Numerical investigation of the evolution of elliptic vortex ring

In this paper, a three-dimensional vortex filament method is implemented to study the axis-switching period of an elliptic vortex ring. The change of the semi-axis length and the projection of a single elliptic ring are first compared with the literature. Then, the evolution of elliptic vortex rings with different circulations, aspect ratios and core radius-to-ring radius ratios are numerically reproduced, and the evolution of the velocity and aspect ratios are also studied to determine their influence on the motion of vortex rings. Furthermore, the axis-switching periods of elliptic rings for different cases are investigated, and an expression to fit all the cases is obtained.