Regular and chaotic particle motion near a helical vortex filament
Identifieur interne : 000597 ( Main/Exploration ); précédent : 000596; suivant : 000598Regular and chaotic particle motion near a helical vortex filament
Auteurs : Igor Mezi [États-Unis] ; Anthony Leonard [États-Unis] ; Stephen Wiggins [États-Unis]Source :
- Physica D: Nonlinear Phenomena [ 0167-2789 ] ; 1998.
Abstract
In this paper we analyze the flow induced by a helical vortex filament in an axisymmetric, time-dependent strain field. We first discuss bifurcations and the structure of particle paths in the unperturbed velocity field of the helical filament (no strain). There are three qualitatively different phase portraits arising, depending on the thickness and 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 for small thicknesses and pitch angle smaller than a critical value. These particles travel in the axial direction. The underlying geometrical structures in the unperturbed problem are cylinders and two-dimensional 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 perturbation. There is an exchange of fluid between the “inside” and “outside” of the helix. The degree to which this happens is dependent on the stream 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, away from separatrices we transform the system into coordinates that enable us to use KAM theory to show the persistence of infinite cylinders in the perturbed flow. Finally, we discuss the consequences of our analysis for the particle motion in flows that possess helical vortical structures of finite length.
Url:
DOI: 10.1016/S0167-2789(97)80011-5
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We first discuss bifurcations and the structure of particle paths in the unperturbed velocity field of the helical filament (no strain). There are three qualitatively different phase portraits arising, depending on the thickness and 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 for small thicknesses and pitch angle smaller than a critical value. These particles travel in the axial direction. The underlying geometrical structures in the unperturbed problem are cylinders and two-dimensional 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 perturbation. There is an exchange of fluid between the “inside” and “outside” of the helix. The degree to which this happens is dependent on the stream 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, away from separatrices we transform the system into coordinates that enable us to use KAM theory to show the persistence of infinite cylinders in the perturbed flow. Finally, we discuss the consequences of our analysis for the particle motion in flows that possess helical vortical structures of finite length.</div></front></TEI><affiliations><list><country><li>États-Unis</li></country></list><tree><country name="États-Unis"><noRegion><name sortKey="Mezi, Igor" sort="Mezi, Igor" uniqKey="Mezi I" first="Igor" last="Mezi">Igor Mezi</name></noRegion><name sortKey="Leonard, Anthony" sort="Leonard, Anthony" uniqKey="Leonard A" first="Anthony" last="Leonard">Anthony Leonard</name><name sortKey="Mezi, Igor" sort="Mezi, Igor" uniqKey="Mezi I" first="Igor" last="Mezi">Igor Mezi</name><name sortKey="Wiggins, Stephen" sort="Wiggins, Stephen" uniqKey="Wiggins S" first="Stephen" last="Wiggins">Stephen Wiggins</name></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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