Small-scale turbulence : Theory, Phenomenology and Applications

Petites échelles de la Turbulence : Théorie, Phénoménologie et Applications

Cargèse, August 13th to 25th, 2007

Invited speakers and lecture
Organizing Committee
Scientific Committee
Registration fees
Travel information
Acknowledgements to:

CNRS           ERCOFTAC           AFM           OCA           CASSIOPE           WD           DGA
        Ecole Vortex, 2004


Topics :
Despite its large number of applications such as climate, biological flows, chemical engineering, turbulence is still today one of the least understood phenomena in physics. Though the Navier-Stokes equations describing the fluid 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 sensitivity to initial conditions, has been only recently understood via dynamical systems theory. In the absence of 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 goal for industrial and environmental applications : reducing noise and pollution, energy economy, optimisation of chemical reactors, better combustion efficiency etc. Because of the complexity of these applications, a reliable description and modelling of turbulent flows is based on a good understanding of turbulence, from a fundamental viewpoint.

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

In this context, one fundamental question is are these small scales universal? If so, under which conditions? If not, when? The non-universality of the small-scale behaviour, closely related to small-scale anisotropy, can be recast 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. Particular attention must be paid to the dissipation rate of the scalar variance, as well as to its local anisotropic behaviour. 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 scenarios.

* In the context of the statistical approach, when the small scales are explicitly linked to the turbulence forcing. Different subjects are to be discussed :
o The role played by coherent structures. Turbulence in rotation.
o Inertial transport, e.g. droplets transport.
o Etc...

Another important question concern the correct measurements of small-scale quantities (using either hot/cold wires, or lasers : PIV, LDV, PLIF). This exclusively aspect experimental is worth discussing, with the aim of discussing on the limits of the experimental techniques.

Another aspect to be discussed concerns the practical application of the fundamental description of small-scale turbulence. We particularly aim at non-reacting mixing, as a first-level stage of 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 connection with better turbulent combustion, is recently of particular importance (expensive fuels, pollution reduction, energy economy etc.). In this direction, it is important to better understand the micromixing properties, i.e. of small-scale mixing, where the chemical reactions that constitute combustion take place. A number of questions concerning reactive flows remain. 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 turbulent mixing would be useful for the LES technique, in the context of sub-grid scale models.

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.

The communities traditionally involved in turbulence are numerous (classical fluid mechanics, physical mechanics, magneto-hydrodynamics, chemical engineering, etc....). However, while some of them have already developed regular contacts and discussions, some others are still isolated. 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 : 1) provide a general and interdisciplinary teaching on the subject of small-scale turbulence, 2) generate contacts and collaborations.

The Institute of Scientific Studies of Cargèse offers unique opportunity to bring together people from different domains of physics (statistical physics, signal treatment, fluid mechanics, etc. ...) directly involved in the study of turbulence. The project is thus interdisciplinary : people with different horizons, such as GDR (french research group) turbulence, sub-grid scale models, micromixing, combustion.

Scientific aims of the school :
The aim is to bring together people from different scientific communities, that have turbulence as a common point. This would identify different manners to treat turbulent flows. The final aim of this school is to point out open questions, and possibly answers,as well as contacts and collaborations among people.

Participants :
- Academic researchers, Ph.D. and post-doctoral students.
- Industrial researchers.

Pedagogical method :
During the two weeks, courses will be taught by a number (10-12) of turbulence specialists. Each course will be 1h30 long, with the aim of stimulating exchanges and discussions among participants. Most of the classes are scheduled in the morning and late afternoon. Less formal meetings, as well as poster sessions, are scheduled during the two weeks. Young scientists will also have 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). See below

Invited speakers

F. Anselmet,
Measurements in a hydrodynamical channel to study environmental problems
          Lecture : Anselmet1.pdf & Anselmet2.pdf

R. A. Antonia,
On the measurement of small-scale turbulence
          Lecture : Antonia1.pdf
On the correlation between small-scale velocity and scalar characteristics in a turbulent channel flow
          Lecture : Antonia2.pdf

C. Baudet,
Lagrangian investigation of turbulence : experimental techniques and statistical results
          Lecture : Baudet1.pdf,
Turbulence measurements under extreme conditions : the example of cryogenic flows
          Lecture : Baudet2.pdf

J. Bec,
Preferential concentrations of impurities in turbulent suspensions
          Lecture : Bec.pdf

C. Cambon,
Strongly anisotropic turbulence structure and cascade: stably-stratified and rotating flows (mainly) revisited
          Lecture : Cambon.pdf

M. Cencini,
Active versus passive scalar turbulence
          Lecture : Cencini.pdf

P. Comte,
Large eddy simulations and subgrid scale modelling of turbulent shear flows
          Lecture : Comte.pdf

F. X. Demoulin,
Some aspects of turbulent mixing in two phase flows
          Lecture : Demoulin.pdf

R. Fox,
Micromixing model for turbulent reacting flows
          Lecture : Fox.pdf

Y. Kaneda,
DNS study of the universality at small scales of turbulence at high Reynolds number
          Lecture : Kaneda1.pdf
Small-Scale Anisotropy in High Reynolds Number Turbulence
          Lecture : Kaneda2.pdf

A. Lanotte,
Two-dimensional turbulence
          Lecture : Lanotte.pdf

A. Pouquet,
MHD Turbulence
          Lecture : Pouquet.pdf

D. Pullin,
Evidence for the existence of eddy-structure in fine-scale turbulence
          Lecture : Pullin1.pdf
Physical models for small-scale structures
          Lecture : Pullin2.pdf
Stretched vortices as a basis for subgrid-scale modeling
          Lecture : Pullin3.pdf
Large-eddy simulation of turbulence with the stretched-vortex SGS model
          Lecture : Pullin4.pdf

