Nature of project: theory, software
Available to students on full-time physics degree schemes or joint students.
Shock waves can form due to steepening of linear small amplitude sound waves in the atmospheres of the Sun and other stars. These sound waves are generated by random convective motions in the interior of the Sun. The amplitudes of these waves increase as they propagate up into the atmosphere. Also, the occurrence of a coronal mass ejection containing a huge erupting solar prominence is likely to generate a shock wave. The aim of the project is to investigate the formation and propagation of the shock waves.
A successful project will develop beyond the above in one/some of the following directions:
The steepening of waves with different initial amplitudes and wavelengths will be estimated using an analogue of the Burger's equation. The braking times of these waves due to the steepening will be calculated for wave pulses of different initial shapes. The problem will be tackled both analytically and numerically. A computer program to solve the equation governing the wave steepening and visualising the results will be provided.
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 spatiotemporal evolution of the acoustic waves will be investigated analytically using a method described by Drazin (Introduction to Hydrodynamic Stability, p. 85).
Please speak to Youra Taroyan if you consider doing this project.
Initial literature for students:
Basic understanding of programming is desirable although no prior experience in computer programming is necessary. Instructions and assistance will be provided.
|milestone||to be completed by|
|Review of gravitational effects on sound waves||end of October|
|Setting up and running the code||Christmas|
|Exploring the effects of gravity on sound waves||end of February|
|Interpretation of the results and discussion||Easter|