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Regular and Chaotic Dynamics, 2022, Volume 27, Issue 2, Pages 183–197
DOI: https://doi.org/10.1134/S1560354722020046
(Mi rcd1159)
 

Alexey Borisov Memorial Volume

On the Topology of the Atmosphere Advected by a Periodic Array of Axisymmetric Thin-cored Vortex Rings

Emad Masroora, Mark A. Stremlerb

a Engineering Mechanics Program, Virginia Polytechnic Institute & State University, Blacksburg, VA 24061, United States
b Department of Biomedical Engineering & Mechanics, Virginia Polytechnic Institute & State University, Blacksburg, VA 24061, United States
References:
Abstract: The fluid motion produced by a spatially periodic array of identical, axisymmetric, thin-cored vortex rings is investigated. It is well known that such an array moves uniformly without change of shape or form in the direction of the central axis of symmetry, and is therefore an equilibrium solution of Euler's equations. In a frame of reference moving with the system of vortex rings, the motion of passive fluid particles is investigated as a function of the two nondimensional parameters that define this system: $\varepsilon = a/R$, the ratio of minor radius to major radius of the torus-shaped vortex rings, and $\lambda=L/R$, the separation of the vortex rings normalized by their radii. Two bifurcations in the streamline topology are found that depend significantly on $\varepsilon$ and $\lambda$; these bifurcations delineate three distinct shapes of the “atmosphere” of fluid particles that move together with the vortex ring for all time. Analogous to the case of an isolated vortex ring, the atmospheres can be “thin-bodied” or “thick-bodied”. Additionally, we find the occurrence of a “connected” system, in which the atmospheres of neighboring rings touch at an invariant circle of fluid particles that is stationary in a frame of reference moving with the vortex rings.
Keywords: vortex rings, integrability, streamline topology, bifurcations.
Funding agency Grant number
National Science Foundation 1840995
This research was funded in part by the National Science Foundation’s Graduate Research Fellowship under Grant No. 1840995.
Received: 11.12.2021
Accepted: 01.03.2022
Bibliographic databases:
Document Type: Article
MSC: 76B47
Language: English
Citation: Emad Masroor, Mark A. Stremler, “On the Topology of the Atmosphere Advected by a Periodic Array of Axisymmetric Thin-cored Vortex Rings”, Regul. Chaotic Dyn., 27:2 (2022), 183–197
Citation in format AMSBIB
\Bibitem{MasStr22}
\by Emad Masroor, Mark A. Stremler
\paper On the Topology of the Atmosphere Advected by a Periodic
Array of Axisymmetric Thin-cored Vortex Rings
\jour Regul. Chaotic Dyn.
\yr 2022
\vol 27
\issue 2
\pages 183--197
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\crossref{https://doi.org/10.1134/S1560354722020046}
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