MASTER OF SCIENCE (2024) (School of Computational Science and Engineering) McMaster University Hamilton, Ontario, Canada TITLE: Vortex Analysis – Clustering and Temporal Tracking of Vortices AUTHOR: Yucheng Feng M.Eng. (Electrical Engineering) Xi’an Jiaotong University, Xi'an, Shaanxi, China B.Eng. (Electrical Engineering) Shandong University, Jinan, Shandong, China SUPERVISOR: Dr. Li Xi NUMBER OF PAGES: xix, 75 / 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. / Thesis / Master of Science (MSc) / In turbulence research, efficient clustering and tracking of vortices are appealing. Hence, the fundamental motivation of this research is to investigate vortex clustering techniques and vortex tracking techniques to analyze vortices in turbulent flows automatically and objectively. With the proposed vortex clustering technique, the hidden features immersed in input data space that can efficiently distinguish different types of vortices can be extracted objectively to classify vortices into various groups. With the proposed vortex tracking technique, the temporal behaviours of vortices, such as their detailed developing routines, can be fully tracked, and recorded in a simple but efficient way. With these two techniques, our understanding of the differences between various types of vortices, the ways vortices evolve under different conditions, etc., can be further improved. Besides, embedding these two techniques in existing vortex analyzing tools makes them more powerful.

La rencontre entre une couche limite laminaire se développant sur une plaque plane sous une surface libre et un obstacle rectangulaire émergent mène à l’apparition d’une zone de recirculation complexe appelée tourbillon en fer à cheval à l’amont de l’obstacle. Cette zone de recirculation est composée d’un certain nombre de vortex s’enroulant autour de l’obstacle et pouvant présenter des dynamiques variées. Le but de ce travail est de réaliser une étude expérimentale paramétrique du tourbillon en fer à cheval laminaire et faiblement turbulent. Les mesures sont réalisées par PIV et par trajectographies et des méthodes de détection basés sur la décomposition modale (POD) et la détection des points critiques sont utilisées afin de faciliter l’étude de la dynamique tourbillonnaire. Ce manuscrit se propose de : (i) Déterminer l’évolution des caractéristiques du tourbillon en fer à cheval en fonction des paramètres adimensionnels de l’écoulement. (ii) Mettre en place une typologie des différentes dynamiques exhibées. (iii) Déterminer les mécanismes à l’origine de l’apparition de ces différentes dynamiques à l’aide d’un modèle conceptuel. (iv) Et finalement, étudier l’influence de la longueur de l’obstacle sur le tourbillon en fer à cheval. / A laminar boundary layer developing under a free-surface and interacting with an emerging obstacle lead to the creation of a complex recirculation zone called horseshoe vortex upstream from the obstacle. This recirculation zone is composed of a given number of vortices wrapping around the obstacle with various kind of dynamics. The aim of this work is to perform an experimental parametric study of the laminar, and slightly turbulent horseshoe vortex. Measurements are obtained by PIV and trajectographies and detection method based on modal decomposition (POD) and critical points are used to ease the study of the vortex dynamics. This manuscript intends to : (i) Explain the horseshoe vortex main characteristics evolution with the non-dimensional parameters of the flow. (ii) Define a typology of the different observed vortex dynamics. (iii) Identify the physical mechanisms at the origin of those dynamics through the use of a conceptual model. (iv) And finally, show the influence of the obstacle length on the horseshoe vortex.