Graduation Semester and Year
Spring 2026
Language
English
Document Type
Dissertation
Degree Name
Doctor of Philosophy in Mathematics
Department
Mathematics
First Advisor
Dr. Chaoqun Liu
Second Advisor
Dr. Jianzhong Su
Third Advisor
Dr. Tuncay Aktosun
Fourth Advisor
Dr. Endel Iarve
Abstract
Fluid vortices are found everywhere in our universe. A vortex can take the form of almost anything - from the classical spiral vortex to chaotic plumes. Defining a vortex physically and mathematically is absolutely necessary if we desire to study vortices and their interactions with each other as well as our physical world. Fluid vortices are incredibly important in the study of turbulent flows. From determining wear, optimizing design for better flow, efficiency, etc., to even predicting the weather on Earth or other planets, having the ability to measure vortices in fluid flow is invaluable. In this study, I investigate Liutex as a viable and definitive definition for a fluid vortex and explore its capabilities using real-life Tropical Cyclone storm data from the National Oceanic and Atmospheric Administration (NOAA), Direct Numerical Simulation (DNS) data of the early boundary transition-to-turbulent-layer data from a UTA and NASA collaboration, and simulated Tornado data provided by the University of Wisconsin-Madison. Since the discovery of Liutex in 2018 by Dr. Chaoqun Liu and his team at UTA, many Liutex-based tools/methods have been developed. In this investigation based on my studies/work, I also explore select Liutex-based methods (ones which I find having incredible impact on vortex visualization technology); these methods include the Liutex magnitude gradient vector, Modified Omega Liutex method, Liutex Core Line, and Liutex Core Tube. The main contribution of this study was to the Liutex Core Tube. In this dissertation, I contribute a new algorithm that mathematically defines the locations of the seed points which create the Liutex Core Tube at a particular Liutex Core Line point (the location of the local maximum of Liutex Magnitude is equal to the location of the local maximum of angular speed). The Liutex Core Tube is not an iso-surface. An iso-surface is scalar-based, cannot show direction, and can only represent one magnitude at a time. The Liutex Core Tube is Liutex-vector-based and shows both direction and magnitude of a vortex structure simultaneously and should be the preferred method for visualizing vortex structures.
Keywords
liutex, fluid vortex, vortex, code
Disciplines
Atmospheric Sciences | Fluid Dynamics | Meteorology | Other Applied Mathematics
License
This work is licensed under a Creative Commons Attribution 4.0 International License.
Recommended Citation
Alvarez, Oscar, "Liutex - A Fluid Vortex" (2026). Mathematics Dissertations. 3.
https://mavmatrix.uta.edu/math_dissertations2/3
Included in
Atmospheric Sciences Commons, Fluid Dynamics Commons, Meteorology Commons, Other Applied Mathematics Commons
Comments
- for science -