Nonlinear acoustic-gravity wave theory
In the linear theory, gravity waves are virtually decoupled from acoustic (compression) waves, because the propagation speed of acoustic waves far exceeds the maximum phase speed of gravity waves.
However, we found recently that these two types of wave motion could exchange energy via resonant triad nonlinear interactions.
This energy exchange is crucial and has various different implications in oceanography, geophysics, multi-phase flow in pipelines, and even hydrodynamic quantum analogs. Thus, having a complete nonlinear mathematical model is essential, which is the main objective of this project.
You will be trained to use multiple scale analysis along with other standard mathematical techniques to derive the general solution in a three-dimensional space. The nonlinear asymptotic theory will have a broad application in science and engineering.
We are interested in pursuing this project and welcome applications if you are self-funded or have funding from other sources, including government sponsorships or your employer.
Please contact the supervisor when you want to pursue this project, citing the project title in your email, or find out more about our PhD programme in Mathematics.