``Instanton for the Kraichnan passive scalar problem"

Abstract: We consider high-order correlation functions of the passive
scalar in the Kraichnan model. Using the instanton formalism we find the
scaling exponents of the structure functions of order $n\gg 1$ under the
additional condition $d\gg 1$, where $d$ is the dimensionality of space.

Jeremie Beck (Nice)

``Hyperbolicity and Statistics in forced Burgers turbulence"

Abstract: The dynamics of the multi-dimensional randomly forced Burgers equation
is studied in the limit of vanishing viscosity. In the case of periodic
boundary conditions, the analysis of the Lagrangian dynamics leads to
the distinguishing of a particular trajectory, the "global minimizer",
corresponding to the unique fluid particle that is never absorbed by a
shock. The hyperbolicity of this trajectory (proven in 1D but only
supported numerically in higher dimensions) plays a crucial role in
the understanding of many statistical properties of the velocity field.
For instance in 1D, it explains the power-law tail behavior of the PDF
of velocity gradients.
Most of the features present in the space-periodic case can be extended
to the limit when the size of the system tends to infinity by
considering intermediate time asymptotics. As a consequence, most of the
statistical features associated to the periodic situation can be
extended to large-size systems.

Eli Ben-Naim (Los Alamos)

``Granular Gases: scaling, multiscaling, nontrivial exponents, and Burgers' Shocks''
 

Abstract: Velocity statistics of inelastic gases, ensembles of hard sphere
particles undergoing dissipative inelastic collisions, will be
discussed.  In one-dimension, simulation results and scaling arguments
show that the dynamics of freely evolving granular gases are governed
by the inviscid limit of the Burgers equation. The formation of shocks
in the velocity profile correspond to a finite time singularity, the
inelastic collapse. Then, analytic results on the inelastic Maxwell
model the Boltzmann equation with a uniform collision rate, will be
presented.
The velocity distribution approaches a scaling solution with an algebraic
large velocity tail. The corresponding exponent, a nontrivial root of an
integral equation, varies continuously with the dimension and the
restitution coefficient. Despite scaling of the velocity distribution,
moments of the distribution exhibit multiscaling asymptotic behavior.
 

``Shell Models for Turbulence"

Abstract:
We intend to review the most important theoretical and numerical
results obtained on the realm of dynamical
models for the energy turbulent cascade.
Shell models for the energy cascade are interesting for both communities
working on dynamical system theory and on fluid-dynamics.
We mainly focus on those results which had {\it or will have}
some impacts on the fluid-dynamics community.

Eberhard Bodenschatz (Cornell)

``Acceleration Measurements in Turbulence  with and without  Polymers"

Stanislav Boldyrev (UCSB)

"Turbulent structure of star-forming molecular clouds"

Abstract: The process of star formation in interstellar molecular clouds is
believed to be controlled by driven supersonic turbulence. We suggest that
in the inertial range such turbulence looks like divergence-free, shear-dominated
flow, while in the dissipative range it develops shock  singularities.
On the base of the She-Leveque analytical model we then predict the velocity
power spectrum in the inertial range, as well as higher-order velocity structure
functions.  The results are in good agreement with the observational Larson laws
and with recent numerical findings by Padoan and Nordlund. The application of
the model to more general dissipative structures, with higher fractal dimensionality,
leads to better agreement with recent
observational results.

Qiaoning Chen (Johns Hopkins)

``A Gibbs Hypothesis in Turbulence"

Abstract:In 1993, Benzi, Biferale and Parisi (BBP) made a remarkable
  hypothesis for a shell model of turbulence: namely, that the invariant
  measure, in suitably chosen variables, is a Gibbs measure with a
  sufficiently local Hamiltonian. The variables identified by BBP were
  continuous "real-valued spins" obtained by taking logarithms of the
  multipliers (ratios) of the amplitudes of the shell modal variables.
  For a complete description of the shell model, one requires also "XY spins"
  obtained from the phases of the shell variables. By a direct numerical
  simulation of the shell model, we are able to calculate various
  "thermodynamic" functions of these spin variables, such as the "free
  energy". The Gibbs Hypothesis of BBP implies certain parameter-free
  relations between these quantities, which can be used as tests of
  the hypothesis. We present numerical results on these tests, for 3D
  Navier-Stokes as well as the shell model.

