Recent studies reveal that at large friction Reynolds number delta^+ the outer, inertially-dominated region of the turbulent boundary layer is composed of large scale zones of uniform momentum segregated by narrow fissures of concentrated vorticity. Experiments show that, when scaled by the boundary layer thickness, the fissure thickness is O(1/sqrt{delta^+}), while the dimensional jump in streamwise velocity across each fissure scales in proportion to the friction velocity u_tau. A simple model that exploits these essential elements of the turbulent boundary layer structure at large delta^+ is developed. First, a master wall-normal profile of streamwise velocity is constructed by placing a discrete number of fissures across the boundary layer. The number of fissures and their wall-normal locations follow scalings informed by analysis of the mean momentum equation. The fissures are then randomly displaced in the wall-normal direction, exchanging momentum as they move, to create an instantaneous velocity profile. This process is repeated to generate ensembles of streamwise velocity profiles from which statistical moments are computed. The modelled statistical moments are shown to agree remarkably well with those acquired from direct numerical simulations of turbulent channel flow at large delta^+. In particular, the model robustly reproduces the empirically observed sub-Gaussian behaviour for the skewness and kurtosis profiles over a large range of input parameters.
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An input–output based analysis of convective velocity in turbulent channels
This paper employs an input–output based approach to analyse the convective velocities and transport of fluctuations in turbulent channel flows. The convective velocity for a fluctuating quantity associated with streamwise–spanwise wavelength pairs at each wall-normal location is obtained through the maximization of the power spectral density associated with the linearized Navier–Stokes equations with a turbulent mean profile and delta-correlated Gaussian forcing. We first demonstrate that the mean convective velocities computed in this manner agree well with those reported previously in the literature. We then exploit the analytical framework to probe the underlying mechanisms contributing to the local convective velocity at different wall-normal locations by isolating the contributions of each streamwise–spanwise wavelength pair (flow scale). The resulting analysis suggests that the behaviour of the convective velocity in the near-wall region is influenced by large-scale structures further away from the wall. These structures resemble Townsend’s attached eddies in the cross-plane, yet show incomplete similarity in the streamwise direction. We then investigate the role of each linear term in the momentum equation to isolate the contribution of the pressure, mean shear, and viscous effects to the deviation of the convective velocity from the mean at each flow scale. Our analysis highlights the role of the viscous effects, particularly in regards to large channel spanning structures whose influence extends to the near-wall region. The results of this work suggest the promise of an input–output approach for analysing convective velocity across a range of flow scales using only the mean velocity profile.
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- Award ID(s):
- 1652244
- NSF-PAR ID:
- 10136190
- Date Published:
- Journal Name:
- Journal of Fluid Mechanics
- Volume:
- 888
- ISSN:
- 0022-1120
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Abstract Decimeter‐scale early‐stage aeolian bedforms represent topographic features that differ notably from their mature dune counterparts, with nascent forms exhibiting more gently sloping lee sides and a reverse asymmetry in their flow‐parallel bed profile compared to mature dunes. Flow associated with the development of these “protodunes,” wherein the crest gradually shifts downstream towards its mature state, was investigated by studying the perturbation of the turbulent boundary layer over a succession of representative bedforms. Rigid, three‐dimensional models were studied in a refractive‐index‐matched experimental flume that enabled near‐surface quantification of mean velocities and Reynolds stresses using particle‐image velocimetry in wall‐normal and wall‐parallel measurement planes. Data indicate strong, topographically induced flow perturbations over the protodunes, to a similar relative degree to that found over mature dunes, despite their low‐angled slopes. The shape of the crest is found to be an important factor in the development of flow perturbations, and only in the case with the flattest crest was maximal speed‐up of flow, and reduction in turbulent stresses, found to occur upstream of the crest. Investigation of the log‐linearity of the boundary layer profile over the stoss sides showed that, although the profile is strongly perturbed, a log‐linear region exists, but is shifted vertically. A streamwise trend in friction velocity is thus present, showing a behavior similar to the trends in mean velocity. Analysis of the growth of the internal boundary layer on the dune stoss sides, beginning at the toe region, reveals a similar development for all dune shapes, despite clear differences in mean velocity and turbulent stress perturbations in their toe regions. The data presented herein provide the first documentation of flow over morphologies broadly characteristic of subtle, low‐angle, aeolian protodunes, and indicate key areas where further study is required to yield a more complete quantitative understanding of flow–form–transport couplings that govern their morphodynamics.
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Highly-resolved, direct numerical simulations of turbulent channel flows with sub- Kolmogorov grid resolution are performed to investigate the characteristics of wall-bounded turbulent flows in the presence of sinusoidal wall waviness. The wall waviness serves as a simplified model to study the effects of well-defined geometric parameters of roughness on the characteristics of wall-bounded turbulent flows. In this study, a two-dimensional wave profile with steepness ranging from 0.06 to 0.25 and wave amplitudes ranging from 9 to 36 wall units were considered. For the smooth and wavy-wall simulations, the Reynolds number based on the friction velocity was kept constant. To study the effects of wave amplitude and wavelength on turbulence, two-dimensional time and spanwise averaged distributions of the mean flow, turbulent kinetic energy, and Reynolds stresses as well as turbulent kinetic energy production and dissipation are examined. Furthermore, in order to provide a more direct comparison with the smooth-wall turbulent channel flow one-dimensional pro- files of these quantities are computed by averaging them over one wavelength of the wave profile. A strong effect of the wall-waviness and, in particular, the wave amplitude and wavelength on the characteristics of the turbulence was obtained. Wall waviness mainly affected the inner flow region while all recorded turbulent statistics collapsed in the outer flow region. Significant reductions in turbulent kinetic energy, production and dissipation were obtained with increasing wave amplitudes when reported in inner scale. While production is lower for all wavy wall cases considered here in comparison to the smooth wall, reducing the wavelength caused an increase in production and a decrease in dissipation.more » « less
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A direct numerical simulation of incompressible channel flow at a friction Reynolds number (Reτ) of 5186 has been performed, and the flow exhibits a number of the characteristics of high-Reynolds-number wall-bounded turbulent flows. For example, a region where the mean velocity has a logarithmic variation is observed, with von Kármán constant k = 0.384 ± 0.004. There is also a logarithmic dependence of the variance of the spanwise velocity component, though not the streamwise component. A distinct separation of scales exists between the large outer-layer structures and small inner-layer structures. At intermediate distances from the wall, the one-dimensional spectrum of the streamwise velocity fluctuation in both the streamwise and spanwise directions exhibits k-1 dependence over a short range in wavenumber (k) . Further, consistent with previous experimental observations, when these spectra are multiplied by k (premultiplied spectra), they have a bimodal structure with local peaks located at wavenumbers on either side of the k-1 range.more » « less
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1017/jfm.2020.48
