Flow measurements in the near wake of a smooth sphere and one mimicking a pine cone

A combination of time-resolved particle image velocimetry (PIV) and tomographic PIV was used to study the instantaneous three-dimensional vortex shedding as well as mean velocities and turbulent stresses in the near wake of a smooth and a rough sphere. Sphere roughness was modeled by spiraling grooves found in nature on pine cones. The measurements extended up to five sphere diameters D, downstream of the sphere, and were performed across a Reynolds number range of 226<ReD< 5067, spanning several vortex shedding regimes. Our results showed that the main effect of the sphere roughness on the near-wake flow was to lower ReD for which the clear, temporally averaged recirculating wake pattern observed at low ReD disappeared. Furthermore, mean velocities and root-mean-square (rms) values of fluctuating velocities scaled best with the mean recirculating wake length, L¯w, instead of D that is commonly used in the far wake. Normalized, maximum rms values of velocity fluctuations measured in a horizontal equatorial plane increased with increasing ReD and were well fitted by a logarithmic function. The mean velocity defect recovery was well described by a power law with exponents decreasing from -1 to -3 at ReD≈ 2000, and subsequently increasing to -2.3 at ReD≈ 5000. Most surprisingly, our results showed that L¯w/D was locally minimum at ReD≈900. At these ReD, the wake transitioned from a well-organized laminar wake, characterized by a single vortex shedding frequency, to one exhibiting high and low shedding frequency branches. By analyzing the instantaneous centroid positions of the velocity defect in a transverse plane, we showed that the local minimum value of L¯w/D was the result of increased wake "meandering"that resulted in enhanced mixing at this ReD. Moreover, at the transition, the wake alternated between the organized shedding pattern observed at low ReD and the one lacking any preferred orientation at higher ReD.