Nature of project: **theory**, software

Available to full-time physicists or joint students.

The distinction between absolute and convective instabilities is important in many areas of research such as aerodynamics, plasma and space physics, meteorology.

A flow is said to be absolutely unstable if an initial perturbation grows with time at any fixed spatial position. For example, an instability occurring around the wings of an aircraft could have a destabilising effect.

It is also possible that the initial perturbation grows in time but simultaneously is convected away by the flow so fast that eventually it decays at any fixed spatial location. This situation is referred to as a convective instability.

The type of instability, absolute or convective, depends on the reference frame: a perturbation can be absolutely unstable in one reference frame and convectively unstable in another.

An elegant method for distinguishing between the two types of growth was developed in plasma physics by Briggs and then extended to hydrodynamics. The method will be applied to one or two problems in hydrodynamics in order to establish the evolution of a signal and the nature of the instability under various conditions.

*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 numerically for given parameter values. An arbitrary perturbation will be traced in time and space to establish growth or decay. The results will be compared with Briggs' analytical criteria.

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:* The analysis will be extended to a number of toy problems will be examined analytically. This requires some level of analytical skills.

*Initial literature for students:*

- Drazin & Reid, Introduction to Hydrodynamic Stability, Cambridge University Press, 2002.
- L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics: Physical Kinetics (Pergamon Press, New York, 1981).
- Briggs R. J., Electron-stream interactions with plasmas, Research Monograph, M.I.T. Press 1964

The physical understanding of the problem may require assistance. The degree of difficulty and the novelty of the results will depend on the progress. Only a basic understanding of computer programming is required as a prerequisite. Assistance will be provided.

milestone | to be completed by |
---|---|

Review of the concept, understanding Briggs' criterion | end of October |

Analytical results | Christmas |

Numerical results | end of February |

Comparison and physical interpretation of the results | Easter |