Course title: Magnetohydrodynamics

Course number: ES 275

Instructor: Gary A Glatzmaier

Course description:

This is the study of fluid flow and magnetic fields for electrically conducting fluids flowing at non-relativistic speeds, i.e., for problems for which the magnetohydrodynamic approximation of Maxwell's equations is valid. After a review of the fundamental equations governing this subject, several example problems are described, including convection and magnetic field generation in the interiors of planets and stars. An assigned computer modeling project on magneto-convection gives the students experience in defining a conceptual problem in geophysics, planetary physics, or astrophysics, setting up a system of equations that mathematically approximates the problem, developing a numerical method for solving the equations, programming the method on a computer, using a graphical post-processor to analyze the computer solutions, running a series of computer jobs that surveys the relevant parameter space, and writing a paper on what was learned.

 

Topics:

Review of Fluid Dynamics
Conservation of mass, momentum and energy
Equation of state
Rotation and buoyancy

Magnetohydrodynamics
Magnetic induction equation
Lorentz force
MHD energetics
Magnetic induction and diffusion
Magnetic pressure, tension and buoyancy
Alfven's theorem
Ferraro isorotation law
Alfven waves

Dynamo theory
Bullard one-disc dynamo
Rikitake two-disc dynamo
Ponomarenko dynamo
Cowling's theorem
Mean field dynamos
MHD dynamos
Geodynamo
Solar dynamo
Jovian dynamo

Magneto-rotational instability

 

This course is designed for graduate students but available for qualified undergraduates with permission of instructor.