Speaker: Bérengère Dubrulle, CNRS, SPEC, CEA Saclay, Université Paris-Saclay, 91190 Gif sur Yvette Cedex, France

Time : 15:00 - 16.00 CEST (Rome/Paris)

Hosted at: SISSA, International School of Advanced Studies, Trieste, Italy

Zoom :  A zoom meeitng link will appear here, one hour before the talk

Organizers : Pavan Pranjivan Mehta* (pavan.mehta@sissa.it) and Arran Fernandez** (arran.fernandez@emu.edu.tr)

* SISSA, International School of Advanced Studies, Italy

** Eastern Mediterranean University, Northern Cyprus

Keywords:  turbulence; multi-fractals; universality; singularity

Abstract: In most geophysical flows, vortices (or eddies) of all sizes are observed. In 1941, Kolmogorov devised a theory to describe the hierarchical organization of such vortices via a homogeneous self-similar process. This theory correctly explains the universal power-law energy spectrum observed in all turbulent flows. Finer observations however prove that this picture is too simplistic, owing to intermittency of energy dissipation and high velocity derivatives. In this review, we discuss how such intermittency can be explained and fitted into a new picture of turbulence. We first discuss how the concept of multi-fractality (invented by Parisi and Frisch in 1982) enables to generalize the concept of self-similarity in a non-homogeneous environment and recover a universality in turbulence. We show how to derive useful bounds on the multifractal spectrum using the Navier-Stokes equations and how it connects with the singular set of Caffarelli, Kohn and Nirenberg.We further review the local extension of this theory, and show how it enables to probe the most irregular locations of the velocity field, in the sense foreseen by  Lars Onsager in 1949. Finally, we discuss how the multi-fractal theory connects to possible singularities, in the real or in the complex plane, as first investigated by Frisch and Morf in 1981.

Biography: Bérengère Dubrulle is senior scientist at the Centre National de la Recherche Scientifique and presently Director of the Les Houches Physics School. She received her PhD in astrophysics in 1990 under the supervision of J-P. Zahn. She is a specialist of turbulence, and its application to astro and geophysical flows using theoretical, numerical or experimental approaches. She is fellow of the APS and member of the French Academy of Sciences.

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