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Dynamical systems analysis of fluid transport in time-periodic vortex ring flows

Shariff, Karim and Leonard, Anthony and Ferziger, Joel H. (2006) Dynamical systems analysis of fluid transport in time-periodic vortex ring flows. Physics of Fluids, 18 (4). Art. No. 047104. ISSN 1070-6631. doi:10.1063/1.2189867.

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It is known that the stable and unstable manifolds of dynamical systems theory provide a powerful tool for understanding Lagrangian aspects of time-periodic flows. In this work we consider two time-periodic vortex ring flows. The first is a vortex ring with an elliptical core. The manifolds provide information about entrainment and detrainment of irrotational fluid into and out of the volume transported with the ring. The likeness of the manifolds with features observed in flow visualization experiments of turbulent vortex rings suggests that a similar process might be at play. However, what precise modes of unsteadiness are responsible for stirring in a turbulent vortex ring is left as an open question. The second situation is that of two leapfrogging rings. The unstable manifold shows striking agreement with even the fine features of smoke visualization photographs, suggesting that fluid elements in the vicinity of the manifold are drawn out along it and begin to reveal its structure. We suggest that interpretations of these photographs that argue for complex vorticity dynamics ought to be reconsidered. Recently, theoretical and computational tools have been developed to locate structures analogous to stable and unstable manifolds in aperiodic, or finite-time systems. The usefulness of these analogs is demonstrated, using vortex ring flows as an example, in the paper by Shadden, Dabiri, and Marsden [Phys. Fluids 18, 047105 (2006)].

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Additional Information:©2006 American Institute of Physics (Received 18 October 2005; accepted 28 February 2006; published online 17 April 2006)
Subject Keywords:vortices; stratified flow; flow instability; turbulence; flow visualisation
Issue or Number:4
Record Number:CaltechAUTHORS:SHApof06a
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:4108
Deposited By: Archive Administrator
Deposited On:27 Jul 2006
Last Modified:08 Nov 2021 20:14

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