Tim Clark (LANL)

``Self-Similarity of the Turbulent Rayleigh-Taylor Mixing Layer"

Abstract: The turbulent Rayleigh-Taylor mixing layer represents an archetypical,
transient, inhomogeneous turbulent flow.  Beginning from a quiescent, unstable,
perturbed interface between two fluids of different densities, the Rayleigh-Taylor
mixing layer rapidly evolves into a turbulent flow.  This flow is characterized
by a strong turbulent kinetic energy production and baroclinic production of
vorticity and enstrophy, at the mixing layer interface, and weak production of
energy and weaker production of vorticity in the far field. Using numerical
simulations, we will examine the crucial differences between this turbulent
field and the more typically studied homogeneous systems. In addition, we will
discuss some of the restrictions implied by self-similarity, and an alternate
characterization of the interface suggested by E. Ben Naim, and G. Doolen.

Andrzej Domaradzki (UCLA)

``Modern methods for large eddy simulations of turbulent flows"

For typical turbulent flows encountered in practice the resolution
requirements to numerically solve  Navier-Stokes equations are several
orders of magnitude too large for the present day computers. The large
eddy simulation technique (LES) attempts to overcome this difficulty
by simulating directly only the largest scales of a turbulent flow.
Effects of all the neglected small, subgrid scales (SGS), must be modeled.
Subgrid scale models for large eddy simulations of turbulent flows
fall into two general categories. One category consists of the models that
provide expressions for the subgrid scale terms such as a stress tensor or a
heat flux and usually employ eddy viscosity concepts. The LES methodology
and several traditional SGS models will be reviewed. The other category
models the unresolved primitive variables such as a velocity or a
temperature and the subgrid scale stresses are secondary quantities
that are computed directly from the definitions. The fundamentals of such
modern approaches to the problem of  SGS modeling will be described and
illustrated on the example of the SGS estimation model
(Phys. Fluids, Vol. 11, 2330 (1999)). The new method
estimates a range of unknown, subgrid scales in terms of the resolved,
large scales and determines their effect on the resolved scales of interest.
The estimation model was applied to a variety of turbulent flows including
wall bounded flows, compressible and convective turbulence,
high Reynolds number isotropic turbulence, and rotating flows. Results for
a few flows of interest will presented.

Gregory Falkovich (Weizmann)

``Passive, active and emancipated scalars"

Abstract: I shall present a brief review of two recent achievements in the
theory of turbulent advection: large deviation approach to the advection in
locally smooth flows and zero mode approach to the anomalous scaling in
non-smooth flow. I shall discuss then the obtacles and open problems one
encounters in continuing along both those lines. The focus is on two
problems: dramatic differences between passive and active advected  fields
and the role of velocity intermittency.

Alexander  Fouxon (Weizmann)

``Collision rate of water  droplets in a cloud"

Abstract: The probability of the collision
of two water droplets in a cloud increases
significantly due to the presence of turbulence.
We describe the increase and the resulting
change in the process of rain formation.

Uriel Frisch (Nice)

"A review of Navier-Stokes turbulence with emphasis on
 multifractality and finite-time singularities:
 what is the evidence and do we need them?"

Walter Goldburg (Pittsburg)

``Turbulence on a free surface"

Abstract: We have studied turbulence on a free surface by tracking the
motion of floating particles.  The effect of wave motion appears
negligible.  The flow is unconventional in that, while it is confined to
two dimensions, enstrophy (and energy) can be exchanged with the fluid
below.  Another notable feature of the turbulence at the free surface is
that it is strongly compressible. The measurements will be compared with
computer simulations.

Toshiyuki Gotoh  (Nagoya)

``Inertial range statistics in homogeneou steady turbulence by DNS"

Abstract: Velocity field statistics in the inertial range at large
          Reynolds numbers are studied by large scale DNS.
          Isotropy, scalewise energy budgets, scaling of the higher
          order velocity structure functions and so on are quantitatively
          examined. Also the statistics of the locally averaged energy
          dissipation rate are compared to statitical theories.

Alex Groisman (CalTech)

``Elastic turbulence in polymer solutions at low Reynolds numbers
- a realization of the Batchelor regime of mixing"

Abstract: We present experimental data on mixing in flow of a polymer
solution in a curvilinear channel
at low Reynolds numbers. The mixing is induced by a purely elastic flow
instability, which creates a random three-dimensional flow with turbulent
features. We show that the  flow corresponds to the Batchelor regime of mixing.
We analyze a number of statistical  characteristics of the passive scalar
distribution and find very good agreement with existing theoretical  predictions.

