Spectral analysis of the net turbulent force in accelerating turbulent pipe flow

This investigation examines the dynamic response of an accelerating turbulent pipe flow using direct numerical simulation data sets. A low/high-pass Fourier filter is used to investigate the contribution and time dependence of the large-scale motions (LSM) and the small-scale motions (SSM) into the transient Reynolds shear stress. Additionally, it analyses how the LSM and SSM influence the mean wall shear stress using the Fukagata–Iwamoto–Kasagi identity. The results reveal that turbulence is frozen during the early flow excursion. During the pretransition stage, energy growth of the LSM and a subtle decay in the SSM is observed, suggesting a laminarescent trend of SSM. The transition period exhibits rapid energy growth in the SSM energy spectrum at the near-wall region, implying a shift in the dominant contribution from LSM to SSM to the frictional drag. The core-relaxation stage shows a quasisteady behaviour in large- and small-scale turbulence at the near-wall region and progressive growth of small- and large-scale turbulence within the wake region. The wall-normal gradient of the Reynolds shear stress premultiplied energy cospectra was analysed to understand how LSM and SSM influence the mean momentum balance across the different transient stages. A relevant observation is the creation of a momentum sink produced at the buffer region in large- and very large-scale (VLSM) wavelengths during the pretransition. This sink region annihilates a momentum source located in the VLSM spectrum and at the onset of the logarithmic region of the net-force spectra. This region is a source term in steady wall-bounded turbulence.