Vortex mode selection of a rigid cylinder subject to VIV at low mass-damping

We present direct numerical simulations results of vortex-induced vibrations of a freely vibrating rigid cylinder with low mass-damping parameter using a spectral/hp element method. We investigate several reduced velocities to assess the validity of the "three-branch response" and its sensitivity to Reynolds number in the range 1000-3000. This study addresses the numerical challenge of capturing large amplitude responses in the upper branch and the 2P vortex shedding mode in the lower branch, which has been observed in experiments. We focus, in particular, on the region of reduced velocities around the mode transition between the upper and the lower branch of response. In this region, there exists a sharp drop in the spanwise correlation of the wake and forces, which, surprisingly, does not diminish the response of the cylinder. Therefore, detailed measurements of the phasing along the span are crucial to understanding the system and its mechanism for vortex mode selection. We use complex demodulation analysis to quantify the spatio-temporal phase relationship between the forces and cylinder displacement. We also compute the correlation length of the forces along the span of the cylinder.