Despite being an old and well studied problem, there are fundamental aspects of how wind generates waves that are not fully understood. One question I hope to answer is what generates the initial wrinkles that are seen at the surface of the ocean? This will be based on theoretical analysis and laboratory experiments.

How does geometry impact flows? I have been investigating exact solutions to Euler's equations for a range of geometries, focusing on vortex waves. This project would employ theoretical analysis (variational methods, symmetry approaches to differential equations, geometric techniques) and numerical analysis to investigate Lagrangian solutions.

Steep wave instabilities are thought to be responsible for wave overturning and breaking, a crucial process at the air-sea interface. However, little is known about these instabilities when an underlying current is present. From a Lagrangian perspective, I plan on theoretically and numerically investigating this scenario.