Description

Tsunamis (also sometimes colloquially known as tidal waves), are large, long-wavelength waves caused by the displacement of large bodies of water - for example by landslides or underwater earthquakes. They can travel incredible distances and cause massive devestation when they hit land. As a result, they have been studied by researchers in a number of fields, but aspects of their formation and behaviour still remain unkown.

This project will explore simple mathematical models of tsunamis. We will begin by developing a general mathematical description of tsunami waves and how they propagate over long distances. There is a lot of scope for students to shape the direction of the project: from looking at how sea depth influences tsunamis, to how they interact with coastlines. It is expected that students will use computational numerical methods for at least part of the project, but some analytic approaches may be possible. Students looking numerical models may choose to compare their results to real world data (in which case you will have the opportunity to examine how simplifications in your model cause it to deviate from the real world situation), or develop more theoretical models.

Essential prior modules

Analysis in Many Variables II (MATH2031) recommended

Mathematical Modelling II (MATH2637) required if you wish your project to look at numerical models

Suggested companion modules

Fluid Mechanics (MATH3101) recommended, but a motivated student will be able to cover the relevant material themselves without taking this course

Resources

For a brief, relatively simple, technical introducation to the topic, including some approaches that you may wish to take during the course of the project, you may wish to review the following sources:

• Margarito, G. Explaining the physics of tsunamis to undergraduate and non-physics students Eur. J. Phys. 26 (2005) 401-407
• Helene, O., Yamashita, M.T. Understanding the tsunami with a simple model Eur. J. Phys. 27 (2006) 855-863
MATH 3382
• Weisstein, E.W., Trott, M. The Mathematics of Tsunamis Wolfram MathsWorld

For an overview description of a more advanced treatment of the topic (which will likely go a bit beyond what we will cover in the course of the project) you may wish to look at

Contact

Feel free to contact me before selecting this project - in particular if you are not taking the suggested companion modules. My email is m.t.matuszewski@durham.ac.uk.