Titre/Title :
Inverse and Direct cascades in turbulence, revisited.
Contact :
Achim Wirth (MEIGE)
Résumé/Abstract :
Abstract : By performing numerical investigations of Navier-Stokes (NS) equations decimated on a Helical-Fourier basis we show that all 3D flows in nature possess a subset of non-linear evolution leading to a reverse energy transfer : from small to large scales. Up to now, such inverse cascade was only observed in flows under strong rotation and in quasi two-dimensional geometries. We show here that the energy flux is always reversed when the mirror symmetry is broken, leading to a distribution of helicity in the system with a definite sign at all wavenumbers.
Our findings broaden the range of flows where an inverse energy cascade may be detected and rationalize the role played by helicity in the energy transfer process, showing that both 2D and 3D properties naturally coexist in all flows in nature. The numerical methodology here proposed is based on a Galerkin projection of the NS dynamics on a given class of Helical-Fourier modes. Discussion about how to apply it to study the influence of helicity on small-scales intermittency, to investigate the regularity properties of Navier-Stokes solutions and to improve sub-grid-scale models for Large-Eddy-Simulations will be presented. Finally, it may play a key role also to understand the role of the three inviscid invariants in magnetohydrodynamics.