Skeletons of patterned vortex cores

Abstract

The process of freely attenuating and intensifying coherent structures in the form of satellite vortices, within a quasi two-dimensional rotating shallow layer of water confined to a circular tank, is visualized using the finite-time Lyapunov exponent technique. The visualizations show that the intensification, given by the transition from a system of two to three satellite vortices, and the attenuation, given by the reverse transition, each involve the two-step process of destruction and re-emergence of satellite vortices. In the intensification process, the two satellite vortices first collapse into the central region of the main vortex before re-emerging as three satellite vortices through the roll-up of material lines at the main vortex boundary. Conversely, in the attenuation process, the three satellite vortices first shed their structure into the region outside the main vortex boundary before re-emerging as two satellite vortices from material lines drawn from the walls of the container.