1 Facts about the Workshop
This workshop was convened on November 13-15 1995 by E. Falgarone and D. Schertzer
within the framework of the Groupe de Recherche Mecanique des Fluides Geophysiques et
Astrophysiques (GdR MFGA, Research Group of Geophysical and Astrophysical Fluid Mechanics)
of Centre National de la Recherche Scientifique (CNRS, (French) National Center for
Scientific Research). This Research Group is chaired by A. Babiano and the meeting was
held at Ecole Normale Superieure, Paris, by courtesy of its Director E. Guyon. More than
sixty attendees participated to this workshop, they came from a large number of
institutions and countries from Europe, Canada and USA. There were twenty-five oral
presentations as well as a dozen posters. A copy of the corresponding book of abstracts
can be requested to the conveners.
The theme of this meeting is somewhat related to the series of Nonlinear Variability in
Geophysics conferences (NVAG1, Montreal, Aug. 1986; NVAG2, Paris, June 1988; NVAG3,
Cargese (Corsica), September, 1993), as well as seven consecutive annual sessions at EGS
general assemblies and two consecutive spring AGU meeting sessions devoted to similar
topics. One may note that NVAG3 was a joint American Geophysical Union Chapman and
European Geophysical Society Richardson Memorial conference, the first topical conference
jointly sponsored by the two organizations. The corresponding proceedings were published
in a special NPG issue (Nonlinear Processes in Geophysics 1, 2/3, 1994). In comparison
with these previous meetings, MFGA-IDT2 is at the same time specialized to fluid
turbulence and its intermittency, and an extension to the fields of astrophysics. Let us
add that Nonlinear Processes in Geophysics was readily chosen as the appropriate journal
for publication of these proceedings since this journal was founded in order to develop
interdisciplinary fundamental research and corresponding innovative nonlinear
methodologies in Geophysics. It had an appropriate editorial structure, in particular a
large number of editors covering a wide range of methodologies, expertises and schools. At
least two of its sections (Scaling and Multifractals, Turbulence and Diffusion) were
directly related to the topics of the workshop, in any case contributors were invited to
choose their editor freely.
2 Goals of the Workshop
The objective of this meeting was to enhance the confrontation between turbulence
theories and empirical data from geophysics and astrophysics fluids with very high
Reynolds numbers. The importance of these data seems to have often been underestimated for
the evaluation of theories of fully developed turbulence, presumably due to the fact that
turbulence does not appear as pure as in laboratory experiments. However, they have the
great advantage of giving access not only to very high Reynolds numbers (e.g. 1012 for
atmospheric data), but also to very large data sets.
It was intended to:
(i) provide an overview of the diversity of potentially available data, as well as the
necessary theoretical and statistical developments for a better use of these data (e.g.
treatment of anisotropy, role of processes which induce other nonlinearities such as
thermal instability, effect of magnetic field and compressibility ... ),
(ii) evaluate the means of discriminating between different theories (e.g. multifractal
intermittency models) or to better appreciate the relevance of different notions (e.g.
Self-Organized Criticality) or phenomenology (e.g. filaments, structures),
(iii) emphasise the different obstacles, such as the ubiquity of catastrophic events,
which could be overcome in the various concerned disciplines, thanks to theoretical
advances achieved.
3 Outlines of the Workshop
During the two days of the workshop, the series of presentations covered many
manifestations of turbulence in geophysics, including: oceans, troposphere, stratosphere,
very high atmosphere, solar wind, giant planets, interstellar clouds... up to the very
large scale of the Universe. The presentations and the round table at the end of the
workshop pointed out the following:
- the necessity of this type of confrontation which makes intervene numerical
simulations, laboratory experiments, phenomenology as well as a very large diversity of
geophysical and astrophysical data,
- presumably a relative need for new geophysical data, whereas there have been recent
astrophysical experiments which yield interesting data and exciting questions;
- the need to develop a closer intercomparison between various intermittency models (in
particular Log-Poisson /Log Levy models).
