A numerical investigation of three-dimensional flow past an oscillating cylinder at Re = 400 was carried out to investigate the effects of oscillation mode on flow structure and forces. The cylinder is forced to oscillate with a frequency in the in-line direction twice that of the transverse frequency, thus following a figure-eight trajectory. It is found that the flow three-dimensionality and forces on the cylinder depend strongly on the direction in which the figure eight is traversed.

Bluff body wakes are characterized by very rich physics.

Flow past a circular cylinder is the most representative bluff body wake. At very low Reynolds number, the flow is steady, characterized by a region of two counter-rotating standing vortices placed symmetrically in the wake. Bifurcation to oscillatory flow (Kármán street) occurs at Re˜49. Up to Re˜190, the oscillatory flow remains two-dimensional. Studies on the transition to three-dimensional flow have been initiated by Roshko (1954). It is now well assessed that the cylinder wake becomes three-dimensional for Re>190, as shown by experimental and numerical studies (Williamson, 1996; Barkley and Henderson, 1996).Three-dimensional wakes are characterized by the presence of spanwise Kármán rolls and streamwise vortex pairs. Two modes of vortex shedding have been identified as the dominant features of three-dimensionality in the wake, and are referred to as "Mode A" and "Mode B". Mode A is associated with an instability with a spanwise wavelength of 3-4 cylinder diameters; see Williamson, 1996. On the other hand, Mode-B instability is characterized by a shorter wavelength (approximately one cylinder diameter). The presence of Mode A and Mode B in the wake of a circular cylinder has been reported by Williamson and Roshko (1988) and Williamson (1996a), and confirmed by several other studies (Zhang et al., 1995; Henderson, 1997; Brede et al.,1996; Thompson et al., 1996; Thompson et al., 2001).

Because of the dynamic nature of the lift and drag forces exerted by the flow, cylindrical structures undergo free oscillations, commonly characterized by a trajectory resembling a figure eight.

To shed light on the wake instabilities, several numerical studies of three-dimensional flow past a stationary cylinder have been performed. Studies relevant to Vortex Induced Vibrations (VIV) have considered the flow past a cylinder oscillating either in the transverse or the in the inline direction with respect to the incoming stream. However, computational studies considering a simultaneous oscillation in both directions are limited. The present study thus concerns the flow past an oscillating cylinder following a figure eight trajectory (commonly encountered in VIV), at a Reynolds number equal to 400, where the flow past the stationary cylinder is known to be three-dimensional. The approach is that of Direct Numerical Simulation (DNS) using a Spectral Element Method (SEM).

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