312 research outputs found
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
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]
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]
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
Parametric Generation of Second Sound by First Sound in Superfluid Helium
We report the first experimental observation of parametric generation of
second sound (SS) by first sound (FS) in superfluid helium in a narrow
temperature range in the vicinity of . The temperature dependence
of the threshold FS amplitude is found to be in a good quantitative agreement
with the theory suggested long time ago and corrected for a finite geometry.
Strong amplitude fluctuations and two types of the SS spectra are observed
above the bifurcation. The latter effect is quantitatively explained by the
discreteness of the wave vector space and the strong temperature dependence of
the SS dissipation length.Comment: 4 pages, 4 postscript figures, REVTE
Cooper pair turbulence in atomic Fermi gases
We investigate the stability of spatially uniform solutions for the
collisionless dynamics of a fermionic superfluid. We demonstrate that, if the
system size is larger than the superfluid coherence length, the solution
characterized by a periodic in time order parameter is unstable with respect to
spatial fluctuations. The instability is due to the parametric excitations of
pairing modes with opposite momenta. The growth of spatial modulations is
suppressed by nonlinear effects resulting in a state characterized by a random
superposition of wave packets of the superfluid order parameter. We suggest
that this state can be probed by spectroscopic noise measurements.Comment: 4 pages, 2 figure
Possibility to study eta-mesic nuclei and photoproduction of slow eta-mesons at the GRAAL facility
A new experiment is proposed with the aim to study eta-mesic nuclei and
low-energy interactions of eta with nuclei. Two decay modes of eta produced by
a photon beam inside a nucleus will be observed, namely a collisional decay
\eta N \to \pi N inside the nucleus and the radiative decay \eta \to \gamma
\gamma outside. In addition, a collisional decay of stopped S_{11}(1535)
resonance inside the nucleus, S_{11}(1535) N \to N N, will be studied. The
experiment can be performed using the tagged photon beam at ESRF with the
end-point energy 1000 MeV and the GRAAL detector which includes a
high-resolution BGO calorimeter and a large acceptance lead-scintillator
time-of-flight wall. Some results of simulation and estimates of yields are
given.Comment: 20 pages, 19 figure
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
- …