Matthew Hastings (LANL)

"DLA Turbulence"

Diffusion-limited aggregation (DLA) is a central model in the field of
fractal growth.  Based on aggregation of random walkers, it gives rise
to complex branching patterns.  The (naive) limit of vanishing walker size
leads to an integrable model with finite time singularities.  The finite
walker size then introduces noise and a short-distance cutoff into the
integrable dynamics.  This leads to a situation very similar to that in
turbulence, with an inertial range where integrals of motion are
conserved, and a viscous scale, where the singularities are resolved.
I will review the DLA model and the related conformal mapping model, with
emphasis on parallels with turbulence.  I will then discuss recent work
on making the dynamics at short-distances more precise, based on
tip-splitting and a renormalization of the long-distance dynamics.
 

Joseph Katz (Johns Hopkins)
 

``Experimental Techniques in Turbulence Measurements: Recent Advances and Future Challenges"
 
 

The presentation introduces recent advances in flow measurement techniques and
demonstrates their applications in turbulence research. Particle Image Velocimetry
(PIV) that measures the instantaneous two-dimensional velocity distribution in a
plane was introduced during the late 1980?s and gained wide acceptance during the 1990?s,
as the acquisition and processing techniques improved substantially. The presently
available PIV systems can generate vector arrays of in the order of 100x100 vectors.
Stereo-PIV is used for measuring all three components of the velocity in a plane.
Recently introduced high-speed cameras enable measurement rates of up to several
hundreds vector maps per second. Applications to turbulence modeling include
measurements of Reynolds stresses and a? priori testing of Sub Grid Scale (SGS)
stress models for Large Eddy Simulations in a variety of geometries and scales.
The presentation includes results of recent turbulence measurements in the bottom
boundary layer of the coastal ocean, where spatial structure functions are used for
calculating the Reynolds stresses uncontaminated by surface waves. The results also
show order of magnitude differences between viscous dissipation and SGS dissipation
rates due to substantial backscatter of energy. Examples of wake-wake interactions
in complex turbomachinery flows will also be introduced. The introduction of
Holographic PIV (HPIV) enables measurements of three dimensional velocity distributions
in a finite volume. Spatial filtering of the data is used for calculating all the
components of the SGS stress tensor, enabling comparisons to the magnitude and alignment
of eigenvalues of model predictions. Our original HPIV concept has been recently improved
both in terms of spatial resolution and substantial simplification of the optical setup.
It is now possible to obtain 3-D instantaneous velocity distributions containing about
400x400x400 vectors in high Reynolds number flows.

Robert Kerr (Tucson)

``A vorticity surge and helicity"

Abstract: A vorticity surge event that could be a paradigm for a wide class of
bursting events in turbulence is studied
to examine how the energy cascade is established and how this event
could serve as a new test of LES turbulence models.
This vorticity surge event is tied to
the formation of the energy cascade in a direct numerical simulation by
the traditional signatures of a turbulent energy cascade
such as spectra approaching -5/3 and strongly Beltramized vortex tubes.
A coherent mechanism is suggested by the nearly simultaneous development of
a maximum of the peak vorticity $\|\omega\|_\infty$, growth of the
dissipation,
the appearance of a helically aligned local vortex configuration and
strong, transient oscillations in the helicity wavenumber spectrum.

Konstantin Khanin (Cambridge)

``Global structure of shocks in Burgers turbulence"
 

We shall discuss new results concerning the global properties
of shocks in Burgers turbulence. In particular, we discuss
topological shocks for compact manifolds and T-global shocks
for spatially extended (noncompact) situation. We also discuss
a new approach to an analysis of the vanishing viscosity limit.

Igor Kolokolov (Budker Inst., Novosibirsk)

"Spatio-temporal intermittency in thermally activated
Burgers turbulence"

Abstract:
" For the one-dimensional velocity field governed by
the Burgers equation with thermal noise short-time
asymptotics of multipoint correlation functions of different orderd are found. The
exponential parts of the correlation functions do not depend on the order,
i.e. the correlations are determined by a rare fluctuation, manifesting intermittency
phenomenon.

Branko Kosovic (Boulder)

``A two-parmeter spectral turbulence closure"

Abstract:

A two-parameter spectral turbulence closure is proposed.
The closure is achieved by assuming that the turbulence is
homogeneous and in statistical equilibrium. The closure model
is first studied using direct numerical simulations
of forced isotropic turbulence. The model performance is evaluated
in large-eddy simulations of homogeneous turbulent flows.

