Séminaire Fluide: Siddhartha Mukherjee (TIFR, India)

  • Science et Société
Publié le 3 juin 2024 Mis à jour le 3 juin 2024

le 6 juin 2024

Institut de Physique de Nice
Conference room 1+2

Local multifractality reveals the calm within the storm of turbulence

Fluid seminars

Understanding turbulence rests delicately on the conflict between Kolmogorov’s 1941 theory of calm, non-intermittent, and uniform energy dissipation characterized by a unique scaling exponent and the overwhelming evidence to the contrary of violent intermittency and consequent multiscaling. This departure has been best rationalized by the Frisch-Parisi multifractal conjecture, which envisions energy dissipation as the accumulating of a measure on interwoven fractal sets with their unique scaling exponents. Curiously, however, multifractality is not typically regarded as a local flow property, variations in which might be clues exposing inroads into the fundamental unsolved issues of anomalous dissipation and finite time blowup. We present a simple construction of local multifractality, which reveals that much of turbulence remains surprisingly monofractal à la Kolmogorov. Multifractality appears as small islands in this calm sea, its strength growing logarithmically with the intensity of local fluctuations in energy dissipation — a seemingly universal feature we found reproduced also in cascade models. These results suggest new ways to understand how singularities could arise and provide a fresh perspective on anomalous dissipation and intermittency. The simplicity and adaptability of our approach also holds great promise in applications ranging from climate sciences to medical data analysis.