Lagrangian Coherent Structures: A Climatological Look

Abstract

A relatively new area at the crossroads of fluid and nonlinear dynamics are objects known as Lagrangian Coherent Structures (LCSs). LCSs are mathematically classified to differentiate parts of fluid flows. They, themselves, are the most influential parts of fluids. These objects have the most influence on the fluids around them and they allow for a sense of hierarchy in an otherwise busy environment of endless variables and trajectories. While all particles of fluids have the same dynamics on an individual basis, areas of fluid are not created equal and to be able to detect which parts will be the most important to look at allows for easier, but just as accurate, prediction of fluid movement. Recent applications include cleanup operations during the BP Deepwater Horizon oil spill, pollutant transfer in oceanic basins, and the analysis of polar storm activity. This thesis explores LCSs from the discrete mathematics to the future climatological impacts using virtual fluid simulations and LCS detection tools to facilitate analysis as well as diving into a case study with real and unapproximated oceanic data in the days following the Fukushima Daiichi nuclear power plant disaster.