Three-dimensional wake transition of a circular cylinder in an oscillatory flow

The two-dimensional to three-dimensional wake transition of a circular cylinder in a sinusoidal oscillatory flow arises from the Honji instability at a critical Keulegan–Carpenter number (denoted $\textit{KC}_{cr}$ ) with a corresponding critical spanwise wavelength (denoted $\lambda _{cr}$ ) for a given Stokes number (denoted $\beta$ ) larger than approximately 50. However, significant discrepancies in the $\textit{KC}_{cr}$ and $\lambda _{cr}$ values exist among the theoretical predictions by Hall ( J. Fluid Mech. , vol. 146, 1984, pp. 347–367), empirical formulae by Sarpkaya ( J. Fluid Mech. , vol. 457, 2002, pp. 157–180) and other experimental and numerical results in the literature. These long-standing discrepancies are addressed in this study, and new equations for $\textit{KC}_{cr}$ and $\lambda _{cr}$ are proposed for $\beta = 55$ – $10^{6}$ . The present $\textit{KC}_{cr}$ and $\lambda _{cr}$ values agree well with the Floquet analysis results of Elston et al. ( J. Fluid Mech. , vol. 550, 2006, pp. 359–389) for $\beta \sim 50$ – $100$ , and asymptotically converge to theoretical predictions by Hall (1984) as $\beta \to \infty$ , but deviate significantly from the empirical formulae by Sarpkaya (2002). The underlying physical mechanisms for these deviations are elucidated. In addition, we reproduce the quasi-coherent structure (QCS) numerically for the first time, and demonstrate that the QCS observed by Sarpkaya (2002), where transient Honji vortices become pronounced near peak flow velocities but diminish during deceleration, is physically induced by ambient disturbances inevitably contained in physical experiments, such that $\textit{KC}_{cr}$ given by Sarpkaya (2002) is specific to the level of disturbance in his experimental setting and is somewhat arbitrary.