Small-Scale Turbulence: Theory, Phenomenology and Applications

Cargèse, Corsica, France.
August 13th - 25th, 2007.



Despite its large number of applications (climate, biological flows, chemical industry etc.), turbulence is still today, one of the less understood phenomena in physics. Though Navier?Stokes equations, describing the fluids motion, are relatively simple, their non-linear character does not allow for a general solution.  The origin of this impossibility, associated with a high number of degrees of freedom and a very high sensibility to initial conditions, has been only recently understood via the dynamical systems theory. In the absence of an unifying theory, progress in  understanding turbulent flows is primarily based on experimental measurements, numerical simulations and on our ability to interpret results using specific tools (wavelets, spectra etc.).  Understanding turbulence is a major point for industrial and environmental applications: reducing noise and pollution, energy economy, optimisation of chemical reactors, better combustion efficiency  etc.  Because of their complexity, a reliable description and modelling of turbulent flows is based on a good understanding of turbulence, from a fundamental viewpoint.

Turbulent flows are known as containing a wide range of scales, each range of scales being characterized by different phenomena. For instance, the dissipation process is known as being a small-scale phenomenon.  Therefore, in different industrial process, a role particularly important is played by the small scales. They are to be properly taken into account in the sub-grid scales (SGS) models.  Another example deals with modelling micromixing (chemical industry, combustion), in which the small scales are the most important players.

In this context, one fundamental question is: are these small scales universal? If yes, under which conditions? If not, when? The non-universality of the small-scale behaviour, in tight connexion with the small?scale anisotropy, can be recasted and presumably explained in different contexts:    

  • In the context of the local structure of turbulence, from a kinematic point of view. It is interesting to detect the role of local velocity gradients, under the effect of strain and rotation. A particular attention is to be paid to the dissipation rate of the scalar variance, as well as to its local anisotropic bahaviour.   The influence of each single mechanism (straining, rotation, molecular diffusion) can be formally studied in model configurations. However, their combination in the case of  a scalar transported by a turbulent flow, leads to complex scenarii. 
  • In the context of the statistical approach, when the small scales are explicitly linked to the turbulence forcing.  Different subjects are to be discussed:
    • The role played by coherent structures. Turbulence in rotation.
    • Inertial transport, e.g. droplets transport.
    • Etc?

Another important question concern the correct measurements of  small?scale quantities (using either hot/cold wires, or lasers: PIV, LDV, PLIF). This aspect exclusively experimental is worth being discussed, with the aim to clearly conclude on the limits of the experimental techniques used in laboratory.

Another aspect to be discussed concerns the practical application of the fundamental description of small-scale turbulence. We particularly aim at the non-reacting mixing, as a first?level stage of the reacting mixing. This phase of ?mixing preparation? is particularly important for reactive flows (chemical industry, combustion etc).  As an example, as far as combustion is concerned,  a fine and precise characterization of the air/gaseous fuel mixing, in connexion with a better turbulent  combustion, is recently of a particular importance (expensive fuels, pollution reduction, energy economy etc.).  In this direction, it is important to better understand the micromixing properties, i.e. of the small-scale mixing, where the chemical reactions that constitute combustion take place. Number of questions concerning reactive flows remain without clear answer. As an example, the alignment of the mixing fraction gradient with the velocity gradient eigenvectors controls the evolution of the scalar dissipation and thus plays an important role in the non-premixed turbulent flames.

We note finally that a correct and quantitative diagnostic of small scales in a turbulent mixing are to be useful  for the LES technique, in the context of sub-grid scales models.

Scientific Committee:

Robert Antonia,  Academician, Sciences Academy, Australia
Jean-Pierre Bertoglio, Ecole Centrale de Lyon
Luminita Danaila, CORIA, Rouen
Rodney Fox,  Iowa State University, U.S.A.
Alain Noullez, Observatoire de la C?te d'Azur, Nice
Philippe Petitjeans, ESPCI, Paris
Michel Trinitè, Engineering Department, CNRS, Paris

Organizing Committee:

Luminita Danaila, Alain Noullez, Philippe Petitjeans

Scientific Situation and Purposes:

Interest of the topic and aims of the School:

In many different scientific domains, significant progress has been possible because of the techniques imported from other domains. This progress was possible only because researchers used knowledge a priori specific to different activity domains.

The communities traditionally involved in turbulence study are numerous (classical fluid mechanics, physical mechanics, magneto-hydrodynamics, chemical industry, etc.?). However, if some of them have already developed regular contacts and discussions, some others are still isolated. In all the cases, turbulence is the common point. This is an important reason for which it seems necessary to bring together researchers originating from some of these communities, in a summer school that would allow for: 1) providing a general and interdisciplinary teaching on the subject of small?scale turbulence, 2) generate contacts and collaborations.

In this context, the Institute of Scientific Studies of Cargèse offers an unique opportunity to bring together people from different domain of physics (statistical physics, signal treatment, fluid mechanics, etc. ?) directly involved in turbulence study. The project is thus interdisciplinary: people with different horizons,  such as GDR (research group) Turbulence, sub-grid scales models, micromixing, combustion etc., that  do not have often the opportunity to meet together and to discuss recent progress in these domains.

Scientific aims of the school:

The aim is to bring together people from different scientific communities, that have a common point, the turbulence. This would allow for clearly identifying different manners to

treat turbulent flows. The final aim of this school is to point out open questions, eventually answers of them, contacts and collaborations among people.

Public concerned:

- Researchers, Ph.D. and post-doctoral students.
- Industrials.

Pedagogical method:

During the 2 weeks, courses will be taught by a number (10-12) of turbulence specialists. Each course will be 1h30 long, in the aim of stimulating exchanges and discussions among participants.  Most of the conferences are scheduled in the morning and late afternoon. Less formal meetings, as well as posters sessions, are scheduled during the 2 weeks. Young scientists will also meet the opportunity to briefly present their work, questions and results.

Documents published

All the presentations will be made available on the school website (.pdf files).