Antti Kupiainen (Helsinki)

``Lagrangian dispersion in gaussian self-similair velocities"

Abstract: We analyze the Lagrangian flow in a family of simple
Gaussian scale-invariant velocity ensembles that exhibit both
spatial roughness and temporal correlations. We show that the
behavior of the Lagrangian dispersion in those models is
determined by the scale dependence of the ratio between the
correlation time of velocity differences and the eddy turnover
time. For a non-trivial scale dependence, the asymptotic regimes
of the dispersion at small scales are described by the models with
either rapidly decorrelating or time independent velocities. This
allows to predict the existence of different phases with
deterministic, stochastic and collapsing Lagrangian trajectories
and to conjecture the location of the phase transitions.

Alessandra Lanotte (CNR/ISAC, Italy)

``Direct Numerical Simulations of Anisotropic Turbulence"

Vladimir Lebedev (Landau, Moscow)

``Turbulence of Polymer Solutions"

Abstratc: We investigate high-Reynolds number (Re) turbulence in dilute polymer solutions.
There is a critical value of Re which separates two
different regimes. In the first regime,
below the transition, the influence of the polymer molecules on the flow is negligible, so they
can be regarded as passively embedded in the flow. This case admits a
detailed investigation of the statistics of the polymer elongations.
The second state is realized when Re is larger  than the critical
value. This regime is characterized by the strong back reaction of polymers
on the flow. In this case a new region of scales appears
below the inertial interval, where  elastic waves propagate. We show
that the spectrum is power in this region. We examine also the
so-called elastic turbulence (chaotic flow at small Re), where both the velocity and polymer
stress tensor have power spectra.

Takeshi Matsumoto (Kyoto)
                  (The other authors of this work :
                   MIYASHITA Hisashi, Yoshiyuki Yamada and Sadayoshi Toh)

``A Numerical search for a singularity of 2D inviscid Boussinesq
                approximation equation"

 Abstract: We study numerically two-dimensional inviscid incompressible Boussinesq
 approximation equation without mean temperature gradient in doubly periodic domain.
 Our goal is to capture a possible finite-time blow-up of vorticity $\omega$ and
 temperature gradient $\nabla T$. We employ a finite-difference scheme with an
 adaptive mesh refinement technique that makes the finest grid-spacing
$10^{-6} \times$ (box size) easily accessible. Moreover, in order to ensure that
finer adapted-grid data are interpolated from sufficiently accurate coarser grid
ones, we implement the following time-rewinding method. We preserve the field data
at every resolution-checking time. When we detect an ill-resoluted sub-domain,
we calculate the data for the finer adapted-mesh there by interpolating the
corresponding coarser-mesh data that have been preserved since the previous checking
time and then redo the simulation with the finer mesh. The result suggests the
existence of blow-up, $|\omega|_{\rm{max}} \propto (t_* - t)^{-1}$ and
$|\nabla T|_{\rm{max}} \propto (t_* - t)^{-2}$. We also discuss where and how the
singularity emerges.

Charles Meneveau (Johns Hopkins)

Title: "Dynamics and statistics of velocity gradients in
spatially filtered turbulence"

Abstract:

The effects of small-scale motions on the inertial range structure
of turbulence are investigated by considering the dynamics of the
velocity gradient tensor filtered at inertial-range scales. In addition to
self-interactions and the filtered pressure Hessian, the evolution of
the filtered velocity gradient tensor is determined by the subgrid-scale stress
tensor. As in so-called Restricted Euler dynamics, the evolution equations can
be simplified by considering two invariants R and Q.  The effects of the
subgrid-scale stress tensor on them can be quantified unambiguously by
evaluating conditional averages that appear in the evolution equation for the
joint PDF of the invariants. The required conditional averages are computed
from three-dimensional HPIV measurements of fully developed turbulence in a
square duct, at a friction Reynolds number of about 2300.  The results show
that the SGS stresses have significant effects, e.g. along the so-called
Vieillefosse tail they oppose the formation of a finite-time singularity that
occurs in Restricted Euler dynamics. A-priori tests of the Smagorinsky,
nonlinear, and mixed models show that  all reproduce the real SGS stress
effect along the Vieillefosse tail, but that they fail in several other
regions. An attempt is made to optimize the mixed model by letting the two
coefficients be functions of the two invariants R and Q.
 

