Three-dimensional Floquet stability analysis of the wake in cylinder arrays

Three-dimensional stability of the periodic wake of tightly packed rotated and inline cylinder arrays is investigated for 60 <= Re <= 270. Results are compared with existing numerical and experimental studies for an isolated cylinder. Numerical Floquet analysis shows that the two-dimensional wakes of the rotated and inline arrays with spacing P/D = 1.5 become unstable at Re(c) = 64 +/- 0.5 and Re, = 132 +/- 1 respectively. Two-dimensional vortex shedding flow is unlikely in practice for such flows. The dominant spanwise wavelength is lambda/D = 0.9 +/- 0.1 for the rotated array at Re = 100 and lambda/D = 3.0 +/- 0.1 for the inline array at Re = 200. Three-dimensional simulations show excellent agreement with the Floquet analysis for the rotated case, and reasonable agreement for the inline case. The instability mechanism appears to be similar to Mode A for an isolated cylinder, although the structure of the three-dimensional vorticity is different due to the spatial periodicity of the flow. Unlike the isolated cylinder, both array flows are unstable as lambda -> infinity (like a thin shear layer). This is the first investigation of three-dimensional wake instability in cylinder arrays, a problem of significant practical and theoretical interest.