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Frequency selection and asymptotic states in laminar wakes

Published online by Cambridge University Press:  26 April 2006

George Em Karniadakis  and
George S. Triantafyllou
George Em Karniadakis
Affiliation:
Department of Mechanical and Aerospace Engineering, Princeton University, D209-A, Princeton, NJ 08544, USA
George S. Triantafyllou
Affiliation:
Department of Ocean Engineering, MIT Room 5-426A, Cambridge, MA 02139, USA
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Abstract

A better understanding of the transition process in open flows can be obtained through identification of the possible asymptotic response states in the flow. In the present work, the asymptotic states in laminar wakes behind circular cylinders at low supercritical Reynolds numbers are investigated. Direct numerical simulation of the flow is performed, using spectral-element techniques. Naturally produced wakes, and periodically forced wakes are considered separately.

It is shown that, in the absence of external forcing, a periodic state is obtained, the frequency of which is selected by the absolute instability of the time-average flow. The non-dimensional frequency of the vortex street (Strouhal number) is a continuous function of the Reynolds number. In periodically forced wakes, however, non-periodic states are also possible, resulting from the bifurcation of the natural periodic state. The response of forced wakes can be characterized as: (i) lock-in, if the dominant frequency in the wake equals the excitation frequency, or (ii) non-lock-in, when the dominant frequency in the wake equals the Strouhal frequency. Both types of response can be periodic or quasi-periodic, depending on the combination of the amplitude and frequency of the forcing. At the boundary separating the two types of response transitional states develop, which are found to exhibit a low-order chaotic behaviour. Finally, all states resulting from the bifurcation of the natural state can be represented in a two-parameter space inside ‘resonant horn’ type of regions.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 199 , February 1989 , pp. 441 - 469
Copyright
© 1989 Cambridge University Press

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