Propagation and transport properties of dipolar vortices on a γ plane

Abstract

The dynamics and transport properties of dipolar vortices on a γ plane (a plane where the Coriolis parameter has a quadratic variation with the latitude) are studied using the modulated point-vortex model. Similarly to the β-plane case, different regimes are found for the evolution of a single dipole, depending on the initial direction of propagation α0. Two steadily translating couples exist: The one rotating eastward (α0=0) has a stable trajectory and the one rotating westward (α0=π) is unstable. For initial angles in the range 0<α0<π, the couple moves along sine-like, 8-shaped and cycloid-like trajectories. In all solutions the dynamically relevant variables (the latitude and the direction of propagation) are periodic. The advection equations of passive particles in the dipole’s velocity field can be exactly written in the form of a periodically perturbed integrable Hamiltonian system. The study of transport is performed using a ‘‘dynamical-systems theory’’ approach. The entrainment and detrainment of fluid as a function of γ and α0 are computed exactly from some invariant curves in the Poincaré map and approximately by using the Melnikov function. The exchange of mass increases with both increasing γ and α0, while the rate at which this occurs has a maximum for some α0 and increases with γ. A major difference in particle spreading exists between dipoles which exactly return to their initial position after an integer number of oscillations and dipoles that do not. In the former case the Poincaré map shows broad areas of unstirred fluid coinciding with the maximum radial displacement in the dipole’s meandering trajectory.