LAUSR

Abstract In order to shed some light upon the mechanism for the free vibrations of the wavy cylinder reported previously (Zhang et al., 2017), we numerically investigate the effect of external forcing on the flow around a wavy cylinder at R e = 5000 . The forcing takes the form of sinusoidal transverse motion with the amplitude fixed at A e / D m  = 0.2 and the frequency spanning from f e D m / U ∞ = 0.1 to 0.3. Even though the wavy cylinder is optimally designed to annihilate the Karman vortex shedding in the fixed configuration, the Strouhal frequency is found to resurrect in the forced vibration cases, leading to very similar responses between the normal and wavy cylinders, especially at high forcing frequencies. By sectional analysis it is revealed that the sectional distribution of the force coefficients undergoes significant changes with the increase of the forcing frequency. Statistical tools such as the correlation and coherence reveals further spanwise features of the force coefficients. In addition, the instantaneous three-dimensional vortical structures are visualized by the spanwise voriticity isosurfaces to collaborate the previous discussions. The cessation of the flow control efficacy in the forced vibration is explained by the recession of the mean streamwise vorticity contours. The results presented in the work imply that the vortex-induced vibration of the wavy cylinder might be ascribed to the typical wake-structure interaction as the normal cylinder, although the mechanism for the initial growth of the oscillations still warrants further investigations.