Entrapping of a vortex pair interacting with a fixed point vortex revisited. II. Finite size vortices and the effect of deformation

Abstract

We investigate the evolution of a pair of two-dimensional, opposite-signed, finite-size vortices interacting with a fixed point vortex. The present paper builds on the accompanying study by Koshel et al. [“Entrapping of a vortex pair interacting with a fixed point vortex revisited. I. Point vortices,” Phys. Fluids 30 , 096603 (2018)] focusing on the motion of a pair of point vortices impinging on a fixed point vortex. Here, by contrast, the pair of opposite-signed finite-size vortices, or vortex dipole for simplicity, can deform. This deformation has an impact on the dynamics. We show that, as expected, finite size vortices behave like point vortices if they are distant enough from each other. This allows one to recover the rich and diverse set of possible trajectories for the dipole. This includes the regimes of intricate bounded motion when the finite-size vortices remain stable near the fixed vortex for a long time. On the other hand, we show that large finite-size vortices can deform significantly and deviate from the trajectories of equivalent point vortices. When the shear that the vortices induce on each other is large enough, the finite size vortices may break into smaller structures or may even be completely strained out.