Vortex ring induced by a disk translating toward or away from a wall

Abstract: This study investigates the time evolution of vortex rings generated by the normal translation of a disk either toward or away from a wall. We systematically vary the control parameters, including the disk size, stroke length, travel time, and distance from the wall, to analyze their influence on vortex dynamics. Experiments are conducted with Particle Image Velocimetry, while numerical simulations are performed using the flow solver Basilisk. The circulation and core radius are used as primary metrics to describe the properties of the vortex ring. A quantitative agreement is observed between the experimental and the numerical results. Both approaches reveal that the vortex circulation increases for disk motions in either direction, toward or away from the wall. However, the effect of the bottom wall on the vortex core radius differs depending on the motion of the disk. The presence of the wall increases the core radius only when the disk moves toward the wall, while no significant effect is observed for a translation away from the wall. Furthermore, we establish scaling laws to describe the maximum circulation and core size of the vortex ring as a function of the control parameters: the disk diameter, the typical time and stroke length of its motion, and the minimal distance from the wall. These scalings, which differ from the unbounded case, contribute to a deeper understanding of vortex dynamics in the vicinity of solid boundaries.