Description

Magnetohydrodynamics (known as MHD for short) is the branch of fluid mechanics which describes electrically-conducting fluids. Examples include plasmas (i.e., ionised gases), liquid metals, or just salt water. Indeed, Michael Faraday carried out one of the early experiments from London's Waterloo Bridge in 1832 when he tried to measure the potential difference between the two river-banks produced by the flow of salty river water through the Earth's magnetic field. (Unfortunately his equipment at the time wasn't sensitive enough.)

The field of MHD was really kick-started by the Swedish physicist Hannes Alfven in the 1940s, who was awarded the 1970 Nobel Prize in Physics for his pioneering work. One of his achievements was to predict mathematically the existence of so-called Alfven waves long before they were observed in the solar system. Nowadays applications of MHD range from magnetic levitation to understanding the generation of cosmic-scale magnetic fields in the interior of the Sun or the Earth.

Simulation of the magnetic field inside a rapidly-rotating star (by Ben Brown).

This project will explore the mathematical description of MHD. We will derive the fundamental equations by combining those of fluid dynamics with Maxwell's equations of electromagnetism. There are then various possible directions to explore. For example, you could study equilibrium solutions of the MHD equations, or linear MHD waves (like those of Alfven). Or you could focus on the "ideal MHD limit" where the fluid - typically a plasma - has zero electrical resistance. This has far-reaching consequences for the behaviour of plasmas, as Alfven realised for the first time.

Prerequisites

Continuum Mechanics III is essential, Electromagnetism III is recommended. Good familiarity with vector calculus will be useful.

Resources

Keith Moffatt's Reflections on Magnetohydrodynamics is a good introductory survey.

Watch the National Committee for Fluid Mechanics Film on "Magnetohydrodynamics" (from the days when university lecturers did experiments with liquid mercury...). Or try your own very simple MHD propulsion.

Books include Goedbloed & Poedts, "Principles of magnetohydrodynamics", or the classic Cowling, "Magnetohydrodynamics".