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Three-dimensional wakes behind cylinders of square and circular cross-section: early and long-time dynamics

Published online by Cambridge University Press:  10 May 2019

G. Agbaglah Open the ORCID record for G. Agbaglah [Opens in a new window]  and
C. Mavriplis Open the ORCID record for C. Mavriplis [Opens in a new window]
G. Agbaglah*
Affiliation:
Department of Mechanical Engineering, University of Ottawa, 161 Louis Pasteur, Ottawa, Ontario, K1N 6N5, Canada
C. Mavriplis
Affiliation:
Department of Mechanical Engineering, University of Ottawa, 161 Louis Pasteur, Ottawa, Ontario, K1N 6N5, Canada
*
†Email address for correspondence: gagbagla@uottawa.ca
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Abstract

The flow in the near wake of a square cylinder at Reynolds numbers of 205 and 225, corresponding to three-dimensional wake instability modes $A$ and $B$, respectively, and that of the square’s circumscribed circular cylinder are examined by using three-dimensional Navier–Stokes numerical simulations. At small times, prior to the streamwise vortex shedding, a self-similar velocity is observed in the wake and no significant difference is observed in the dynamics of the flows past the square and the circular cylinders. The exponential growth of the three-dimensional instability reaches a saturation regime during this early time for the considered Reynolds numbers. Vortical structures in the wake at long times and shedding frequencies are very close for the square and the circular cylinders. The flow separation on the forward top and bottom corners of the square cylinder have the effect of increasing its effective width, making it comparable with the diameter of the circumscribed circular cylinder. Thus, Floquet multipliers and modes of the associated three-dimensional instabilities are shown to be very close for the two cylinders when using the circumscribed circular cylinder as the basis for a characteristic length scale. Most importantly, the wavenumber with the maximum growth rate, for modes $A$ and $B$, is approximately identical for the two cylinders.

JFM classification

Instability: Nonlinear instability Vortex Flows: Vortex shedding Wakes/Jets: Wakes
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 870 , 10 July 2019 , pp. 419 - 432
Copyright
© 2019 Cambridge University Press 

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