Vortex motion is a fundamental state of flowing continua, often characterized by localized vorticity that generates concentrated vortices. Notably, vortex filaments exhibit diverse dynamics, including self-induced motion, instabilities, wave generation, and vortex breakdown, typically manifesting as spiral or helical configurations of the vortex axis. While many hydrodynamics publications explore vortex motion and effects, few focus entirely on concentrated vortices. This work addresses key issues related to vortex formation and behavior, driven by the authors' experimental observations and striking visualizations of concentrated vortices, including helical and spiral forms. The authors developed an approach based on the helical symmetry of swirl flows, enabling the derivation of simplified mathematical models to describe various vortex phenomena. The majority of the content consists of theoretical studies on vortex dynamics, while the final chapter presents detailed results from experiments on concentrated vortices, laying the groundwork for analysis and advancing vortex theory. The mathematical modeling of concentrated vortex dynamics is complex, requiring consideration of three-dimensional and nonlinear effects, singularities, and instabilities, necessitating the use of diverse coordinate frames and equations for different problems.
