Law of the Wake and Scaling of the Mean Velocity Profile in Turbulent Pipe Flow

In this paper we apply a recursive methodology to identify the wake function from mean velocity profiles of turbulent pipe flow ranging 22000 < Re-tau < 40000. Unlike standard methodologies, the present method requires no a priori assumptions on the log-law. The wake function is obtained from pairs of velocity profiles obtained at different Reynolds numbers by applying a recursive procedure originally proposed by Luchini (2018). The velocity profiles have been acquired in the Long Pipe facility in CICLoPE by hot-wire anemometry. We report the law of the wake obtained from 3 different pairs of Reynolds numbers, using the higher Reynolds number case as a reference. We compare the results with those obtained from the standard procedure of subtracting a pre-determined log-law and we discuss the implications of the observed differences on the scaling of the log region.