Note on chaotic advection in an oscillating drop

Mixing by chaotic advection within an oscillating drop is investigated by means of an elementary model (Hill's spherical vortex). The drop remains spherical and the velocity field within the drop is assumed to rotate around a radial axis, in a periodical manner. Poincare sections in the vicinity of fixed points are obtained asymptotically in the limit of small amplitude oscillations, and show that the trajectory of elliptic points undergoes a resonant mechanism. The flow inside the drop can display Lagrangian chaos when the drop oscillates. In particular, tracers located near the boundary of the drop are observed to contaminate the whole drop within a few periods. (C) 2003 American Institute of Physics.