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Résumé |
In this talk I will give a brief overview of homogeneous, isotropic
fluid turbulence; this overview will
highlight similarities between the statistical properties of such
turbulence and the scaling properties
of correlation functions at a critical point in, say, a spin system. I
will then concentrate on our recent work, which
uses a statistical-mechanical perspective to examine two problems in
turbulence, namely, persistence and
dynamic multiscaling. In particular, I will present a natural
framework for studying the persistence
problem in two-dimensional fluid turbulence by using the Okubo-Weiss
parameter to distinguish between vortical and
extensional regions. The results I will present use our direct
numerical simulation (DNS) of the two-dimensional (2D), incompressible
Navier-Stokes (NS) equation with friction to study probability
distribution functions (PDFs) of the persistence times of vortical and
extensional regions by employing both Eulerian and Lagrangian
measurements. I will show that, in the Eulerian case, the
persistence-time PDFs have exponential tails; by contrast, this PDF
for Lagrangian particles, in vortical regions, has a power-law tail
with an exponent that is approximately 2.9. I will then turn to a
discussion of dynamic multiscaling in fluid turbulence. After a brief
review of our earlier work, I will show how different ways of
extracting time scales from time-dependent vorticity structure
functions lead to different dynamic-multiscaling exponents; in the
multifractal model, these are related to equal-time multiscaling
exponents by different classes of bridge relations. I will then
demonstrate how we check this explicitly, for quasi-Lagrangian and
Eulerian structure functions, by using detailed DNSs of statistically
steady turbulence in the 2D incompressible NS
equation with friction.
These studies have been carried out in collaboration with
Prasad Perlekar, Department of Physics and Department of
Mathematics and Computer Science. Eindhoven University of
Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
Samriddhi Sankar Ray, Laboratoire Cassiopee, Observatoire de la
Cote d'Azur, UNS, CNRS, BP 4229, 06304 Nice Cedex 4, France
Dhrubaditya Mitra, NORDITA, Roslagstullsbacken 23, SE-10691
Stockholm, Sweden
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