Collision of dipolar vortices on a β plane

Abstract

The interaction of two dipoles moving perpendicularly to the gradient of background vorticity is studied both numerically and experimentally. In the numerical computations the vorticity distribution is represented either by four point vortices (point-vortex model) or by thousands of them (vortex-in-cell method). The simplest model is used to study the dynamics and the advection of fluid particles in two kinds of interaction: coaxial couples of equal strength but different size, and equal parallel couples with a nonzero impact parameter (the distance between the dipoles’ axis). As a result of the interaction fluid masses are exchanged between the two dipoles and between each dipole and the ambient fluid. In the case of equal coaxial couples the amount of fluid exchanged depends on the gradient of ambient vorticity, with the largest mass exchange occurring always between the eastward traveling dipole and the ambient fluid. The collision of parallel couples with nonzero impact parameter leads to a large mass exchange, either because several interactions may occur or because when two independent couples arise, they have a nonuniform motion. Laboratory experiments in a rotating fluid (with a flat sloping bottom providing the β effect), confirm that an elastic interaction is a rare event. The unstable trajectory of the westward traveling dipole, as well as small perturbations unavoidable in the laboratory, invariably lead to collisions of nonaligned dipoles. The gross features of the vortex motion, as well as of the mass exchange, are well modeled using the point-vortex model, whereas the vortex-in-cell method reproduces many details of the vortex motion, the evolution of the vorticity field, and the exchange of mass.