Fluid turbulence, the phenomenon of cascade of energy and its dynamical formulation

par Laurent Chevillard (ENS Lyon)

vendredi 10 oct. 2025, 14:00 → 15:00 Europe/Paris

Fokko du Cloux (Bat. Braconnier)

We will begin with some reminders on the phenomenology of three-dimensional fluid turbulence and the observational aspects of the statistical behavior of solutions of the Navier-Stokes equations, forced by a smooth term in space. To account for the cascade phenomenon, which asymptotically leads to a velocity field that is continuous yet highly irregular (of Hölderian type), we propose a linear model dynamics capable of generating such rough fields from entirely smooth ingredients over infinite time. This will involve a theoretical and numerical study of a transport phenomenon, not in physical space but in Fourier space, allowing energy to be transferred (or cascaded) across scales. A scheme based on finite spectral volumes will then provide a coherent numerical representation of such dynamics. This is joint work with G. Apolinario, G. Beck, C.-E. Bréhier, I. Gallagher, R. Grande, J.-C. Mourrat and W. Ruffenach.