Description
Turbulence is a complex nonlinear flow with chaotic features that make it difficult to predict and characterize. The aim of this thesis is to study and extract persistent features of complex flows that arise in Bose-Einstein condensates. We numerically simulate Bose-Einstein condensates using the two-dimensional Gross-Pitaevskii equation with stochastic forcing. Using the results of this simulation, we aim to reduce the complexity of the flow using a Time-Moving Average filter to denoise the system and highlight features of interest. We then reduce the dimensionality of our measurements by implementing the data-driven technique, Dynamic-Mode Decomposition (DMD). By grouping the modes found in our DMD approach into meaningful subgroups given by a k-means clustering algorithm, we were able to locate the modes that contain the most energy and provide the most information about the system. After effectively reducing the complexity of our flow, we sought to detect and track vortex solutions as they evolved in time using two methods: a local-minima analysis and a statistical correlation technique.
