Modulated point-vortex couples on a beta-plane: dynamics and chaotic advection

Abstract

The dynamics of modulated point-vortex couples on a β-plane is investigated for arbitrary ratios of the vortex strength. The motion is analysed in terms of an angle- and a location-dependent potential and the structural changes in their shape. The location-dependent potential is best suited for understanding different types of vortex orbits. It is shown to be two-valued in a range of parameters, a feature which leads to the appearance of orbits with spikes, in spite of the integrability of the problem. The advection dynamics in this modulated two-vortex problem is chaotic. We find a transition from closed to open chaotic advection, implying that the transport properties of the flow might be drastically altered by changing some parameters or the initial conditions. The open case, characterized by permanent entrainment and detrainment of particles around the vortices, is interpreted in terms of an invariant chaotic saddle of the Lagrangian dynamics, while the dynamics of the closed case, with a permanently trapped area of the fluid, is governed by a chaotic region and interwoven KAM tori. The transition from open to closed chaotic advection is quantified by monitoring the escape rate of advected particles as a function of the vortex energy.