Decay of an axisymmetric drag wake at Reynolds number (Re) 10⁵

The problem of axisymmetric drag wakes has been studied for nearly a century (Swain 1929), yet the far-field wake decay scaling law is still not fully understood. Recently, there has been substantial evidence that the previously accepted scaling law is incorrect (Bonnier and Eiff 2002, Nedic et al 2013, Saunders et al 2020). Here, the drag wake of a dimpled sphere at Re = 10⁵ is studied experimentally using Stereo Particle Image Velocimetry to a downstream distance of ~90 diameters. The data were used to produce estimates of the mean velocity field, velocity fluctuations, and Reynolds stresses. Self-similar decay was observed with the ensemble mean axial velocity defect decaying as x^-1 and the wake size growing as x^1/2 which matched previous dimpled sphere data at Re = 50,000. Due to the difference in Reynolds number, the two spheres have different drag coefficients (0.13 and 0.25, respectively), but these self-similar decay exponents were not observed to depend on drag coefficient or Reynolds number. The results suggest that the self-similar drag wake decay observed at laboratory scales may extrapolate to the larger Re typical of engineering and geophysical flows.