Tomo-PIV measurements of tethered sphere VIV onset while crossing the Hopf bifurcation

Here, for the first time we examine the transient evolution of the vortical structures in the wake of a tethered sphere as the uniform upstream velocity is slowly increased and the tethered sphere (diameter $D$) dynamics passes through the Hopf bifurcation. Tomo-PIV experiments (at 15Hz) were performed in a closed-loop water tunnel. The volume of interest ($4.5\times6.5\times2.5 D^3$) was located immediately downstream of the sphere. The reduced velocity, $U^* = U/(f_ND$), was stepwise raised from 2.2 to 4.5 in 100s (d$U$/d$t = 4.36\times10^{-4}$m/s), where $U$ is the free-stream velocity, and $f_N$ is the natural frequency of the tethered sphere. Large coherent structures resembling two streamwise oriented, longitudinal ``legs" were observed at $U^*$ = 2.5 while the sphere was stationary. Approaching $U^*$ = 3, hairpin vortices, having a vertical plane of symmetry, were shed, alongside weaker induced hairpins that strengthened with increasing $U^*$. While vertical symmetry was sporadically disturbed, the onset of VIV occurred around $U^*$ = 3.7, peaking at $U^*$ = 4.4, as the plane of symmetry was shifted to the horizontal.