Nature of project: **theory**, software

Available to students on full-time physics degree schemes or joint students.

The vertical propagation of acoustic waves in a gravitationally stratified medium has been studied by Poisson and Lamb back in the 19th century. The latter established that the wave motion is described by the Klein-Gordon equation. Interestingly, the same equation governs the relativistic motion of particles with nonzero mass. The amplification of waves propagating in solar and planetary atmospheres and the associated e-folding distances will be estimated.

*A successful project will develop beyond the above in one/some of the following directions:*

The vertical propagation of a single pulse and a monochromatic wave will be studied numerically under the assumption of an isothermal atmosphere. The results should reveal the response of an atmosphere to various forcing terms and the evolution of the waves as they propagate.

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:* A peculiar feature introduced by stratification is the cut-off frequency which separates high frequency propagating waves from low frequency evanescent waves. The significance of the cut-off frequency will be discussed in the context of acoustic waves. The associated effect of an oscillating wake behind the wavefront will be investigated.

Please speak to **Youra Taroyan** if you consider doing this project.

*Initial literature for students:*

- Roberts, B.: MHD waves in the solar atmosphere, in Proc. of SOHO13 Waves, Oscillations and Small-Scale Transient Events in the Solar Atmosphere: A Joint View From SOHO and TRACE, ESA SP-547, p. 1-14 (2004). http://www-solar.mcs.st-and.ac.uk/~bernie/Robertssoho13-2004.pdf
- G. Sutmann et al., Acoustic wave propagation in the solar atmosphere, Astron. Astrophys. 340, 556, 1998
- Y. Taroyan, R. Erdelyi, Global Acoustic Resonance in a Stratified Solar Atmosphere, Sol. Phys. 251, 523, 2008

The project is suitable for students interested in analytical or numerical work. The problem belongs to an area of current research. Assistance will be available.

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

Describing the different terms and coefficients in the Klein-Gordon equation | end of October |

Estimating e-folding distances in solar and planetary atmospheres | Christmas |

The response of the atmosphere to various forcing terms | end of February |

Interpretation of the results with visualisation | Easter |