Hidden Symmetries in Fluid Dynamics

Explore recently discovered hidden projective symmetries in fluid dynamics equations through this comprehensive lecture series taught by Alexei Mailybaev from IMPA and Simon Thalabard from University of Nice. Delve into the theoretical foundations related to algebraic structures of symmetry groups for both deterministic and statistical formulations of fluid dynamics. Examine applications to hydrodynamic turbulence theory, focusing on how these symmetries underpin Kolmogorov self-similarity and intermittency phenomena. Study the Navier-Stokes and Euler equations, their symmetries and energy properties, then progress through turbulence analysis including Gaussian homogeneous isotropic turbulence and viscous effects. Investigate scaling anomalies, random-h models, and multifractal theory before exploring solvable intermittent turbulence models. Learn about hidden scaling symmetries in shell models and anomalous scaling laws, followed by examination of Kolmogorov multipliers and rescaled Navier-Stokes equations. Master the group theory approach to hidden scaling symmetries and quasi-Lagrangian formalism. Work through examples ranging from rigorously solvable models to numerical challenges in fluid dynamics equations across eight detailed lectures delivered over four weeks.