PhD in Mathematics - Making a splash: Mathematical modelling of resonant wave sloshing in confined basins

About the Project

Motivated by marine and industrial applications, this project concerns nonlinear resonant sloshing of confined water waves. Nonlinear resonance is a mechanism by which energy is continuously exchanged between a small number of linear wave modes, a phenomenon common to many dispersive fluid systems. Nonlinear resonance of free-surface water waves is amplified significantly when the fluid is confined, resulting in sustained large-amplitude wave sloshing and pronounced energy exchange. This sloshing has far-reaching industrial and geophysical implications, including wave energy harvesting, the mitigation of unsafe vessel motions during the loading and shipping of liquefied natural gas, the prevention of flooding induced by wind-driven seiches in lakes, and the formation of beach cusps in partially enclosed bays.

This project investigates strategies for mitigating hazardous sloshing or harnessing its power for energy generation. Particular attention will be paid to formulating novel methods for modelling resonant sloshing, explaining observations from laboratory experiments and field data, and predicting new phenomena induced by fluid confinement for a wide range of industrial and geophysical fluid basins. The research will combine mathematical modelling, asymptotic analysis and numerical computation to build a complete physical picture of this complex, yet fascinating, phenomenon.

The balance between modelling, analysis and computation may be adjusted depending on the candidate’s interests. As relevant fluid mechanical background will be attained during this project, it is not a requirement for admission. However, prior familiarity with techniques across applied mathematics will be an advantage for the successful completion of this project.