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