Linear Model of Vortex Ring

Abstract

Vortex rings represent canonical axisymmetric vortex structures in fluid mechanics, and understanding their dynamic behaviors is crucial for elucidating the generation, transport, and dissipation of vorticity. This paper introduces a novel vortex ring dynamics modeling method predicated on a linear mass-spring-damper system, thereby simplifying the vortex ring's motion to the dynamic response of a three-dimensional linear system. By discretizing the surrounding fluid into a finite number of particles and constructing a three-dimensional linear system to represent the encompassing flow field, the model accurately replicates vortex ring trajectories documented in established literature, achieving an average fitting error of less than 9%. The findings demonstrate that, with a damping coefficient of fv 0, the model effectively reproduces the closed trajectory characteristic of vortex rings in superfluids. Conversely, with fv > 0, it accurately captures the damped spiral motion observed in conventional fluids. This linear model circumvents the inherent complexities of traditional nonlinear approaches, offering an alternative analytical framework for investigating vortex ring dynamics, substantially reducing computational demands, and highlighting its potential for engineering applications in areas such as vortex ring control and fluid mechanical design.