Workshop on statistical mechanics, fractals, instabilities and turbulence, in fluids and superfluids 

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Outline

This workshop can be seen as a follow-up of the Winter school at Les Houches, February 22-26, 2010, but at smaller scale and on a more focussed list of topics.

According to the title of our SIG, ‘Multipoint Turbulence Structure & Modelling’ (MPTSM hereinafter), we continue to address fundamental issues and challenges of turbulence theory and modelling, but we keep in mind practical modelling for engineering and environmental flows. In this sense, a significant overlapping exists with the SIG 15, for instance with common interest in ‘structure-based modelling’ (S. Kassinos and coworkers, C. Cambon and coworkers, among others).

The apparent broad range of themes in the proposed title reflects different domains of competence by the participants (listed below) but we share the same interest for investigating points of contact between our domains with cross-fertilization.

Four themes will be chosen:

• Advances in modelling superfluid. Some studies (M. E. Brachet, B. Dubrulle, F. Daviaud) are at the cross-road of statistical classical mechanics and quantum mechanics. Very recent aspects are new theoretical and numerical results using a spectral closure (EDQNM, from the Kraichnan and Orszag’s legacy) for the dynamics and statistics of superfluid Helium, as a bi-fluid (classical fluid and quantic fluid) medium (P. Sagaut).

• Revisiting instabilities and turbulence using basic concepts of statistical mechanics and new invariants (B. Dubrulle, A. Chiffaudel, A. Naso). The case of the von Karman flow will be mainly addressed, with bifurcations between different flow patterns and transition to turbulence, but other flows, with and without rotation (F. Moisy), will be discussed.

• From stable stratification to instable cases. Stably stratified turbulence is a long-term topic in the Lyon’s team (ECL, list below). New recent elements yield to re-attack, with the tools of MPTSM, buoyancy-driven flows such as thermal convection (destabilising temperature gradient) and even Rayleigh-Taylor instability with transition to turbulence. Collaboration with the CEA (A. Llor, B-J Gr´ea) is particularly encouraging, from spectral approaches (RDT, nonlinear closures, supported by high resolution DNS towards LES) and engineering-oriented models, like bi-fluid k − e. This theme is also important for the SIG 14 (J. M. Redondo).

• Fractal approaches. Experiments are carried out in the team of J. C. Vassilicos, which question the ‘Kolmogorov’s vulgate’. We hope to continue to discuss to what extent this gives new ideas and can suggest a renewest theoretical, and why not numerical, approach.

Provisional list of active participants:

- J. Christos Vassilicos, Pedro Valente, Sylvain Layzet (Imperial College, London, UK)

- Pierre Sagaut (Institut Jean Le Rond d’ Alembert, Paris)

- Frédéric Moisy (FAST, Orsay, near Paris)

- Marc Etienne Brachet (ENS Paris)

- Bérangère Dubrulle, François Daviaud, Arnaud Chiffaudel (CEA, CNRS Paris)

- Antoine Llor, Benoit-Joseph Gréa (CEA, DAM, near Paris)

- Aurore Naso, Wouter Bos, Claude Cambon, Fabien S. Godeferd, Andrew Lawrie (LMFA, Ecole Centrale de Lyon, France)

- Benjamin Favier (Newcastle, UK, formerly Lyon)