MATH-GA.2420-007 Advanced Topics In Analysis: Introduction To Turbulence (1st Half Of Semester)

3 points

Course Description

Two ways of turbulence onset in fluid flows: temporal and spatial. Temporal chaotization in unstable flows and dynamical chaos. Spatial chaotization in stable flows and percolation transition.
Developed turbulence and phenomenology of a cascade by Richardson and Kolmogorov. Turbulent diffusion.
Explicit realization of the cascade scenario in turbulence of weakly interacting waves. Kinetic wave equation and its general properties: conservation laws and entropy growth.
Exact stationary solutions of the kinetic wave equations in isotropic scale-invariant media. Locality of interaction and cascades.
Stationary turbulence spectra in anisotropic media and applications to geophysics and astrophysics. Matching turbulence spectra with sources and sinks. Bottleneck effect.
Strong wave turbulence. Solitons, vortices and shocks.
Intermittency of fluid vortex turbulence. Kolmogorov multipliers.

TBA

TBA

TBA

TBA