Our understanding of turbulence has progressed significantly through combining experiments, observations, theoretical developments, direct numerical simulations and modeling. I will discuss briefly three problems (among many) for which our perception has changed: (i) the derivation of a multitude of exact laws stemming from conservation properties, e.g. in fluid, magnetohydrodynamics (MHD) and Hall-MHD turbulence, and their consequences for constraining scaling relations and dynamical evolutions; (ii) the cascade processes of energy in three dimensional strongly rotating stratified turbulent flows (RST) found to be dual, in the sense that the energy can go in a self-similar manner both to the large scales and to the small scales with (different) contant fluxes, a phenomenon also encountered in MHD, including in solar wind observations; and (iii) turbulent fields themselves (velocity, induction, temperature), together with their gradients, can be intermittent with non-Gaussian wings, as in quantum turbulence and shear flows or in MHD and RST.
I will also mention old and new results concerning the propensity for turbulent flows and nonlinear systems to develop sharp, isolated (intermittent) structures at small and large scales in a variety of physical environments. This will be done in the specific context of normalized moments at third-order (skewness S) and fourth-order (kurtosis K). Indeed, intermittency can be evaluated e.g. through the examination of relations between S and K for fields such as the velocity, temperature and magnetic fields as well as for their local rates of dissipation. The field themselves, in general, have small skewness, but in some cases they display high kurtosis, such as for vertical velocities in RST, as observed in the stable nocturnal planetary boundary layer, as well as for the magnetic field in the solar wind, or more recently in the fast dynamo regime in MHD. On the other hand, the local dissipation rates of these fields follow a parabolic K(S) law whose origin may be linked to kinematic constraints, to the applicability of Langevin models to their dynamics, or to self-organized criticality, as suggested by several authors in various physical contexts, from the atmosphere, the ocean and climate, to fusion plasmas, the solar wind and dwarf galaxies [1,2].
Many thanks to all my collaborators, mentors, colleagues, students and post-docs.
[1] Annick Pouquet, Duane Rosenberg, Raffaele Marino and Pablo Mininni: Intermittency Scaling for Mixing and Dissipation in Rotating Stratified Turbulence at the Edge of Instability. Atmosphere 14, 1375 (2023). Special issue in honor of Jack Herring; B. Galperin, A. Pouquet & P. Sullivan Eds..
[2] Yannick Ponty, Hélène Politano and Annick Pouquet: Spatio-temporal intermittency assessed through kurtosis-skewness relations in MHD in the fast dynamo regime. In preparation (2024).
