Reynolds number effects and outer similarity of pressure fluctuations in turbulent pipe flow

We study the structure of pressure fluctuations in turbulent pipe flow, up to friction Reynolds number Re-tau = 6000, using standard spectral decomposition and proper orthogonal decomposition (POD). The mean pressure distribution is found to be qualitatively different from the case of channel flow, with an additional mean pressure difference caused by combined centrifugal and swirling effects. The variance of the pressure fluctuations exhibits a wide region with negative logarithmic decay with the wall distance, due to the presence of a hierarchy of wall-attached eddies, which we clearly trace in spectral maps, and which are generally isotropic in nature. On the other hand, the largest eddies are strongly non-isotropic, and are mainly elongated in the azimuthal direction. POD is used to prove self-similarity of the attached eddies, whose typical scales are found to be linearly proportional to the wall distance of their center.