Atelier Turbulence and Wave-Vortex Interactions in Fluids and Plasmas


Typical structures in turbulent flows are vortices and waves. The first ones are immediatelyidentified in spatial ‘snapshots’, and are extensively studied in connection with organizedmotion interacting with unstructured motion. On the other hand, nonlocal waves need acomplete spatio-temporal analysis, if we exclude local quasi-stationary shocks (higly com-pressible turbulence and Burger turbulence will be not addressed.) In addition to acousticwaves, which affect weakly compressible flows in the near field (aroacoustics in the far field isoutside our scope), dispersive waves are triggered by external forces (Coriolis, buoyancy) ormean-gradient-effects (stable stratification, shear) in, e.g., quasi-incompressible geophysicalflows: Inertial waves, internal gravity waves, Rossby waves, Kelvin waves, and mixed ones.Even in the simplest case of weakly compressible turbulence, and in stably-stratified turbu-lence with buoyancy, wave and vortex modes are simultaneously present and can interact.

This theme is important from magnetohydrodynamics to plasma physics, but the diversityof wave motion, accounting for coupling with the magnetic field, is enhanced with respect tothe purely ‘hydro’ case, with Alfvèn-type waves and various drift waves. For instance, theLagrangian diffusion can be strongly altered by dispersive waves, so that waves can dominatethe capping of fluid trajectories (or real particles), that is generally attributed to vortexstructures in the ‘hydro’ community. Alteration of single-particle and two-particle diffusionby waves and vortices is therefore a common theme in ‘hydro’ (rather geophysics with waves)and plasmas communities.

Finally, faced with the recent fast development of wave turbulence theory, but more for sur-facic waves or vibrating plates, it is very important to made a state-of-the-art and to explorethe future of a generalized spectral theory, possibly incorporating linear ‘Rapid Distortion’operators and triadic closures. Applications range from engineering to astrophysics: Let usmention the rotating shear flow, which can be used as a model in turbomachinery (interbladechannel) and more recently in astrophysics (accretion discs). Of course, comparisons withDNS results and/or with simpler phenomenological theories/ models will be extensively discussed. Particularly, vortex and waves structures can coexist, introducing a new paradigm ofcoexistence and interaction of cascades in ‘weak’ and ‘strong’ turbulence.

The following list of themes will be addressed:
1. Rotating turbulence, with and without stable stratification, with and without confin-ment. New paradigm of interacting ‘strong’ and ‘weak’ turbulence.
2. Lagrangian diffusion in fluids and plasmas: Capping of trajectories by waves and vor-tices.
3. Organized motion in complex shear flows, and interactions
4. From theory and high resolution DNS to improved models for engineering and environ-ment.
5. And beyond: perspectives in Energy, towards nuclear fusion and ITER project
6. And beyond: perspectives in geophysics, towards prediction of climate


Dates: du Lundi 20 Octobre 2014 au Mardi 21 Octobre 2014

Lieu: École Centrale de Lyon, Amphi 203

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