The classical water wave problem provides a foundational framework for modelling gravity waves on liquid surfaces—from ocean swells to river
flows. Incorporating additional physical mechanisms such as capillarity (surface tension), electrical forces, and shear fields reveals extraordinarily rich physical phenomena and complex wave dynamics. While traditional models focus on waves over flat base states, this research will tackle water-wave dynamics in non-flat geometries. Axisymmetric systems (such as waves on the surface of a liquid jet) provide a fertile ground for exploring and understanding novel wave propagation phenomena in regimes where the underlying no-wave state is inherently unstable. In this project, you will address fundamental open challenges in fluid dynamical wave propagation on non-flat geometries. This will include, for example, studying conjugate flow solutions, solitary waves, and stabilization mechanisms. The project will involve the use of cutting-edge applied mathematics and modelling techniques, including numerical computation and asymptotic analysis. The student will develop a highly-valued skillset, developing expertise across theoretical mechanics, nonlinear partial differential equations (PDEs), computational modelling, and nonlinear mathematical methods. Entry requirements The standard minimum entry requirement is 2:1 in Mathematics or Physics. 1 October 2027 Mode of study Full-time Additional Funding Information This PhD project is in a competition for a Faculty of Science funded studentship. Funding is available to UK applicants and comprises ‘home’ tuition fees and an annual stipend for 3 years. The current UEA / institutional PhD stipend rate is £20,409 and will be subject to any agreed inflationary uplift for 2027/28.
