This six-week program (12 March 2012 to 20 April 2012) will focus on recent development in the understanding of fluid dynamics turbulence with the goal to identify promising breakthrough directions.
From the point of view of theoretical physics, turbulence is a classical field theory, out of equilibrium and in a strong coupling regime.
Turbulence is one of the great problems of classical physics still mainly unsolved. With turbulence we mean a physical state of a flow with many dynamically active variables and far from equilibrium. The first difficulty in theoretical approaches to turbulence consists in the large number of active degrees of freedoms. The scales where energy is injected is typically strongly separated from the scales where energy is dissipated. Non-linear interactions lead to a strong coupling between all degrees of freedoms. Energy transfer may be in average positive, leading to formation of small-scales fluctuations superposed to large scale structures or in average negative, leading to an accumulation of energy at larger and larger scales. Moreover, fluctuations around the mean can be Gaussian or strongly intermittent, depending on the direction of the energy cascade and on the dimensionality of the system. The situation is complicated in presence of active scalar fields, like for the case of thermal convection, active vector fields, as in magnetohydrodynamics and/or by the presence of boundaries, where also a net transfer of momentum is established in the system. The Lagrangian point of view, measuring underlying fluid velocity riding tracers or inertial particles, point-like or with a finite size, is also crucial to control statistical properties at different frequencies.
Among the questions that will be address during the program we cite: is the energy cascade in isotropic turbulence universal? What are the corrections expected in presence of large scale anisotropy? What happens if external or internal mechanism breaks parity invariance? What happens at changing the embedding dimensionality? Can we improve sub grid modeling by a better understanding of the energy cascade mechanism? What are the effects of strong active fields, like in thermal convection and MHD? Are large scale structures universal in these latter cases? What are the statistical connections between Eulerian and Lagrangian descriptions. Can 2d and 3d physics coexist? Can we smoothly change from a 2d to a 3d systems? What about turbulence in 1d turbulence (Burgers equations) in 0d (Shell Models) in larger and larger dimension or even in non-integer dimensions?
A partial answer to even only a small sub-set of these questions will require important synergies between scientists from theory, numerics and experiments and would qualify the program as big success.
The program will be organised in "focused" weeks concerning one or two of the above topics.
12/03-18/03 : sub-grid modeling, wall bounded flows, Non Newtonian flows.
19/03-25/03 : 2d and 3d systems. Turbulence in rotating systems; Geophysical flows.
26/03-01/04 : Lagrangian and Eulerian turbulence.
02/04-06/04 : INTERNATIONAL CONFERENCE.
07/04-13/04 : Thermal convection & Magnetohydrodynamics.
14/04-20/04 : Turbulence modeling and theory.