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.

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.