Dynamics of a small neutrally buoyant sphere in a fluid and targeting in Hamiltonian systems

Abstract

Using a very simple model for the force acting on a small rigid neutrally bouyant spherical tracer particle in an incompressible two-dimensional fluid flow, it is shown that the tracer trajectories separate from fluid trajectories in those regions where the flow has hyperbolic stagnation points. A tracer evolves only on fluid trajectories with Lyapunov exponents bounded by the value of its reciprocal Stokes number. By making the Stokes number large enough, the tracer is forced to settle on either the regular Kolmogorov-Arnol'd-Moser (KAM)-tori dominated regions or to selectively visit the chaotic regions with small Lyapunov exponents.