A. Pumir,
Turbulence phenomenology and the tetrad model
          Lecture : Pumir.pdf

B. Renou,
Towards two-dimensional measurements of small scales (scalar and velocity) : principles and limitations. Application for a highly turbulent flow field
          Lecture : Renou.pdf

E. Villermaux,
Scalar mixing: principles and consequences
          Lecture : Villermaux1.pdf
Liquid fragmentation: from ligaments to drop size distributions
          Lecture : Villermaux2.pdf

Other lectures:
F. Plaza,
Scalar injection and turbulence

W. Bos,
A two-point closure based on a Lagrangian timescale

R. Marino,
The inertial range of solar wind MHD turbulence

S. Danaila,
Turbulence model for predicting heat transfer in boundary layer flows



PDF file of the program: Program.pdf


The summer school will be held in the Institut d'Etudes Scientifiques de Cargèse, an Institute devoted to this type of meetings. It is located close to the beach at walking distance (20 min. via the main road, 15 min. via a 'goat path') from the village of Cargèse.
Lunch for all participants will be served at the Institute (except during the weekend).
Some pictures of a previous summer school...

The Organizing Committee

Luminita Danaila (CORIA, Rouen)
Alain Noullez (Obs. de la Côte d'Azur, Nice)
Philippe Petitjeans (PMMH - ESPCI, Paris)

All e-mail should be sent to

  (e-mail are strongly preferred to postal mail or Fax)

Address :
Philippe Petitjeans, LPMMH - ESPCI
10, rue Vauquelin
75231 Paris Cedex 05
Tel : (33) 1 40 79 44 95

Fax : (33) 1 40 79 45 23

The Scientific Committee

Robert Antonia (Académie des Sciences, Australia)
Jean-Pierre Bertoglio (Ecole Centrale de Lyon, France)
Luminita Danaila (CORIA, Rouen, France)
Rodney Fox (Iowa State University, USA)
Alain Noullez (Observatoire de la Côte d'Azur, Nice, France)
Philippe Petitjeans (PMMH - ESPCI, Paris, France)
Michel Trinité (Département Ingénierie, CNRS, Paris, France)


Please fill the form and sent it back by e-mail or fax : pre-registration form (Word) , pre-registration form (pdf)

Registration should be sent to

  (e-mail are strongly preferred to postal mail or Fax)

Address :
Philippe Petitjeans, LPMMH - ESPCI
10, rue Vauquelin
75231 Paris Cedex 05
Tel : (33) 1 40 79 44 95

Fax : (33) 1 40 79 45 23


Registration still possible.

Registration fees

There is no registration fees .
Accommodations, meals and travel will be at your own expense.
Purchase order (Bon de commande) may be used to cover your lunches and lodging. See below for prices.

Partial financial supports may be available for students or young scientists upon request before May 2007.


Housing, for the duration of the course only, will be arranged by the staff of the Institute following, as much as possible, your preferences.

* Shared room in the Institute or in the village : 28 Euros per night
* Individual room in the Institute or in the village : 38 Euros per night
* Apartment for a couple in the village : 38 + 20 Euros per night
* Apartment for a family in the village : 38 + 20 per person Euros per night
* Camping at the Institute : 5 Euros per night (Showers etc. are available. You have to bring your own camping equipment.)

A mail will be sent to all participant to ask for preferences. Please do not send any request concerning the housing before that.

Lunch for all participants will be served at the Institute (except during the weekend) : 9.40 Euros per lunch (5,50 for children)

Travel information

Because of the other summer schools before and after this one, it is not possible to come to the Institute before or to stay after the meeting. You should arrive on the morning of Monday 13th August, and leave your appartment Saturday 25th August before 10 AM. Ajaccio can be reached by plane from Paris, Marseille or Nice, and by boat from Marseille, Nice or Genova.

Be careful : the school starts at the same time as the big rush for summer holidays in France. It may be difficult to get a reasonable price for your flight/boat to Ajaccio if you wait too long.

The institute is located on the seashore of the island of Corsica, 50 km north of Ajaccio, 2 km south of Cargèse, a pleasant village of considerable charm and historic interest.
If enough participants arrive at Ajaccio airport Monday morning 13th August, transport by bus from and to the Ajaccio airport will be organized. Further information will be available on this site. Otherwise, you will have to go to Cargèse by yourself.
There are regular buses from Ajaccio bus station to Cargèse twice a day (except on Sundays).
Ajaccio to Cargèse : 7:30 and 15:30
Cargèse to Ajaccio : 9:15 and 15:15
The bus station, which is also the maritime station, can be reached via a shuttle from the airport. Ajaccio bus station phone number : (33) (0)4 95 51 55 45.
A taxi can be booked through the Institute at the rate of 80 euros (95 euros for early, late and non working day transfers).
Car rental at preferential rates is available through the Institut.
If you drive to Cargese, from Ajaccio, follow the direction "Calvi par la côte" (or "Calvi" when missing).


List of Participants

Pictures of the BBQ party

Some pictures of the BBQ party

If you have more pictures, we can add them !

En application de la loi 78-17 du 6 janvier 1978 relative à l'informatique des fichiers et aux libertés, chaque personne inscrite dispose des droits d'opposition, d'accès, et de rectification des données le concernant pour vérifier, corriger, ou supprimer les informations le concernant.