Available at: https://digitalcommons.calpoly.edu/theses/2780
Date of Award
6-2023
Degree Name
MS in Mathematics
Department/Program
Mathematics
College
College of Science and Mathematics
Advisor
Paul Choboter
Advisor Department
Mathematics
Advisor College
College of Science and Mathematics
Abstract
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.