Reynolds-number scaling of a vorticity-annihilating boundary layer

To mimic the unsteady vortex-wall interaction of animal propulsion in a canonical test case, a vorticity-annihilating boundary layer was examined through the spin-down of a vortex from solid-body rotation. A cylindrical, water-filled tank was rapidly stopped, and the decay of the vortex from solid-body rotation was observed by means of planar and stereo particle image velocimetry. High Reynolds-number (Re) measurements were achieved by combining a large-scale facility (diameter, D = 13 m) with a novel approach to reduce end-wall effects. The influence of the boundary-layer formation at the tank's bottom wall was minimised by introducing a saturated salt-water layer. The experimental efforts have allowed us to assess the Re dependency of the laminar-turbulent transition of the vorticity-annihilating side-wall boundary layer at scales similar to large cetaceans. The scaling of the transition mechanism and its onset time were found to agree with predictions from linear stability analysis. Furthermore, the growth rate of the curved turbulent boundary layer was also in good agreement with an empirical scaling formulated in the literature for much smaller Re. Eventually, the scaling of vorticity annihilation was addressed. The earlier onset of transition at high Re compensates for the reduced effects of viscosity, leading to similar vorticity annihilation rates during the early stages of the spin-down for a wide Re range.