Mountain waves in geophysical fluids
Undergraduate Project 2025-26 (4H)
Numerical models used for simulating atmospheric and oceanic flows are currently not able to resolve many small scale (in both space and time) motions. Among these are waves generated by flow over mountains, also known as lee waves, recognisable in the picture below from the cloud pattern that is formed.
Understanding the propagation and breaking of these waves is extremely important for improving numerical models. Given that all of our predictions about future climate change are either confirmed or rejected by looking at output from these models, getting this right is a big deal! As an example illustrating their importance for climate change, in the ocean they are thought to play a large role in maintaining the global overturning circulation, which determines how the ocean redistributes heat and carbon. A very short overview of this can be found in [1]. In this project we will study both the theory and numerical simulation of lee waves interacting with non-wave flow. The classical theory of lee wave propagation is based on a small-wave amplitude approximation; a good review paper to introduce these ideas in the oceanic setting is [2]. Investigating the wave behaviour in larger-amplitude settings will rely on numerical experiments and will be done using Oceananigans, a user-friendly package for simulating oceanic flows in the Julia programming language. The documentation for this can be found at [3]. You can also find the lay description of these waves here
Understanding the propagation and breaking of these waves is extremely important for improving numerical models. Given that all of our predictions about future climate change are either confirmed or rejected by looking at output from these models, getting this right is a big deal! As an example illustrating their importance for climate change, in the ocean they are thought to play a large role in maintaining the global overturning circulation, which determines how the ocean redistributes heat and carbon. A very short overview of this can be found in [1]. In this project we will study both the theory and numerical simulation of lee waves interacting with non-wave flow. The classical theory of lee wave propagation is based on a small-wave amplitude approximation; a good review paper to introduce these ideas in the oceanic setting is [2]. Investigating the wave behaviour in larger-amplitude settings will rely on numerical experiments and will be done using Oceananigans, a user-friendly package for simulating oceanic flows in the Julia programming language. The documentation for this can be found at [3]. You can also find the lay description of these waves here
This project is co-supervised by Hossein Kafiabad and Cai Maitland-Davies. Interested students should have taken a course in fluid dynamics, and be familiar with numerical methods for solving differential equations. This project will also run alongside the course Geophysical and Astrophysical Fluids, and it will be beneficial to take this class too.
[1] Ferrari, R., 2014: What goes down must come up. Nature, 513, 179–180
[2] Legg, S., 2021: Mixing by oceanic lee waves. Annu. Rev. Fluid Mech., 53, 173–201
[3] https://clima.github.io/OceananigansDocumentation/stable/