The physical structures of velocity are examined from a recent direct numerical simulation of fully developed incompressible turbulent pipe flow (Wu, Baltzer & Adrian, J. Fluid Mech., vol. 698, 2012, pp. 235–281) at a Reynolds number of ${\mathit{Re}}_{D} = 24\hspace{0.167em} 580$ (based on bulk velocity) and a Kármán number of ${R}^{+ } = 685$. In that work, the periodic domain length of $30$ pipe radii $R$ was found to be sufficient to examine long motions of negative streamwise velocity fluctuation that are commonly observed in wall-bounded turbulent flows and correspond to the large fractions of energy present at very long streamwise wavelengths (${\geq }3R$). In this paper we study how long motions are composed of smaller motions. We characterize the spatial arrangements of very large-scale motions (VLSMs) extending through the logarithmic layer and above, and we find that they possess dominant helix angles (azimuthal inclinations relative to streamwise) that are revealed by two- and three-dimensional two-point spatial correlations of velocity. The correlations also reveal that the shorter, large-scale motions (LSMs) that concatenate to comprise the VLSMs are themselves more streamwise aligned. We show that the largest VLSMs possess a form similar to roll cells centred above the logarithmic layer and that they appear to play an important role in organizing the flow, while themselves contributing only a minor fraction of the flow turbulent kinetic energy. The roll cell motions play an important role with the smaller scales of motion that are necessary to create the strong streamwise streaks of low-velocity fluctuation that characterize the flow.

Fully developed incompressible turbulent pipe flow at Reynolds number Re D = 24 580 (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 (delÁlamo & 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 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.

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The precise dynamics of breakdown in pipe transition is a centuryold unresolved problem in fluid mechanics. We demonstrate that the abruptness and mysteriousness attributed to the Osborne Reynolds pipe transition can be partially resolved with a spatially developing direct simulation that carries weakly but finitely perturbed laminar inflow through gradual rather than abrupt transition arriving at the fully developed turbulent state. Our results with this approach show during transition the energy norms of such inlet perturbations grow exponentially rather than algebraically with axial distance. When inlet disturbance is located in the core region, helical vortex filaments evolve into large-scale reverse hairpin vortices. The interaction of these reverse hairpins among themselves or with the near-wall flow when they descend to the surface from the core produces small-scale hairpin packets, which leads to breakdown. When inlet disturbance is near the wall, certain quasi-spanwise structure is stretched into a Lambda vortex, and develops into a large-scale hairpin vortex. Small-scale hairpin packets emerge near the tip region of the large-scale hairpin vortex, and subsequently grow into a turbulent spot, which is itself a local concentration of small-scale hairpin vortices. This vortex dynamics is broadly analogous to that in the boundary layer bypass transition and in the secondary instability and breakdown stage of natural transition, suggesting the possibility of a partial unification. Under parabolic base flow the friction factor overshoots Moody's correlation. Plug base flow requires stronger inlet disturbance for transition. Accuracy of the results is demonstrated by comparing with analytical solutions before breakdown, and with fully developed turbulence measurements after the completion of transition.T he vast and expanding realm of fluid mechanics research on transition and turbulence can actually be traced back to a single point in history: the publication of Osborne Reynolds' 1883 pipe flow paper (1) in which the concept of Reynolds number was introduced. Given the historical, fundamental, and applied importance of the problem, it is ironic that the Osborne Reynolds pipe transition remains to this day "abrupt and mysterious" (2, 3).Significant progress has been made during the past decade, mostly concentrating on the detection of traveling wave (4, 5), and on the lifetime and reverse transition (relaminarization) of existing pipe flow turbulence produced by strong jet-in-crossflow type of blowing and suction (6, 7). Refs. 8 and 9 reported insightful relaminarization simulations using the axially periodic boundary condition.We tackle directly the Osborne Reynolds pipe transition problem with spatially developing direct numerical simulation (DNS). The disturbance energy growth rate with respect to axial distance, and how the friction factor and vortex structures develop during pipe transition with the distance, is currently unknown. We anticipate that weakly finite and localized disturbances introduced at ...

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