209 research outputs found
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
Exact Resummations in the Theory of Hydrodynamic Turbulence: II A Ladder to Anomalous Scaling
In paper I of this series on fluid turbulence we showed that exact
resummations of the perturbative theory of the structure functions of velocity
differences result in a finite (order by order) theory. These findings exclude
any known perturbative mechanism for anomalous scaling of the velocity
structure functions. In this paper we continue to build the theory of
turbulence and commence the analysis of nonperturbative effects that form the
analytic basis of anomalous scaling. Starting from the Navier-Stokes equations
(at high Reynolds number Re) we discuss the simplest examples of the appearance
of anomalous exponents in fluid mechanics. These examples are the nonlinear
(four-point) Green's function and related quantities. We show that the
renormalized perturbation theory for these functions contains ``ladder``
diagrams with (convergent!) logarithmic terms that sum up to anomalous
exponents. Using a new sum rule which is derived here we calculate the leading
anomalous exponent and show that it is critical in a sense made precise below.
This result opens up the possibility of multiscaling of the structure functions
with the outer scale of turbulence as the renormalization length. This
possibility will be discussed in detail in the concluding paper III of this
series.Comment: PRE in press, 15 pages + 21 figures, REVTeX, The Eps files of figures
will be FTPed by request to [email protected]
Fusion Rules in Turbulent Systems with Flux Equilibrium
Fusion rules in turbulence specify the analytic structure of many-point
correlation functions of the turbulent field when a group of coordinates
coalesce. We show that the existence of flux equilibrium in fully developed
turbulent systems combined with a direct cascade induces universal fusion
rules. In certain examples these fusion rules suffice to compute the
multiscaling exponents exactly, and in other examples they give rise to an
infinite number of scaling relations that constrain enormously the structure of
the allowed theory.Comment: Submitted to PRL on July 95, 4 pages, REVTe
Exact Resummations in the Theory of Hydrodynamic Turbulence: III. Scenarios for Anomalous Scaling and Intermittency
Elements of the analytic structure of anomalous scaling and intermittency in
fully developed hydrodynamic turbulence are described. We focus here on the
structure functions of velocity differences that satisfy inertial range scaling
laws , and the correlation of energy dissipation
. The goal is to understand the
exponents and from first principles. In paper II of this series
it was shown that the existence of an ultraviolet scale (the dissipation scale
) is associated with a spectrum of anomalous exponents that characterize
the ultraviolet divergences of correlations of gradient fields. The leading
scaling exponent in this family was denoted . The exact resummation of
ladder diagrams resulted in the calculation of which satisfies the
scaling relation . In this paper we continue our analysis and
show that nonperturbative effects may introduce multiscaling (i.e.
not being linear in ) with the renormalization scale being the infrared
outer scale of turbulence . It is shown that deviations from K41 scaling of
() must appear if the correlation of dissipation is
mixing (i.e. ). We derive an exact scaling relation . We present analytic expressions for for all
and discuss their relation to experimental data. One surprising prediction is
that the time decay constant of scales
independently of : the dynamic scaling exponent is the same for all
-order quantities, .Comment: PRE submitted, 22 pages + 11 figures, REVTeX. The Eps files of
figures will be FTPed by request to [email protected]
Electromagnetic Polarizabilities of Nucleons bound in Ca, O and He
Differential cross sections for elastic scattering of photons have been
measured for Ca at energies of 58 and 74 MeV and for O and He
at 61 MeV, in the angular range from 45 to 150. Evidence is obtained
that there are no significant in-medium modifications of the electromagnetic
polarizabilities except for those originating from meson exchange currents.Comment: 20 pages including 5 Figure
On Conditional Statistics in Scalar Turbulence: Theory vs. Experiment
We consider turbulent advection of a scalar field T(\B.r), passive or
active, and focus on the statistics of gradient fields conditioned on scalar
differences across a scale . In particular we focus on two
conditional averages and
. We find exact relations between
these averages, and with the help of the fusion rules we propose a general
representation for these objects in terms of the probability density function
of . These results offer a new way to analyze
experimental data that is presented in this paper. The main question that we
ask is whether the conditional average is linear in . We show that there exists a dimensionless
parameter which governs the deviation from linearity. The data analysis
indicates that this parameter is very small for passive scalar advection, and
is generally a decreasing function of the Rayleigh number for the convection
data.Comment: Phys. Rev. E, Submitted. REVTeX, 10 pages, 5 figs. (not included) PS
Source of the paper with figure available at
http://lvov.weizmann.ac.il/onlinelist.html#unpub
Inertial- and Dissipation-Range Asymptotics in Fluid Turbulence
We propose and verify a wave-vector-space version of generalized extended
self similarity and broaden its applicability to uncover intriguing, universal
scaling in the far dissipation range by computing high-order (\leq 20\/)
structure functions numerically for: (1) the three-dimensional, incompressible
Navier Stokes equation (with and without hyperviscosity); and (2) the GOY shell
model for turbulence. Also, in case (2), with Taylor-microscale Reynolds
numbers 4 \times 10^{4} \leq Re_{\lambda} \leq 3 \times 10^{6}\/, we find
that the inertial-range exponents (\zeta_{p}\/) of the order - p\/
structure functions do not approach their Kolmogorov value p/3\/ as
Re_{\lambda}\/ increases.Comment: RevTeX file, with six postscript figures. epsf.tex macro is used for
figure insertion. Packaged using the 'uufiles' utilit
Universality in Turbulence: an Exactly Soluble Model
The present note contains the text of lectures discussing the problem of
universality in fully developed turbulence. After a brief description of
Kolmogorov's 1941 scaling theory of turbulence and a comparison between the
statistical approach to turbulence and field theory, we discuss a simple model
of turbulent advection which is exactly soluble but whose exact solution is
still difficult to analyze. The model exhibits a restricted universality. Its
correlation functions contain terms with universal but anomalous scaling but
with non-universal amplitudes typically diverging with the growing size of the
system. Strict universality applies only after such terms have been removed
leaving renormalized correlators with normal scaling. We expect that the
necessity of such an infrared renormalization is a characteristic feature of
universality in turbulence.Comment: 31 pages, late
Hydrodynamics of the Kuramoto-Sivashinsky Equation in Two Dimensions
The large scale properties of spatiotemporal chaos in the 2d
Kuramoto-Sivashinsky equation are studied using an explicit coarse graining
scheme. A set of intermediate equations are obtained. They describe
interactions between the small scale (e.g., cellular) structures and the
hydrodynamic degrees of freedom. Possible forms of the effective large scale
hydrodynamics are constructed and examined. Although a number of different
universality classes are allowed by symmetry, numerical results support the
simplest scenario, that being the KPZ universality class.Comment: 4 pages, 3 figure
Anomalous Scaling in the N-Point Functions of Passive Scalar
A recent analysis of the 4-point correlation function of the passive scalar
advected by a time-decorrelated random flow is extended to the N-point case. It
is shown that all stationary-state inertial-range correlations are dominated by
homogeneous zero modes of singular operators describing their evolution. We
compute analytically the zero modes governing the N-point structure functions
and the anomalous dimensions corresponding to them to the linear order in the
scaling exponent of the 2-point function of the advecting velocity field. The
implications of these calculations for the dissipation correlations are
discussed.Comment: 16 pages, latex fil
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