Advection by Interacting Vortices on A β Plane

Abstract

Particle advection by two equal vortices under the influence of a background-vorticity gradient (α) is studied using a dynamical systems approach. The velocity field is a data set obtained by numerically solving the Euler equation with a vortex-in-cell model. Two methods are used to identify finite-time invariant manifolds: the first one relies on the use of Eulerian information and applies to flows with slowly moving stagnation points; the second one combines Eulerian and Lagrangian information and does not depend on the existence of stagnation points. The invariant manifolds are used to quantify the efficiency of merger, which is defined as the ratio of the area of the resultant vortex to the total area of the original vortices. It is found that the original vortices always contribute unequally to the merger or exchange processes. When the vortices are cyclonic the one located to the pole or west dominates the interaction; and when the vortices are anticyclonic, the one located to the equator or west is dominant.