Date of Award


Degree Name

MS in Mathematics




College of Science and Mathematics


Paul Choboter

Advisor Department


Advisor College

College of Science and Mathematics


Ocean surface transport plays a critical role in marine ecosystems, influencing the complex spatiotemporal patterns of both marine species and pollutants. The theory of Lagrangian coherent structures (LCSs) aims to identify fundamental patterns within time-dependent, nonlinear fluid flows. LCSs are material surfaces that act as dividing lines which fluid does not cross for a relevant period of time. LCS theory is still under active development, and there are multiple proposed ways to mathematically determine an LCS. Each proposed mathematical definition aims to capture the same physical properties, and some capture those properties more successfully and consistently than others. Here we examine two proposed definitions from the founder of the LCS field: finite time Lyapunov exponents (FTLEs) and geodesic detection. While geodesic detection was developed as an improvement on FTLEs, FTLEs remain the most popular method for using LCSs as an analytical tool. We apply both methods to a novel application. We analyze ocean surface current data in an area off the coast of central California slated for wind energy development, comparing their relative strengths and weaknesses both in theory and in practice.