**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.