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Three-dimensional instability in the flow past two side-by-side square cylinders

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10.1063/1.4813628

### Abstract

The onset of the three-dimensional (3D) instability in the flow past two side-by-side square cylinders has been studied via Floquet stability analysis. The gap between the two cylinders is the key parameter that alters flow topology, leading to change of stability characteristics. Depending on the gap, four distinct flow patterns have been identified for base flow. For each pattern of base flow, distinctive Floquet modes of 3D instability have been found. The spatial and temporal characteristics of the Floquet modes are similar to those of mode A or mode B of the single square cylinder case, namely, odd or even Reflection-Translation symmetries. Six distinct Floquet modes have been identified in total, and the spatial and temporal characteristics of each mode are described in detail. The criticality of Floquet modes, including their critical Reynolds number and the associated dominant spanwise wave number, is presented for each gap considered in the current study. For a small gap, the flow past the two cylinders resembles that of a single object, resulting in an approximately doubled characteristic length. Consequently, the critical Reynolds number becomes low with a small gap between the two cylinders. When the two cylinders are moderately apart, the interaction between the two wakes diminishes, and the criticality of 3D instabilities approaches that of the single cylinder case. Coexisting 3D instabilities for a specific base-flow topology are also noticed with a moderate gap. Neutral stability curves are computed and presented for some selected values of the gap.

© 2013 AIP Publishing LLC

Received 28 October 2012
Accepted 12 April 2013
Published online 31 July 2013

Acknowledgments: This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MEST) (Grant No. 2012R1A2A2A01013019).

Article outline:

I. INTRODUCTION

II. FORMULATION AND NUMERICAL METHODS

A. Base flow

B. Floquet stability analysis

III. RESULTS AND DISCUSSION

A. Review of the secondary instability for flow past a single square cylinder

B. Patterns of base flow

C. Characteristics of three-dimensional instability modes

1. Mode SA1 (0 **≤** *G/h* **≤** 0.3)

2. Mode SA2 (0.6 ≤ *G/h* ≤ 0.9)

3. Mode SA3 (1.6 **≤** *G/h* **≤** 2.1)

4. Mode SA4 (*G/h* ≥ 2.5)

D. Coexisting three-dimensional instabilities (SB3/SB4)

E. Critical spanwise wavelength

IV. CONCLUSION

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2013-07-31

2014-04-17

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