Do logarithmic terms exist in the drag coefficient of a single sphere at high Reynolds numbers?

At the beginning of the second half of the twentieth century, Proudman and Pearson (J. Fluid. Mech.,2(3), 1956, pp.237–262) suggested that the functional form of the drag coefficient (C_D) of a single sphere subjected to uniform fluid flow consists of a series of logarithmic and power terms of the Reynolds number (Re). In this paper...