J. Phys. A: Math. Gen. 29 (1996) 3749–3759. Printed in the UK Trapping of passive tracers in a point vortex system

Abstract. The advection of passive markers in the flow generated by two point vortices in a disc is studied. This Hamiltonian dynamics is investigated by means of Poincare ́ sections, via a set of appropriate canonical transformations. As is shown by numerical simulations, the existence of islands of regular motion around the vortices appears to be a generic feature of this system. The width of these islands is found to be proportional to the minimal distance attained by the vortices, bridging Lagrangian and Eulerian characteristics of the motion. Attention is drawn to the relevance of these results for all two-dimensional flows ruled by strong vorticity concentrations. 1