Mark Nelkin (NYU)

``Tuning intermittency, or how can we slightly change the Navier-Stokes equations to make
1941 Kolmogorov exact?"
 

Although the corrections due to anomalous scaling in Navier-Stokes turbulence are divergent,
1941 Kolmogorov normal scaling (K41) remains a good first approximation. This suggests that a
small change in the dynamical equations might make K41 exact.   I discuss some results which
support this proposal, but this line of inquiry remains speculative.  The first results are
based on the assumption that anomalous scaling will only occur if it reduces the number of
degrees of freedom in a statistically stationary state.  Kraichnan showed in 1985, that for
fractally homogeneous turbulence, this is only true for dimensions $d<4$.  Meneveau and
Nelkin in 1989 extended this result to a general multifractal model. These results depend,
however, on the mechanism of viscous dissipation.  Nelkin and Meneveau showed in 1999 that a
change from an ordinary viscous term $\nu k^2$ to a hypoviscous term $\nu k^p$ leads to an
analogous transition in three dimensions when $p=5/3$. This is difficult but not impossible
to check by direct numerical simulation.  Although nobody knows why shell models work, it is
tempting to look for similar transitions in shell models.  Varying the free parameter
$\delta$ in the GOY model is known to lead to a stable K41 fixed point when $\delta$ becomes
small corresponding to decreased backward energy transfer.  Nelkin suggested in 2001 that
this could correspond to an increase in spatial dimensionality, but it is likely that this
transition is quite model dependent, and the analogous transition for the SABRA model would
not show a stable K41 fixed point. Finally we have studied the SABRA model numerically with
hypoviscosity.  The corrections to K41 are definitely reduced, but we can not yet be sure
that this corresponds to a genuine change in scaling exponents.
 
 

J.-F. Pinton (Lyon)

``Lagrangian velocity measurement in fully developped turbulence "

Abstract:            The understanding of the dynamics of turbulent flows has been
a major goal for fundamental and applied fluid dynamics research for almost a century
now. On the fundamental side, turbulence is the head figure of a non-linear
dissipative system with a very large number of degrees of freedom. On the applied
side, the properties of turbulent flows govern the dispersion of pollutants, the
physics of mixing, etc. In very recent years, analytical and numerical studies have
shown that progress can be made by analysing the flow properties in the reference
frame of a moving fluid particle (the Lagrangian viewpoint), instead of considering
the velocity field at a fixed point in space (the Eulerian viewpoint).
In order to completely address turbulence in the Lagrangian frame, one needs to
describe the dynamics over the entire range of scales of motion. We have developed
such technique, based on sonar principles, to measure directly the velocity of
individual small tracer particles over long times. We have analysed the statistics
of the Lagrangian velocity of single particles for flows with turbulent Reynolds
numbers between 100 and 1100.  We observe that the Lagrangian spectrum has a
Lorentzian form in agreement with a Kolmogorov-like scaling in the inertial range.
The probability density function (PDF) of the velocity time increments displays a
change of shape from quasi-Gaussian a integral time scale to stretched exponential
tails at the smallest time increments. This intermittency, when measured from
relative scaling exponents of structure functions, is more pronounced than
in the Eulerian framework.
    Another important observation is that in the erratic course of the particle motion,
infinitesimal changes of velocity occur with `random' decorrelated directions but
with a correlation of magnitude which persists over the longest times of the flow.
Using an analogy with the properties of Multifractal Random Walks, we propose that
this feature is essential in the development of intermittency in turbulence.

   Annick Pouquet, GTP/NCAR (Boulder)
 

``SOME ISSUES IN GEOPHYSICAL TURBULENCE"
 

Turbulence is present in many instances in geophysical and astrophysical
flows, such as in convective clouds, in the atmosphere and oceans,
or in the solar convection zone, the solar corona, the interstellar medium
and beyond.

A few examples, including in the presence of magnetic fields,
will be given with specific problems encountered in such
contexts, when one introduces other forces besides pressure and dissipation
in the equation of motion.

Itamar Procaccia (Weizmann)

"Statistically Preserved Structures in Passive and Active
Scalar Advection: Shell Models, Operators and Zero Modes"

Abstract: We address turbulent advection of passive
and active scalar by "generic" velocity fields with normal
time-correlations. We consider shell models of passive and
active scalar turbulent advection. These offer a convenient
framework to study the role of Statistically Preserved
Structures in the anomalous statistics of the advected fields.
One can explicitly find the (time-dependent) operators whose
eigenfunctions of eigenvalue 1 are preserved by the
dynamics, and show how these dominate the statistics of the
forced problem. Thus the issue of anomalous scaling of the
advected fields can be adequately described and explained.

