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Stabilization of absolute instability in spanwise wavy two-dimensional wakes

Published online by Cambridge University Press:  21 June 2013

Yongyun Hwang ,
Jinsung Kim  and
Haecheon Choi
Yongyun Hwang*
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WA, UK
Jinsung Kim
Affiliation:
School of Mechanical and Aerospace Engineering, Seoul National University, Seoul 151-744, Korea
Haecheon Choi
Affiliation:
School of Mechanical and Aerospace Engineering, Seoul National University, Seoul 151-744, Korea
*
†Email address for correspondence: [email protected]
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Abstract

Controlling vortex shedding using spanwise-varying passive or active actuation (namely three-dimensional control) has recently been reported as a very efficient method for regulating two-dimensional bluff-body wakes. However, the mechanism of how the designed controller regulates vortex shedding is not clearly understood. To understand this mechanism, we perform a linear stability analysis of two-dimensional wakes, the base flow of which is modified with a given spanwise waviness. Absolute and convective instabilities of the spanwise wavy base flows are investigated using Floquet theory. Two types of base-flow modification are considered: varicose and sinuous. Both of these modifications attenuate absolute instability of two-dimensional wakes. In particular, the varicose modification is found to be much more effective in the attenuation than the sinuous one, and its spanwise lengths resulting in maximum attenuation show good agreement with those in three-dimensional controls. The physical mechanism of the stabilization is found to be associated with the formation of streamwise vortices from tilting of two-dimensional Kármán vortices and the subsequent tilting of these streamwise vortices by the spanwise shear in the base flow. Finally, the sensitivity of absolute instability to spanwise wavy base-flow modification is investigated. It is shown that absolute instability of two-dimensional wakes is much less sensitive to spanwise wavy base-flow modification than to two-dimensional modification. This suggests that the high efficiency observed in several three-dimensional controls is not due to the sensitive response of the wake instability to the spanwise waviness in the base flow.

JFM classification

Instability: Absolute/convective instability Flow Control: Instability control Wakes/Jets: Wakes/Jets
Type
Papers
Information
Journal of Fluid Mechanics , Volume 727 , 25 July 2013 , pp. 346 - 378
Copyright
©2013 Cambridge University Press 

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