Chaotic trapping phenomena in extended systems.

Abstract

The interaction of fluid structures with bodies in the flow field is an important and topical research area, and recently a new phenomena has been proposed involving the metastable capture of vortex structures by bluff bodies. The fundamental mechanism for this capture phenomenon is the generation of chaos in the perturbed Hamiltonian point-vortex model for the system, and a variety of numerical results have been quoted in this framework. In this paper, we present the results of a study of the capture phenomenon in a more realistic context, i.e., by a numerical solution of the Navier-Stokes equations for the system. A mixed spectral\char21{}finite-difference numerical scheme is used to study the interactions of extended vorticity profiles with a bluff body and comparisons are made to the previous point-vortex results. In general, we find that the capture phenomenon exists generically in the extended system and that many of the physical characteristics of the phase-space topology of the Hamiltonian system persist, even for relatively large vortex diameters. For even larger profiles, we find that the internal degrees of freedom of the vortex structure are sufficient to generate a trapping phenomena without an explicit perturbation and that several additional types of dynamical behavior occur. We comment on the general mechanisms for these phenomena and make connections with possible applications to physical systems.