Abstract
Abstract Analysis on eddy motion is the essential method for understanding viscous flows. Compared with the current methods to identify the vortex, the study presents a method to investigate vortex structures based on topological analysis and nonlinear dynamics, and establishes a connection between the direction of the vortex and the real eigenvalue of the velocity gradient tensor. The study highlights the significance of the real and imaginary parts of complex eigenvalues in vortex development, wherein the real part indicates topological stability and the imaginary part represents swirling strength, contributing to get the characters of the viscous flows.
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