within the spherically symmetric jellium model. This correction
represents a pseudopotential which originates from the comparison between an
accurate ab initio calculation and the jellium model calculation. It is shown
that such a correction to the jellium model allows one to account, at least
partly, for the sp2-hybridization of carbon atomic orbitals. Therefore, it may
be considered as a more physically meaningful correction as compared with a
structureless square-well pseudopotential which has been widely used earlier.Comment: 16 pages, 10 figure
Mean- Field Approximation and a Small Parameter in Turbulence Theory
Numerical and physical experiments on two-dimensional (2d) turbulence show
that the differences of transverse components of velocity field are well
described by a gaussian statistics and Kolmogorov scaling exponents. In this
case the dissipation fluctuations are irrelevant in the limit of small
viscosity. In general, one can assume existence of critical
space-dimensionality , at which the energy flux and all odd-order
moments of velocity difference change sign and the dissipation fluctuations
become dynamically unimportant. At the flow can be described by the
``mean-field theory'', leading to the observed gaussian statistics and
Kolmogorov scaling of transverse velocity differences. It is shown that in the
vicinity of the ratio of the relaxation and translation
characteristic times decreases to zero, thus giving rise to a small parameter
of the theory. The expressions for pressure and dissipation contributions to
the exact equation for the generating function of transverse velocity
differences are derived in the vicinity of . The resulting equation
describes experimental data on two-dimensional turbulence and demonstrate onset
of intermittency as and in three-dimensional flows in
close agreement with experimental data. In addition, some new exact relations
between correlation functions of velocity differences are derived. It is also
predicted that the single-point pdf of transverse velocity difference in
developing as well as in the large-scale stabilized two-dimensional turbulence
is a gaussian.Comment: 25 pages, 1 figur
Resonances in 1D disordered systems: localization of energy and resonant transmission
Localized states in one-dimensional open disordered systems and their
connection to the internal structure of random samples have been studied. It is
shown that the localization of energy and anomalously high transmission
associated with these states are due to the existence inside the sample of a
transparent (for a given resonant frequency) segment with the minimal size of
order of the localization length. A mapping of the stochastic scattering
problem in hand onto a deterministic quantum problem is developed. It is shown
that there is no one-to-one correspondence between the localization and high
transparency: only small part of localized modes provides the transmission
coefficient close to one. The maximal transmission is provided by the modes
that are localized in the center, while the highest energy concentration takes
place in cavities shifted towards the input. An algorithm is proposed to
estimate the position of an effective resonant cavity and its pumping rate by
measuring the resonant transmission coefficient. The validity of the analytical
results have been checked by extensive numerical simulations and wavelet
analysis
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
Towards a Nonperturbative Theory of Hydrodynamic Turbulence:Fusion Rules, Exact Bridge Relations and Anomalous Viscous Scaling Functions
In this paper we derive here, on the basis of the NS eqs. a set of fusion
rules for correlations of velocity differences when all the separation are in
the inertial interval. Using this we consider the standard hierarchy of
equations relating the -th order correlations (originating from the viscous
term in the NS eq.) to 'th order (originating from the nonlinear term) and
demonstrate that for fully unfused correlations the viscous term is negligible.
Consequently the hierarchic chain is decoupled in the sense that the
correlations of 'th order satisfy a homogeneous equation that may exhibit
anomalous scaling solutions. Using the same hierarchy of eqs. when some
separations go to zero we derive a second set of fusion rules for correlations
with differences in the viscous range. The latter includes gradient fields. We
demonstrate that every n'th order correlation function of velocity differences
{\cal F}_n(\B.R_1,\B.R_2,\dots) exhibits its own cross-over length
to dissipative behavior as a function of, say, . This length depends on
{and on the remaining separations} . When all these
separations are of the same order this length scales like with ,
with being the scaling exponent of the 'th order structure
function. We derive a class of exact scaling relations bridging the exponents
of correlations of gradient fields to the exponents of the 'th
order structure functions. One of these relations is the well known ``bridge
relation" for the scaling exponent of dissipation fluctuations .Comment: PRE, Submitted. REVTeX, 18 pages, 7 figures (not included) PS Source
of the paper with figures avalable at
http://lvov.weizmann.ac.il/onlinelist.htm
Dispersive stabilization of the inverse cascade for the Kolmogorov flow
It is shown by perturbation techniques and numerical simulations that the
inverse cascade of kink-antikink annihilations, characteristic of the
Kolmogorov flow in the slightly supercritical Reynolds number regime, is halted
by the dispersive action of Rossby waves in the beta-plane approximation. For
beta tending to zero, the largest excited scale is proportional to the
logarithm of one over beta and differs strongly from what is predicted by
standard dimensional phenomenology which ignores depletion of nonlinearity.Comment: 4 pages, LATEX, 3 figures. v3: revised version with minor correction
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