Turbulence in Astrophysics: Reynolds Decomposition

This lecture covers the modeling of fluid instabilities with linear perturbation theory, focusing on the Rayleigh-Taylor instability at the interface of two fluids. It delves into chaotic motion and the closure problem of turbulence, exploring the origin of unpredictability through the Navier-Stokes equations. The lecture discusses the statistical approach to turbulence, the two-point correlation function, and the special case of homogeneous, isotropic, incompressible turbulence. It also introduces the concept of mean-field theory and turbulent viscosity, emphasizing its importance in stellar structure models and the interstellar medium driven by supernova explosions and galactic shear.