Direct numerical simulation of a 30R long turbulent pipe flow at R + = 685: large- and very large-scale motions

Abstract Fully developed incompressible turbulent pipe flow at Reynolds number ${\mathit{Re}}_{D} = 24\hspace{0.167em} 580$ (based on bulk velocity) and Kármán number ${R}^{+ } = 684. 8$ is simulated in a periodic domain with a length of $30$ pipe radii $R$. While single-point statistics match closely with experimental measurements, questions have been raised of whether streamwise energy spectra calculated from spatial data agree with the well-known bimodal spectrum shape in premultiplied spectra produced by experiments using Taylor’s hypothesis. The simulation supports the importance of large- and very large-scale motions (VLSMs, with streamwise wavelengths exceeding $3R$). Wavenumber spectral analysis shows evidence of a weak peak or flat region associated with VLSMs, independent of Taylor’s hypothesis, and comparisons with experimental spectra are consistent with recent findings (del Álamo & Jiménez, J. Fluid Mech., vol. 640, 2009, pp. 5–26) that the long-wavelength streamwise velocity energy peak is overestimated when Taylor’s hypothesis is used. Yet, the spectrum behaviour retains otherwise similar properties to those documented based on experiment. The spectra also reveal the importance of motions of long streamwise length to the $uu$ energy and $uv$ Reynolds stress and support the general conclusions regarding these quantities formed using experimental measurements. Space–time correlations demonstrate that low-level correlations involving very large scales persist over $40R/ {U}_{\mathit{bulk}} $ in time and indicate that these motions convect at approximately the bulk velocity, including within the region approaching the wall. These very large streamwise motions are also observed to accelerate the flow near the wall based on force spectra, whereas smaller scales tend to decelerate the mean streamwise flow profile, in accordance with the behaviour observed in net force spectra of prior experiments. Net force spectra are resolved for the first time in the buffer layer and reveal an unexpectedly complex structure.