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Lagrangian transport and chaos in the near wake of the flow around an obstacle: a numerical implementation of lobe dynamics

Duan, J. and Wiggins, S. (1997) Lagrangian transport and chaos in the near wake of the flow around an obstacle: a numerical implementation of lobe dynamics. Nonlinear Processes in Geophysics, 4 (3). pp. 125-136. ISSN 1023-5809. http://resolver.caltech.edu/CaltechAUTHORS:20120119-143548832

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Abstract

In this paper we study Lagrangian transport in the near wake of the flow around an obstacle, which we take to be a cylinder. In this case, for the range of Reynolds numbers investigated, the flow is two-dimensional and time periodic. We use ideas and methods from transport theory in dynamical systems to describe and quantify transport in the near wake. We numerically solve the Navier-Stokes equations for the velocity field and apply these methods to the resulting numerical representation of the velocity field. We show that the method of lobe dynamics can be used in conjunction with computational fluid dynamics methods to give very detailed and quantitative information about Lagrangian transport. In particular, we show how the stable and unstable manifolds of certain saddle-type stagnation points on the cylinder, and one in the wake, can be used to divide the flow into three distinct regions, an upper wake, a lower wake, and a wake cavity. The significance of the division using stable and unstable manifolds lies in the fact that these invariant manifolds form a template on which the transport occurs. Using this, we compute fluxes from the upper and lower wakes into the wake cavity using the associated turnstile lobes. We also compute escape time distributions as well as compare transport properties for two different Reynolds numbers.


Item Type:Article
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http://dx.doi.org/10.5194/npg-4-125-1997DOIUNSPECIFIED
http://www.nonlin-processes-geophys.net/4/125/1997/PublisherUNSPECIFIED
Additional Information:© 1997 European Geophysical Society. This work is licensed under a Creative Commons License. Received 27 May 1997; Accepted: 3 April 1998. This research was supported by ONR Grant No. N00014-97-1-0071. We would like to thank Paul Fischer for discussions regarding the spectral element methods, Ron Henderson for help in generating the velocity fields and Karim Shariff for discussions in particle tracking and graphics programming.
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Funding AgencyGrant Number
Office of Naval Research (ONR)N00014-97-1-0071
Record Number:CaltechAUTHORS:20120119-143548832
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20120119-143548832
Official Citation:Duan, J. and Wiggins, S.: Lagrangian transport and chaos in the near wake of the flow around an obstacle: a numerical implementation of lobe dynamics, Nonlin. Processes Geophys., 4, 125-136, doi:10.5194/npg-4-125-1997, 1997
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:28871
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:21 Mar 2012 21:10
Last Modified:26 Dec 2012 14:43

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