Turbulence and Nonlinear Processes in Fluids and Plasmas

This course is a mixture of a qualitative survey of important concepts, and rigorous derivations of a few things. Goals of other topics to be covered include instabilities in fluids and plasmas like the Kelvin-Helmholtz instability and the toroidal Ion Temperature Gradient Instability, statistical absolute equilibria and inverse cascades, two-scale local and full-F global approaches to gyrokinetics, gyro-Landau-fluid closure approximations, turbulence saturation mechanisms, secondary instability analysis, zonal flows, transport barriers and methods of reducing turbulence, and a survey of results from gyrokinetic turbulence simulations. There will be a guest lecture by Dr. Walter Guttenfelder on experimental studies of plasma turbulence in fusion research. The course will use some of Frisch's textbook on fluid turbulence, and Krommes's recently updated extensive notes. A more complete description will be on the course web site.

Other information: This course is intended for advanced graduate students (both theorists and experimentalists) primarily in Plasma Physics but may be of interest to students in Astrophysics, Applied Math, Physics, or MAE, who are interested in theoretical and computational aspects of turbulence. Roughtly 1/2 of the course is generic fluid turbulence and 1/2 on general and fusion-specific plasma turbulence (but should still be of interest to others). (This year I am trying to put more emphasis on fusion topics.) Postdocs and research staff who wish to sit in on the lectures are also welcome.

Prerequisites: The course assumes some knowledge of electromagnetic theory and of probability theory, including random walks and Fokker-Planck equations, and of course knowledge of PDEs, Fourier transforms, and vector calculus. A background equivalent to AST 554, "Irreversible Processes in Plasma," is useful but not essential. Non-plasma students should e-mail the instructor (hammett@princeton.edu) before first day of class for further information.

Official course catalog entry: https://registrar.princeton.edu/course-offerings/course-details?term=1212&courseid=000750

Main references:

• U. Frisch, (1995) Turbulence
• John A. Krommes, (2018) Introductory Lectures on Plasma Kinetic Theory, Turbulence, and Transport, Volume II: Stochasticity and Transport. (These are extensive lecture notes from Prof. Krommes' teaching of this course in past years.)

• P. A. Davidson, (2004) Turbulence, An Introduction for Scientists and Engineers
• S. A. Orszag, (1977) Lectures on the statistical theory of turbulence
• W. D. McComb, (1990) The Physics of Fluid Turbulence
• M. Lesieur, (2008) Turbulence in Fluids
• B. B. Kadomtsev, (1965) Plasma Turbulence
• other selected plasma physics research papers