Yifei Yu, Ph.D., is an Assistant Professor of research at the University of Texas at Arlington. He received his B.Eng. from the Nanjing University of Aeronautics and Astronautics in 2018 and Ph.D. from the University of Texas at Arlington in 2023. His research interests include vortex identification, vortex dynamics, and the mechanism of large vortex formation. He received the "Mathematics Academic Excellence Fund" at the University of Texas at Arlington in 2020 and 2021.

Chaoqun Liu, Ph.D., is a Tenured and Distinguished Professor and Director of Center for Numerical Simulation and Modeling at the University of Texas at Arlington. He has worked on high order direct numerical simulation (DNS) and large eddy simulation (LES) for flow transition and turbulence for almost 30 years. In addition, he has been awarded by the U.S. Air Force, U.S. Navy, and NASA with 50 federal research grants of over $5.7 million. Dr. Liu has published 14 professional books, approximately 130 journal articles, and 150 conference papers. He is the founder and major contributor of Liutex.

This book presents the importance of the mechanism of hairpin vortex formation to understanding flow transition, turbulence, and flow control. This book blends direct numerical simulation (DNS) and mathematical analysis with experiments to create a foundation for understanding turbulence. The authors discuss hairpin vortex as a main component of transitional flow and turbulent flow. In addition, Liutex is utilized and described as a theoretical system that presents valid tools for turbulence research. Readers are exposed to understanding 3D and non-linear instability; the Lambda vortex formation; sweeps, ejections, and shear instability; the Kelvin-Helmholtz instability and vortex ring formation; and turbulence generation and sustenance.

Review of Hairpin Vortex Research History.- Receptivity.- 2-D Instability.- Flow Instability at Critical Points.- 3-D Non-linear Instability.- Sweeps and Ejections.- Shear Layer Instability.- Liutex and Third Generation of Vortex Identification.- Hairpin Vortex Formation.- Multiple Levers of Hairpin Vortices.- Concluding Remarks.