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In this 52-minute lecture, explore the complex space-time dependence of correlation functions in turbulence and related models with Léonie Canet. Delve into the challenging theoretical problem of calculating statistical properties of homogeneous and isotropic fully developed turbulence from Navier-Stokes equations, with particular focus on intermittency effects. Learn how the functional renormalization group (FRG) provides a promising approach to achieve controlled closure in the large wavenumber limit, enabling analytical results on space-time dependence of multi-point velocity correlation functions. Compare these theoretical predictions with direct numerical simulations and experimental findings. Examine simplified turbulence models including Kraichnan's model for passive scalar turbulence and the stochastic Burgers equation, discovering the universal behavior in temporal decay of correlation functions and how this emerges from underlying extended symmetries shared across these models.
