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Transition from order to chaos in the wake of an airfoil

Williams-Stuber, K. and Gharib, M. (1990) Transition from order to chaos in the wake of an airfoil. Journal of Fluid Mechanics, 213 . pp. 29-57. ISSN 0022-1120. doi:10.1017/S0022112090002208.

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An experimental effort is presented here that examines the nonlinear interaction of multiple frequencies in the forced wake of an airfoil. Wakes with one or two distinct frequencies behave in an ordered manner – being either locked or quasi-periodic. When a third incommensurate frequency is added to the system, the flow demonstrates chaotic behaviour. Previously, the existence of the three-frequency route to chaos has been reported only for closed system flows. It is important to note that this chaotic state is obtained at a low Reynolds number. However, the chaotic flow shows localized characteristics similar to those of high Reynolds number turbulent flows. The degree of chaotic behaviour is verified by applying ideas from nonlinear dynamics (such as Lyapunov exponents and Poincaré sections) to the experimental data, thus relating the basic physics of the system to the concepts of mode interaction and chaos. Significant changes to the vortex configuration in the wake and to the r.m.s. velocity profile occur during the transition from order to chaos.

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Additional Information:Copyright © 1990 Cambridge University Press. Reprinted with permission. (Received 7 June 1988 and in revised form 14 July 1989) This paper is based on thc work from the Ph.D. thesis of K. Stuber which was carried out at the University of California, San Diego. The work was sponsored by the Defense Advanced Research Projects Agency - ACMP through the URI program under contract number DARPA/ONR N00014-86-K-0758. The assistance of INLS/UCSD is also acknowledged. The authors would like to thank Professor M. Markovin with whom we had worthwhile discussions regarding the nature of chaos and turbulence.
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Deposited On:10 Dec 2007
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