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Nonlinear acoustic-gravity wave theory

Cardiff School of Mathematics

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Dr U Kadri Applications accepted all year round Self-Funded PhD Students Only

About the Project

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).


Applicants should submit an application for postgraduate study via the Cardiff University webpages:

In the research proposal section of your application, please specify the project title and supervisors of this project and copy the project description in the text box provided. In the funding section, please select the ’self -funding’ option.

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.

If are applying for more than one Cardiff University project please note this in the research proposal section.
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