Rose is a 4th year studying for concurrent degrees in the Bachelor of Science (Advanced) and Bachelor of Mathematical and Computer Science programs at the University of Adelaide. She is majoring in Physical Chemistry and Applied Mathematics, with the aim of pursuing a Masters degree in an area related to Fluid Mechanics and Differential Equations Analysis. In her spare time she likes to cycle, bush walk and draw.
Extracting coherently moving flow structures from fluid flows
The equations governing the physics of fluids, with the exception of specific, simplified cases, are notoriously intractable. Their solutions, however, are of great importance in many fields of applied mathematics, including the modelling of geophysical flows, oceanic currents and atmospheric dynamics. Consequently, it is often of interest to analyse a flow’s coherent structure, rather than seek specific solutions to its governing equations. Such analysis is of significance in many physical applications, such as in examining the extent to which an oil spill will spread, the transport of air pollution or heat flow in the atmosphere. In time-independent flows this is a fairly straight-forward process, however; add time-dependence and identifying flow barriers becomes much more challenging. This project will investigate the theory and application of mathematical techniques capable of elucidating the coherent structure of time-dependent fluid flows, including flow boundaries and transport across boundaries. In particular, the Lagrangian Averaged Vorticity Deviation (LAVD) technique will be employed to investigate the structure of classic vortical flows with important applications in atmospheric and oceanic modelling, such as Rossby wave flow. LAVD is a recent, lesser-studied and promising technique with great potential for the analysis of vortical flows. The theory behind LAVD will also be examined to explore its implications for physical models and its limitations. Time permitting, its application to more complicated models, such as those incorporating three-dimensions, may also be considered.