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An analytical study of transport, mixing and chaos in an unsteady vortical flow

Rom-Kedar, V. and Leonard, A. and Wiggins, S. (1990) An analytical study of transport, mixing and chaos in an unsteady vortical flow. Journal of Fluid Mechanics, 214 . pp. 347-394. ISSN 0022-1120. doi:10.1017/S0022112090000167.

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We examine the transport properties of a particular two-dimensional, inviscid incompressible flow using dynamical systems techniques. The velocity field is time periodic and consists of the field induced by a vortex pair plus an oscillating strainrate field. In the absence of the strain-rate field the vortex pair moves with a constant velocity and carries with it a constant body of fluid. When the strain-rate field is added the picture changes dramatically; fluid is entrained and detrained from the neighbourhood of the vortices and chaotic particle motion occurs. We investigate the mechanism for this phenomenon and study the transport and mixing of fluid in this flow. Our work consists of both numerical and analytical studies. The analytical studies include the interpretation of the invariant manifolds as the underlying structure which govern the transport. For small values of strain-rate amplitude we use Melnikov's technique to investigate the behaviour of the manifolds as the parameters of the problem change and to prove the existence of a horseshoe map and thus the existence of chaotic particle paths in the flow. Using the Melnikov technique once more we develop an analytical estimate of the flux rate into and out of the vortex neighbourhood. We then develop a technique for determining the residence time distribution for fluid particles near the vortices that is valid for arbitrary strainrate amplitudes. The technique involves an understanding of the geometry of the tangling of the stable and unstable manifolds and results in a dramatic reduction in computational effort required for the determination of the residence time distributions. Additionally, we investigate the total stretch of material elements while they are in the vicinity of the vortex pair, using this quantity as a measure of the effect of the horseshoes on trajectories passing through this region. The numerical work verifies the analytical predictions regarding the structure of the invariant manifolds, the mechanism for entrainment and detrainment and the flux rate.

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Additional Information:© 1990 Cambridge University Press. Received 2 May 1988. Published Online April 26 2006. This work was supported in part by Caltech's Program in Advanced Technologies, sponsored by Aerojet General, General Motors, and TRW, and by the Air Force Office of Scientific Research through the Jet Propulsion Laboratory. V. R. Acknowledges the support of a Zonta Amelia Earhart Fellowship and of a PEO International Peace Scholarship.
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Caltech Program in Advanced TechnologiesUNSPECIFIED
Air Force Office of Scientific Research (AFOSR)UNSPECIFIED
PEO International Peace ScholarshipUNSPECIFIED
Aerojet GeneralUNSPECIFIED
Zonta Amelia Earhart FellowshipUNSPECIFIED
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Official Citation:An analytical study of transport, mixing and chaos in an unsteady vortical flow preview V. Rom-Kedar, A. Leonard and S. Wiggins Journal of Fluid Mechanics / Volume 214 / May 1990, pp 347 - 394 DOI:
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:31389
Deposited By: Ruth Sustaita
Deposited On:09 May 2012 21:10
Last Modified:09 Nov 2021 19:52

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