Graduation Semester and Year




Document Type


Degree Name

Doctor of Philosophy in Mathematics



First Advisor

Chaoqun Liu


A vortex can be intuitively recognized as the rotational swirling motion of the fluids. The fascination of this phenomenon brought about many years of research to define, classify, and identify the vortical structure. Throughout the decades, many vortex identification methods were developed and can be characterized into three generations. The generational methods are vorticity-based, eigenvalue-based such as Q, ��_ci, and ��_2, and Liutex-based. Before the development of Liutex, there was no mathematical definition for vortex. Is Liutex superior to vorticity and the eigenvalue-based methods? Is the vorticity vector the local rotational axis? Should vorticity be considered vortex? In this dissertation, I answer these questions by utilizing dimensional analysis to examine and compare the eigenvalue-based methods with Liutex. Then, an analysis of vector candidates for the local rotational axis is conducted to identify which candidates satisfy the definition of the local rotational axis. Lastly, a statistical analysis of vorticity, Liutex, and shear is performed to show their behavior and relationship in the boundary layer from laminar flow to turbulent flow. The results of these three procedures show that: Out of the four eigenvalue-based methods analyzed, ��_ci was the only one that was dimensionally consistent with Liutex. The Liutex directional vector was the only candidate that satisfied the definition of the local rotational axis, and vorticity should not be considered vortex as shear highly contaminates it.


Liutex; Vortex; Vorticity; Fluid transition; Local fluid rotational Axis; Vortex identification method, Vortex, Vorticity, Fluid transition, Local fluid rotational axis, Vortex identification method


Mathematics | Physical Sciences and Mathematics


Degree granted by The University of Texas at Arlington

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