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 Rec =64 ± 0.5 and Rec =132 ± 1 respectively. Two-dimensional vortex shedding flow is unlikely in practice for such flows. The dominant spanwise wavelength is λ/D=0.9±0.1 for the rotated array at Re=100 and λ/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 λ → ∞ (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. 1