Alain Pumir (Nice)

``The lagrangian view of energy transfer in turbulent flows"

Seth Putterman (UCLA)

``Is wave turbulence as challenging as vortex turbulence?"

Michael Riviera (LANL)

``The effects of external drag on the direct cascade of two-dimensional turbulence"

Experimental measurements obtained from a turbulent soap film are compared to
numerical work in an attempt to characterize the role that external drag plays in
the statistics of two-dimensional turbulence.  Two approaches are taken in the analysis:
 measurement of coherent structure statistics in decaying 2D turbulence and the
measurement of scale to scale enstrophy transfer in the direct cascade range of
2D turbulence.  The first of these is done by performing a vortex census, similar
to that used by McWilliams in earlier numerical work, on decaying turbulence
velocity fields.  The results of the census fits into the coherent structure description
of aggregrate statistics developed by Carnevale, demonstrating that the decay process
is dominated by the development of large scale coherent structures.  However, the time
evolution of aggregrate and vortex census quantities deviates strongly from numerical
work, a fact associated with the presence of an external damping on the system.
The second approach measures scale to scale enstrophy transfer by use of large scale
field statistics.  Without the presence of external damping one expects the enstrophy
tranfer rate over the scales in the direct cascade range to be constant, i.e. an
enstrophy inertial range.  Measurements from the soap film deviate from constant over
these length scales.  When compared with recent numerical work this deviation can
be accounted for by the existence of an external drag.

Boris Shraiman (Lucent)

``Lagrangian Tetrads and Statistical Geometry of Turbulence"

K.R. Sreenivasan (Yale & Maryland)
 

``The Impact of Using Low Temperature Fluids on Classical Turbulence
Research"
 

Hydrodynamic turbulence is important in applications and as a paradigm
of spatially extended nonlinear systems with many degrees of freedom.
The recent use of liquid and gaseous helium at low temperatures has
extended the ranges of relevant parameters that need to be explored, and
thus has had an impact on our understanding of turbulence. We outline a
few of these advances and stress the role played by the use of low
temperature helium. We also attempt to identify the technical
limitations that limit further progress. Our focus will be helium above
the lambda line, but, time permitting, superfluidity will also be
discussed.

Victor Steinberg (Weizmann)

``Elastic turbulence and polymer stretching in polymer solution flows."

Harry Swinney ( Austin)

``Scaling in 2D and 3D turbulence in a rotating annulus*[1]"

Abstract:
Our velocity measurements on turbulent flow in a rapidly rotating
annulus show that the flow is two-dimensional (2D) for large rotation
rates, while for small rotation rates the flow becomes 3D. Flow in the 2D
(quasi-geostrophic) regime exhibits anomalous scaling behavior [1]: the
energy spectrum is described by E(k) ~ k^(-2) rather than the expected
E(k) ~ k^(-5/3), and the structure functions for velocity differences V(x)
(for points separated by a distance x) are described by S_p(x) = <V(x)^p>
~ x^(p/2), rather than scaling with the expected exponent, p/3. The
velocity difference PDFs are strongly non-Gaussian for the 2D turbulent
flow, yet are self-similar for the full range of length scales examined
(x=0.5 to 20 cm).  For small rotation rates the flow becomes 3D and the
velocity difference PDFs are not self-similar, varing from exponential at
small separations x to Gaussian for large x.  The structure function
exponents for the 3D flow are in agreement with those found in other
strongly turbulent 3D flows.  We have applied the beta and gamma tests of
the hierarchical symmetry model of She and Leveque [Phys. Rev. Lett. 72,
336 (1994)], and our results are compared with those obtained in
simulations and other experiments for both 2D and 3D flows.

*Supported by ONR
*1. C.N. Baroud, B.B. Plapp, H.L. Swinney, and Z.S. She, to be published.
 

``Experiments on turbulent dispersion"

Abstract: Two experiments, carried out with 2D turbulent flows, will be presented.
The first one corresponds to the observation of the Batchelor regime, in which the
tracer field is analysed and particles are followed. The second one corresponds to
the case where the tracer is dispersed by a velocity field displaying a Kolmogorov
spectrum. We study the tracer field, and the evolution of pairs and triads.
Kraichnan model offers in this case a remarkably relevant frame of interpretation.

