What is TILT?
This project is devoted to studying and modeling the fine structure
of fluid turbulence, which affects a wide range of phenomena in
science and engineering.
A surprising and still poorly understood
property of the infinite-Reynolds-number limit for turbulent flow is
the existence of a finite viscous dissipation, even when
viscosity becomes vanishingly small. To maintain such an efficient
way of dissipating energy, the flow self-organizes, following a
cascading process, and develops a tortuous spatial structure at
small scales. Asymptotically, various kinematic quantities, such as
the velocity, become rough and non-differentiable. The finiteness
of the rate at which injected energy is turned into heat in the
fully developed turbulent regime is known as the dissipative
anomaly. This property rests on the singular nature and deep
irreversibility of turbulent flows, and is the source of severe
difficulties when applying concepts developed in equilibrium
statistical mechanics.
The present project aims at obtaining quantitative progress in the
understanding of this highly singular behavior. For this, we propose
to build a consortium of leading theoretical and computational
physicists from this field of research, and to put the focus on the
irreversible nature of turbulence. There will be special emphasis
regarding the signature of irreversible processes on the motion of
tracers transported by the flow.
The collaborative network will be articulated around the generation
of a database containing results of state-of-the-art simulations of
(i) the Navier-Stokes equation, of (ii) a newly proposed systems,
describing a fluid velocity field, with a \textit{reversible}
dissipation, of (iii) weak dissipative solutions of the Euler
equations, following a recently proposed method of construction, and
last, (iv) synthetic random fields allowing us to study the
signature of various key statistical ingredients of turbulence
phenomenology. This database will be made accessible to all the
participants for answering questions raised in several workpackages
developed in the course of the project.
The consortium consists of 3 groups with complementary numerical and
theoretical expertise, in statistical mechanics and fluid
turbulence. They are located in Saclay, at CEA (B. Dubrulle), in Lyon, at ENSL (L. Chevillard, A.
Pumir), and in Nice, both at MINES
ParisTech and at the Observatoire de la Cote d'Azur (J. Bec,
N. Besse, U. Frisch). The potential knowledge gained will be
key in developing a better description and improved models of
turbulent fluctuations in processes such as transport or mixing.