Three-dimensional Floquet instability of the wake of square cylinder

• Published in: Physics of fluids (1994) 1999-03, Vol.11 (3), p.560-578
• Main Authors: Robichaux, J., Balachandar, S., Vanka, S. P.
• Format: Article
• Language: English
• ISSN: 1070-6631; 1089-7666
• DOI: 10.1063/1.869930

In this study we investigate the onset of three-dimensionality in an otherwise two-dimensional periodic wake of a square cylinder. Floquet stability analysis is employed to extract the different modes of three-dimensional instabilities. It is observed that the three-dimensional transition process for a square cylinder is similar to that of a circular cylinder. Most notably, there is a long-wavelength (mode A) three-dimensional disturbance that becomes unstable first at a Reynolds number of about 161, followed by a short-wavelength (mode B) three-dimensional disturbance that becomes unstable at a Reynolds number of about 190. In addition, a third intermediate-wavelength mode is also observed to become unstable at around Re=200. Unlike modes A and B, the intermediate-wavelength mode is subharmonic with a period of twice the shedding period of the two-dimensional base state. This mode also breaks the reflection translation symmetry observed in the other two modes and as a result appears with multiplicity two. The space–time symmetries of the three modes are explored in detail.