Bo Tao (Purdue)

``Characterizing the structures of turbulence by using holographic PIV measurements"

A holographic PIV system is developed for measuring the instantaneous, 3-D velocity
distributions in the core region of a turbulent duct flow. Employing spatial
filtering of the measured velocity field, the subgrid-scale (SGS) stress and other
velocity gradient parameters such as the filtered strain-rate and vorticity are
computed directly from the data. In the context of large-eddy simulation, the scale
and geometry relationships between the parameters of the resolved and subgrid scales
are characterized. New, intriguing trends are observed and their implications on the
SGS modeling are discussed. To examine these trends, several analysis tools for
realizing the tensorial structures and orientations have been developed. They can
be readily applied to study the characteristics of other flows obtained either
experimentally or from numerical simulations.

Edriss Titi (UC Irvine)

``The Navier-Stokes-alpha model and  Turbulence Theory"

Abstract: In this talk we will show the global well-posedness of the three dimensional
 Navier--Stokes-alpha model (also known as a viscous Camassa-Holm equations).
The dimension of its  global attractor will be esitmated and shown
to be  comparable with the number of degrees of freedom suggested by
classical theory of turbulence.  We will present semi-rigorous arguments
showing that up to a certain wave number, in the inertial range,
 the translational energy power specturm obeys the Kolmogorov power
law for the energy decay of the three dimensional turbulent flow.
However for the rest the inertial range the energy spectrum of this
model obeys the Kraichnan power law for the energy decay
of the two dimensional turbulent follows. This observation makes the
 Navier--Stokes-alpha model more computable than the Navier--Stokes
equations. Furthermore, we will show that by using the
 Navier--Stokes-alpha model as a closure model to the
Reynolds averaged equations of the Navier--Stokes one gets very good
agreement with empirical and numerical data of turbulent flows in
infinite pipes and channels.

Eric Vanden-Eijnden (Courant)

``Statistical Theory for the Stocahstic Burgers Equation
in the Inviscid Limit"

Abstract:
  A statistical theory is developed for the stochastic Burgers
  equation in the inviscid limit. Master equations for the probability
  density functions of velocity, velocity difference and velocity
  gradient are derived.  No closure assumptions are made. Instead
  closure is achieved through a dimension reduction process, namely
  the unclosed terms are expressed in terms of statistical quantities
  for the singular structures of the velocity field, here the shocks.
  Master equations for the environment of the shocks are further
  expressed in terms of the statistics of singular structures on the
  shocks, namely the points of shock generation and collisions.  The
  scaling laws of the structure functions are derived through the
  analysis of the master equations.  Rigorous bounds on the decay of
  the tail probabilities for the velocity gradient are obtained using
  realizability constraints.  We also establish that the probability
  density function $Q(\xi)$ of the velocity gradient decays as
  $|\xi|^{-7/2}$ as $\xi \to -\infty$.

Massimo Vergassola (Nice)

``Kinematic Dynamo Theory"

Abstract: The theory of magnetic dynamo in a Batchelor incompressible
flow is presented. An explicit formula for the growth rate of the magnetic
field is in particular discussed.

Zelmann Warhaft (Cornell)

``Anisotropy of inertial and dissipation-scale
statistics in high Reynolds number turbulence."

Abstract:We examine small scale statistics derived from wind tunnel
measurements with imposed mean shear.We study statistics that are
sensitive to flow anisotropy,such as transverse odd moments of
longitudinal velocity derivatives and differences, and mixed
structure functions of the transverse and longitudinal velocity
components.We compare our findings with recent results of
atmospheric data using SO(3) symmetry decomposition.Our results show
that the ratio of the scaling exponents of the j=2 (anisotropic)
sector to the j=0 (isotropic) sector decreases with increasing order
suggesting that at higher orders isotropy may not be restored at the
small scales,a result consistent with our earlier findings (Shen and
Warhaft Phys. Fluids 11,2976(2000)).

Oleg Zaboronski (Warwick)

``On Intemittency in Stochastic Aggregation "
Abstract: We show that the Kolmogorov scaling of the average mass distribution of the
system of sticky partciles breaks down due to intermittency of mass cascade. We also
show how dynamical RG can be used to compute corrections to Kolmogorov scaling.