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.

We investigate numerically the elastic interaction between a dipole and an axisymmetrical vortex in inviscid isochoric two-dimensional (2D), as well as in three-dimensional (3D) flows under the quasi-geostrophic (QG) approximation. The dipole is a straight moving Lamb-Chaplygin (L-C) vortex such that the absolute value of either its positive or negative amount of vorticity equals the vorticity of the axisymmetrical vortex. The results for the 2D and 3D cases show that, when the L-C dipole approaches the vortex, their respective potential flows interact, the dipole’s trajectory acquires curvature and the dipole’s vorticity poles separate. In the QG dynamics, the vortices suffer little vertical deformation, being the barotropic effects dominant. At the moment of highest interaction, the negative vorticity pole elongates, simultaneously, the positive vorticity pole evolves towards spherical geometry and the axisymmetrical vortex acquires prolate ellipsoidal geometry in the vertically stretched QG space. Once the L-C dipole moves away from the vortex, its poles close, returning the vortices to their original geometry, and the dipole continues with a straight trajectory but along a direction different from the initial one. The vortices preserve, to a large extent, their amount of vorticity and the resulting interaction may be practically qualified as an elastic interaction. The interaction 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.

We investigate numerically the elastic interaction between an eddy-pair and an axisymmetrical cyclonic eddy in inviscid isochoric two-dimensional (2D), as well as in three-dimensional (3D) flows under the quasi-geostrophic (QG) approximation. The eddy-pair is a straight moving Lamb-Chaplygin dipole where the absolute value of either its positive or negative amount of vorticity equals the vorticity of the axisymmetrical eddy. The results for the 2D and 3D cases show that interactions with almost no vorticity exchange or vorticity loss to the background field between ocean eddies, but changing their displacement velocity, are possible. When the eddy-pair approaches the axisymmetrical eddy, their respective potential flows interact, the eddy-pair’s trajectory acquires curvature and their vorticity poles separate. In the QG dynamics, the eddies suffer little vertical deformation, being the barotropic effects dominant. At the moment of highest interaction, the anticyclonic eddy of the pair elongates, simultaneously, the cyclonic eddy of the pair evolves towards spherical geometry, and the axisymmetrical eddy acquires prolate ellipsoidal geometry in the vertically stretched QG space. Once the eddy-pair moves away from the axisymmetrical eddy, its poles close, returning to their original geometry, and the anticyclonic and cyclonic eddy continue as an eddy-pair with a straight trajectory but along a new direction. The interaction is sensitive to the initial conditions and, depending on the initial position of the eddy-pair, as well as on small changes in the vorticity distribution of the axisymmetrical eddy, inelastic interactions may instead occur.