Two main questions were underlined, in particular during the round table:
- the behaviour of the extremes of intermittency, in particular the question of
divergence or convergence of the highest statistical moments (equivalently, do the
probability distributions have algebraic or more rapid falloffs?);
- the extension of scaling ranges; in other words do we need to divide geophysics and
astrophysics in many small (nearly) isotropic subranges or is it sufficient to use
anisotropic scaling notions over wider ranges?
4 The contributions in this special issue
Recalling that some of the most useful insights into the nature of turbulence in fluids
have come from observations of geophysical flows, Van Atta gives a review of the impacts
of geophysical turbulence data into theories. His paper starts from Taylor's inference of
the nearly isotropy of atmospheric turbulence and the corresponding elegant theoretical
developments by von Karman of the theory of isotropic turbulence, up to underline the fact
that the observed extremely large intermittency in geophysical turbulence also raised new
fundamental questions for turbulence theory. The paper discusses the potential
contribution to theoretical development from the available or currently being made
geophysical turbulence measurements, as well as from some recent laboratory measurements
and direct numerical simulations of stably stratified turbulent shear flows.
Seuront et al. consider scaling and multiscaling properties of scalar fields
(temperature and phytoplankton concentration) advected by oceanic turbulence in both
Eulerian and Lagrangian frameworks. Despite the apparent complexity linked to a
multifractal background, temperature and fluorescence (i.e. phytoplankton biomass
surrogate) fields are expressed over a wide range of scale by only three universal
multifractal parameters, H, \alpha and C_l. On scales smaller than the characteristic
scale of the ship, sampling is rather Eulerian. On larger scales, the drifting platform
being advected by turbulent motions, sampling may be rather considered as Lagrangian.
Observed Eulerian and Lagrangian universal multifractal properties of the physical and
biological fields are discussed.
Whereas theoretical models provide different scaling laws for fluid and MHD turbulent
flows, no attempt has been done up to now to experimentally support evidence for these
differences. Carbone et al. use measurements from the solar wind turbulence and from
turbulence in ordinary fluid flows, in order to assess these differences. They show that
the so-called Extended Self-Similarity (ESS) is evident in the solar wind turbulence up to
a certain scale. Furthermore, up to a given order of the velocity structure functions, the
scaling laws of MHD and fluids flows axe experimentally indistinguishable. However,
differences can be observed for higher orders and the authors speculate on their origin.
Dudok de Wit and Krasnosel'skikh present analysis of strong plasma turbulence in the
vicinity of the Earth's bow shock with the help of magnetometer data from the AMPTE UKS
satellite. They demonstrate that there is a departure from Gaussianity which could be a
signature of multifractality. However, they point out that the complexity of plasma
turbulence precludes a more quantitative understanding. Finally, the authors emphasise the
fact that the duration of records prevents to obtain any reliable estimate of structure
functions beyond the fourth order.
Sylos Labini and Pietronero discuss the problem of galaxy correlations. They conclude
from all the recently available three dimensional catalogues that the distribution of
galaxies and clusters is fractal with dimension D ~ 2 up to the present observational
limits without any tendency towards homogenization. This result is discussed in contrast
to angular data analysis. Furthermore, they point out that the galaxy-cluster mismatch
disappears when considering a multifractal distribution of matter. They emphasise that a
new picture emerges which changes the standard ideas about the properties of the universe
and requires a corresponding change in the related theoretical concepts.
Chilla et al. investigate with the help of a laboratory experiment the possible
influence of the presence of a large scale structure on the intermittency of small scale
structures. They study a flow between coaxial co-rotating disks generating a strong axial
vortex over a turbulent background. They show that the cascade process is preserved
although strongly modified and they discuss the relevance of parameters developed for the
description of intermittency in homogeneous turbulence to evaluate this modification. |