Elastic Interaction between a Vortex Dipole and an Axisymmetrical Vortex in Two-Dimensional Flows

We investigate numerically the elastic interaction between a dipole and an axisymmetrical vortex in inviscid isochoric two-dimensional flows satisfying Euler’s vorticity conservation equation. This work contributes to previous studies addressing inelastic vortex interactions. The dipole is a straight moving Lamb-Chaplygin (L-C) vortex, where the absolute value of either the positive or the negative amount of vorticity equals the amount of vorticity of the target vortex. The results show that, when the straight moving L-C dipole approaches the axisymmetrical vortex, the potential flows of both vortices interact, the dipole’s trajectory acquires curvature and the dipole’s vorticity poles separate. Once the L-C dipole moves away from the target vortex, the poles close and the dipole continues with a straight trajectory but along a direction different from the initial one. Though there is very small vorticity exchange between the dipole’s poles and a small vorticity leakage to the background field, the vortices preserve, to a large extent, their amount of vorticity and the resulting interaction may be practically qualified as an elastic interaction. This process is sensitive to the initial conditions and, depending on the initial position of the dipole as well as on small changes in the vorticity distribution of the axisymmetrical vortex, inelastic interactions may instead occur. Since the initial vorticity distributions are based on the eigenfunctions of the two-dimensional Laplacian operator in circular geometry these results are directly applicable to three-dimensional baroclinic geophysical flows under the quasi-geostrophic approximation.