Project IV 2025-26

Modelling Tsunamis

Maciej Matuszewski

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. By the end of the project you will be able to:

  • Understand the key mathematical principles underlying fluid mechanics as applied to shallow water waves such as tsunamis.
  • Write Python code to model tsunamis.
  • Be able to analyse and interpret your results.

Animation of wave in shallow water, showing movement of select water particles.

Wave motion in shallow water. Copied from https://commons.wikimedia.org/wiki/File:Shallow_water_wave.gif under GNU Free Documentation Licence.

Mode of operation and evidence of learning

The project will initally revolve around reading material provided by the project supervisor and synthesising that reading into a detailed understanding of the mathematical topic. Students will begin with quality sources provided by the supervisor, but they will develop skills to identify and judge appropriate sources themselves. They should be able to make simple extensions to the models they find in their reading, and then write advanced Python code for these models. They should be able to compare them to theory and (where appropriate) real world data.

Essential prior modules

Analysis in Many Variables II (MATH2031) recommended

Mathematical Modelling II (MATH2637) (or equivalent personal programming experience)

Suggested prior 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:

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

  • Behrens, J., Dias, F. New computational methods in tsunami science Phil. Trans. R. Soc. A 373: 20140382

    • 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.