Large-scale motions in turbulent pipe flow

Abstract

Direct numerical simulations (DNSs) of turbulent pipe flow at $Re_\tau$ = 180, 544, 934 and 3008 were performed. The range of the present Reynolds numbers covered being from low to high turbulent flow. $Re_\tau$ = 3008 became the highest Reynolds number in the area of pipe DNSs, which can provide clear comparison with the previous experimental studies and resolve the several controversial issues so far. Scale separation, one of the prominent features in high Reynolds number, was examined and interpreted in the perspective of turbulence structures. Scale separation between SSM and LSM (& VLSM) was achieved due to the occurrence of the strong outer energy from VLSM, whereas the power law occurred instead of the log law in the overlap layer, implying that the scale separation between the inner and outer length scales was not achieved. The contribution of the LSM was not strong enough to show the constant-stress layer in the Reynolds shear stress, which was related to the log law. LSM and VLSM, which played a significant role in the scaling, grew linearly in the statistical manner. The linearly growing behavior was consistent to the helical angles of the energetic proper orthogonal decomposition (POD) modes. The present DNS data and results could be significant in revealing the unknown nature of turbulence.