Ewch i’r prif gynnwys

Nonlinear acoustic-gravity wave theory

This research project is in competition for funding with one or more projects available across the EPSRC Doctoral Training Partnership (DTP). Usually the projects which receive the best applicants will be awarded the funding. Find out more information about the DTP and how to apply.

Application deadline: 15 March 2019

Start date: 1 October 2019

This project focuses on the recent finding that acoustic and gravity wave motion could exchange energy via resonant triad nonlinear interactions.


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, multiphase 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.

Project aims and methods

The nonlinear asymptotic theory has a broad application in science and engineering. We will continue developing the (general) nonlinear acoustic-gravity wave equation with compressibility, and gravity terms which involves nonlinear interactions at various scales. 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.

The proposed project requires collaborations with the finest scientists across the Schools of Mathematics, Physics, and Engineering, among others. It is expected that you will be involved in presenting the research work in front of various scientific communities, and will keep a close contact with our relevant network and collaborators in Europe, (JKU Linz; Keele University; University of Bath), and North America (MIT, and University of Delaware).

You would also have the opportunity to widen the spectrum of applications by discussing the outcomes with physicists and mathematicians in Cardiff University, and presenting the work in school seminars and in conferences/professional meetings.


Dr Usama Kadri photograph

Dr Usama Kadri

Lecturer in Applied Mathematics

029 208 75863

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