Time Irreversibility in Lagrangian Turbulence – TILT

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.

To come!

to come

Many papers

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 genuine 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 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 being 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 Côd'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.