<p>With the development of Liutex theory, new applications have emerged, making it an effective tool for identifying and quantifying vortex structures in various fluid flows. The Liutex method provides precise information on vortex strength, size, and location, and enables real-time analysis of vortex evolution and interactions, enhancing the understanding of complex flow patterns. Based on the incompressible Navier-Stokes equations, we derived the Liutex-shear interaction equation by incorporating the Liutex-shear decomposition into the vorticity transport equation to explore the fundamental relationship between Liutex and shear. We first applied it to the two-dimensional Lamb-Oseen vortex, which has an analytical solution, to validate the previously introduced idea of using high dissipation regions to identify vortex boundaries. Then we conducted numerical experiments on a three-dimensional cylindrical flow at <i>Re</i> = 3 900. We computed the key terms in the Liutex-shear interaction equation for comparative analysis, and demonstrate that the Liutex-shear interaction equation offers a clearer insight into the nature of vortices. Utilizing the Sunway TaihuLight supercomputer, we performed large eddy simulations with 2.5×10⁸ grids for the three-dimensional cylindrical flow case, allowing Liutex to reveal more refined vortex structures in turbulence. These findings confirm that the conclusions obtained in two-dimensional cases are consistent with those in three dimensions and show that shear stretching significantly influences the Liutex-shear interaction, enabling us to approximately predict the evolution of the source term.</p>