Vortex Analysis – Clustering and Temporal Tracking of Vortices

Abstract

The vortex is a fundamental concept in fluid dynamics, and analyzing it is crucial for explaining and predicting the behavior of fluids in practical applications. In this thesis, two techniques that can lead to a deeper understanding of vortices will be proposed and verified by applying them to Newtonian turbulence and polymer-added flow. The first technique is vortex clustering. By doing dimension reduction and clustering simultaneously, the performance of vortex clustering is notably improved since the hidden features that are immersed in the original input features but can efficiently distinguish different types of vortices can now be extracted objectively. Then, the reliability of the clustering technique is verified in various Newtonian flows. The second technique is vortex tracking based on vortex axis lines, which can efficiently provide complete evolving routines of each vortex over time. With this tracking method, temporal information of vortices, such as their detailed evolving routines and temporal drift positions, can be fully observed and recorded for a future study. The mechanisms and details of this tracking method will first be illustrated and verified using Newtonian flow. Finally, since these two techniques for vortex analysis are solely developed for Newtonian turbulence, a polymer-added flow, where a small amount of polymer can notably modify the behaviour of vortices in Newtonian turbulence, is introduced to check to which level these two techniques are still reliable. Moreover, these two techniques can be compatibly embedded into existing vortex analyzing tools. By doing this, the interested types of vortices can be found and isolated from others, and their specific features and routines can thus be thoroughly studied.