Nature of project: theory, software
Available to students on full-time physics degree schemes or joint students.
It is usually assumed that an instabilty leads to the amplification of small perturbations. However, the distinction between absolute and convective instabilities is crucial in many areas of research such as aerodynamics, plasma and space physics, meteorology. Does an arbitrary initial perturbation grow in time at a fixed spatial location so that it eventually occupies the whole space or is it swept away by the flow of plasma so fast that eventually it decays at any fixed spatial location? The answer to these questions will determine whether the wing of an airplane is damaged, whether an astrophysical jet is destabilised, or whether mixing of plasma between the solar wind and the magnetosphere occurs.
A successful project will develop beyond the above in one/some of the following directions:
The problem of absolute and convective instabilities will be examined. An arbitrary perturbation will be traced in time and space to establish growth or decay. A computer program will be provided to analyse and visualise the evolution of the perturbations.
When considering where to take your project, please bear in mind the time available. It is preferable to do fewer things well than to try many and not get conclusive results on any of them. However, sometimes it is useful to have a couple of strands of investigation in parallel to work on in case delays occur.
Additional scope or challenge if taken as a Year-4 project: An elegant method for distinguishing between the two types of growth was developed in plasma physics by Briggs and then extended to hydrodynamics. The problem will be examined analytically using Briggs' method (Drazin, Introduction to Hydrodynamic Stability).
Please speak to Youra Taroyan (yot) if you consider doing this project.
Initial literature for students:
The physical understanding of the problem may require assistance. Assistance will be provided with setting up and running the computer program.
|milestone||to be completed by|
|Review of the concept, understanding Briggs' criterion||end of October|
|Numerical results||end of February|
|Comparison and physical interpretation of the results||Easter|