Modification of three-dimensional instability in the planar shear flow around two circular cylinders in tandem

Abstract

Direct stability analysis based on the Floquet theory has been employed to clarify the effects of planar shear on three-dimensional instabilities in the wake of two identical circular cylinders of diameter D in tandem arrangement. The center-to-center separation (Lx) in the range of 1.2 ≤ Lx/D ≤ 2.5 was considered. The onset of the three-dimensional instabilities was calculated, and the critical Reynolds number and corresponding spanwise wavenumber varying with the separation were discussed for different shear rates. Representative configurations were chosen to illustrate different transition scenarios, with the three-dimensional instabilities studied in detail for each case. It was found that three different effects of planar shear on the three-dimensional synchronous instability originally present in the otherwise uniform flow were identified depending on the separation. A subharmonic mode referred to as mode SS was observed to develop in the wake due to the flow asymmetry caused by the planar shear. This subharmonic mode differs from the C-type mode in terms of both the spatial structure and critical spanwise wavelength. Furthermore, the mode SS instability was found to be intensified as the shear becomes stronger, and it develops more rapidly than the synchronous modes.