Using Nonlinear Interactions to Quantify and Improve Timestepping Accuracy in the Rotating Shallow Water Equations

When a bell is struck, its shape creates resonances that produce its primary strike-tone and harmonic spectra. A central question explored in this project is how nonlinear resonance in fluids, rather than in solids, create low frequency, long-lasting dynamical patterns or 'mean' flows, as well as characterizing their evolution and life cycles.
The student will explore the mathematical nature of resonance in fluids, primarily with applications to the atmosphere, ocean, and magnetic field in idealized configurations. In particular the project will seek to understand how nonlinear oscillations give rise to low-frequency mean flows in time-scale separated phenomenon. What creates nonlinear resonance in fluids? How does it depend on the parameters of the physics such as background ocean stratification or magnetic field?This project will involve a combination of theoretical fluid dynamics, numerical analysis and simulation to seek answers to these questions. The student will choose the direction of the project in consultation with the supervisor Professor Beth Wingate.