Three-Dimensional Floquet Stability Analysis of the Flow Produced by an Oscillating Circular Cylinder in Quiescent Fluid

The primary three-dimensional instabilities of the flow generated by a cylinder oscillating in quiescent fluid at low ampli-tudes and frequencies of oscillation are examined using Floquet stability analysis and direct numerical simulation (DNS). Experimental visualisations have observed the formation of a number of regimes which, in part, have been classified by the nature of the three-dimensional structures formed. Using a combination of Floquet analysis and DNS the transition from two-dimensional to three-dimensional flow is studied for the onset of three of these regimes. Neutral stability curves and the spanwise wavelength at the onset of these instabilites are reported for values of the dimensionless oscillation amplitude (Keulegan-Carpenter number) KC < 10 and the frequency (Stokes number) β < 100. Vorticity isosurfaces of the three-dimensionally unstable flows studies are presented