REGULAR AND CHAOTIC PARTICLE MOTION NEAR A HELICAL VORTEX FILAMENT

In this paper we analyze the how induced by a helical vortex filament in an axisymmetric, time-dependent strain field, We first discuss bifu rcations and the structure of particle paths in the unperturbed veloci ty field of the helical filament (no strain). There are three qualitat ively different phase portraits arising, depending on the thickness an d the pitch angle of the filament. Particles close to the axis of the cylinder on which the filament moves are bound to stay near the axis f or small thicknesses and pitch angle smaller than a critical value. Th ese particles travel in the axial direction. The underlying geometrica l structures in the unperturbed problem are cylinders and two-dimensio nal separatrices. We also analyze the motion of passive particles when a perturbation by a time-periodic, three-dimensional strain field is imposed, The lateral confinement of particles is lost upon perturbatio n. There is an exchange of fluid between the ''inside'' and ''outside' ' of the helix, The degree to which this happens is dependent on the s tream function features for the case when there is no strain present. For small perturbations, most of the particles ''inside'' the filament are still transported mainly in the axial direction. To show this, aw ay from separatrices we transform the system into coordinates that ena ble us to use KAM theory to show the persistence of infinite cylinders in the perturbed flow. Finally, we discuss the consequences of our an alysis for the particle motion in flows that possess helical vortical structures of finite length.