An interaction mechanism sustaining near-equilibrium shielded geophysical vortices

We investigate the interaction between two equally signed neutral vortices, namely vortices with a vanishing area integral of vorticity in inviscid non–divergent two-dimensional flows or a vanishing volume integral of potential vorticity anomaly in three-dimensional quasi-geostrophic (QG) flows. The vortices have a continuous (potential) vorticity distribution, and are linear combinations of appropriately normalised cylindrical (or spherical) Bessel functions of order 0, truncated at a zero of the Bessel function of order 1. Some pairs of neutral vortices reach an oscillating near-equilibrium state, attracting and repelling each other as a result of the exchange of small amounts of vorticity in their peripheries. This vorticity exchange generates a dipolar moment within each vortex which separates the vortices slightly, whereas the subsequent radial redistribution of the vorticity causes the vortices to come back closer again. The interaction is slower and weaker in three-dimensional QG flows, as the potential vorticity exchange primarily takes place close to the horizontal mid-plane of the vortices. These results have been corroborated using two radically different numerical models, namely a pseudo-spectral model and a high-resolution contour-advection model, both in two and in three dimensions. The observed oscillation mechanism could explain the persistence of geophysical vortices under the influence of other vortices and their ability to form stable vortex structures without experiencing vortex merging.