Vortex ring deformation, capture, and entrainment by a columnar vortex

A vortex ring placed outside of a columnar vortex is stretched by the local straining flow induced by the vortex. This straining flow is known to lead to wrapping of the ring about the columnar vortex, which is a primary feature of multiscale vortex interactions. In this paper we show that continuous stretching of the ring and wrapping about the columnar vortex is only one of the several possible outcomes of vortex ring interaction with a columnar vortex. For cases where the local straining rate of the flow induced by the columnar vortex is sufficiently small, the shape of the vortex ring is found to oscillate between stretching in the principal direction of stretching of the induced flow and stretching in the direction of compression, all while exhibiting an increase in the average ring radius. This oscillatory behavior allows the ring to escape capture and entrainment into the columnar vortex core. In other cases the vortex ring pinches off on itself as it is strained by the columnar vortex. The paper examines the different types of behavior observed during vortex ring interaction with a columnar vortex using a vortex filament approach together with an approximate analytical theory. The focus of the paper is on understanding the fundamental physics underlying the different types of vortex ring behaviors observed.