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On the structure of shear stress and turbulent kinetic energy flux across the roughness layer of a gravel-bed channel flow



This study examines the structure of shear stress and turbulent kinetic energy (TKE) flux across the roughness layer of a uniform, fully rough gravel-bed channel flow (ks+ ≫ 100, δ/k = 20) using high-resolution acoustic Doppler velocity profiler measurements. The studied gravel-bed roughness layer exhibits a complex random multi-scale roughness structure in strong contrast with conceptualized k- or d-type roughness in standard rough-wall flows. Within the roughness layer, strong spatial variability of all time-averaged flow quantities are observed affecting up to 40% of the boundary layer height. This variability is attributed to the presence of bed zones with emanating bed protuberances (or gravel clusters) acting as local flow obstacles and bed zones of more homogenous roughness of densely packed gravel elements. Considering the strong spatial mean flow variability across the roughness layer, a spatio-temporal averaging procedure, called double averaging (DA), has been applied to the analysed flow quantities. Three aspects have been addressed: (a) the DA shear stress and DA TKE flux in specific bed zones associated with three classes of velocity profiles as previously proposed in Mignot, Barthélemy & Hurther (J. Fluid Mech., vol. 618, 2009, p. 279), (b) the global and per class DA conditional statistics of shear stress and associated TKE flux and (c) the contribution of large-scale coherent shear stress structures (LC3S) to the TKE flux across the roughness layer. The mean Reynolds and dispersive shear structure show good agreement between the protuberance bed zones associated with the S-shape/accelerated classes and recent results obtained in standard k-type rough-wall flows (Djenidi et al., Exp. Fluids, vol. 44, 2008, p. 37; Pokrajac, McEwan & Nikora, Exp. Fluids, vol. 45, 2008, p. 73). These gravel-bed protuberances act as local flow obstacles inducing a strong turbulent activity in their wake regions. The conditional statistics show that the Reynolds stress contribution is fairly well distributed between sweep and ejection events, with threshold values ranging from H = 0 to H = 8. However, the TKE flux across the roughness layer primarily results from the residual shear stress between ejection and sweep of very high magnitude (H = 10–20) and of small turbulent scale. Although LC3S are seen to penetrated the interfacial roughness layer, their TKE flux contribution is found to be negligible compared to the very energetic small-scale sweep events. These sweeps are dominantly produced in the bed zones of local gravel protuberances where the velocity profiles are inflexional of S-shape type and the mean flow properties are of mixing-layer flow type as previously shown in Mignot et al. (2009).


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Aberle, J. 2007 Measurements of armour layer roughness geometry function and porosity. Acta Geophys. 55 (1), 2332.
Adrian, R. J., Meinhart, C. D. & Tomkins, C. D. 2000 Vortex organization in the outer region of the turbulent boundary layer. J. Fluid Mech. 422, 154.
Antonia, R. A. & Atkinson, J. D. 1973 High-order moments of reynolds shear stress fluctuations in a turbulent boundary layer. J. Fluid Mech. 58 (3), 581593.
Blanckaert, K. & de Vriend, H. J. 2004 Secondary flow in sharp open-channel bends. J. Fluid Mech. 498, 353380.
Blanckaert, K. & de Vriend, H. J. 2005 Turbulence structure in sharp open-channel bends. J. Fluid Mech. 536, 2748.
Castro, I. T. 2007 Rough-wall boundary layers: mean flow universality. J. Fluid Mech. 585, 469485.
Cheng, H. & Castro, I. T. 2002 Near wall flow over urban-like roughness. Bound.-Layer Meteorol. 104, 229259.
Christen, A., Van Gorsel, E. & Vogt, R. 2007 Coherent structures in urban roughness sublayer turbulence. Intl J. Climatol. 27, 19551968.
Coceal, O., Thomas, T. G., Castro, I. P. & Belcher, S. E. 2006 Mean flow and turbulence statistics over groups of urban-like cubical obstacles. Bound.-Layer Meteorol. 121, 491519.
Djenidi, L., Antonia, R., Amielh, M. & Anselmet, F. 1994 Lda measurements in a turbulent boundary layer over a d-type rough wall. Exp. Fluids 16 (5), 323329.
Djenidi, L., Antonia, R., Amielh, M. & Anselmet, F. 2008 A turbulent boundary layer over a two-dimensional rough wall. Exp. Fluids 44 (1), 3747.
Finnigan, J. 2000 Turbulence in plant canopies. Annu. Rev. Fluid Mech. 32, 519571.
Franca, M. J. 2005 Flow dynamics over a gravel riverbed. In Proceeding XXXI IAHR Congress, Seoul, Korea.
Ganapathisubramani, B., Longmire, E. K. & Marusic, I. 2003 Characteristics of vortex packets in turbulent boundary layers. J. Fluid Mech. 478, 3546.
Grass, A. J. 1971 Structural features of turbulent flow over smooth and rough boundaries. J. Fluid Mech. 50, 233255.
Grass, A. J., Stuart, R. J. & Mansour-Tehrani, M. 1991 Vortical structures and coherent motion in turbulent flow over smooth and rough boundaries. Phil. Trans. R. Soc. Lond. A 336, 3565.
Hoover, T. M. & Ackerman, J. D. 2004 Near-bed hydrodynamic measurements above boulders in shallow torrential streams: implications for stream biota. J. Environ. Engng Sci. 3, 365378.
Hurther, D. & Lemmin, U. 2000 Shear stress statistics and wall similarity analysis in turbulent boundary layers using a high-resolution 3-d advp. J. Ocean. Engng 25 (4), 446457.
Hurther, D. & Lemmin, U. 2001 A correction method for turbulence measurements with a three-dimensional acoustic doppler velocity profiler. J. Atmos. Ocean. Technol. 18 (3), 446458.
Hurther, D. & Lemmin, U. 2003 Turbulent particle and momentum flux statistics in suspension flow. Water Ressour. Res. 39 (5), doi:10.1029/2001WR001113.
Hurther, D. & Lemmin, U. 2008 Improved turbulence profiling with field adapted acoustic doppler velocimeters using a bi-frequency doppler noise suppression method. J. Atmos. Ocean. Technol. 25 (2), 452463.
Hurther, D., Lemmin, U. & Terray, E. A. 2007 Turbulent transport in the outer region of rough wall open-channel flows: the contribution of large coherent shear stress structures (lc3s). J. Fluid Mech. 574, 465493.
Jimenez, J. 2004 Turbulent flows over rough walls. Annu. Rev. Fluid Mech. 36, 173196.
Lemmin, U. & Rolland, T. 1997 Acoustic velocity profiler for laboratory and field studies. J. Hydraul. Engnng 123, 10891098.
Liou, T. M., Chang, Y. & Hwang, D. W. 1990 Experimental and computational study of turbulent flows in a channel with two pairs of turbulence promoters in tandem. J. Fluid Engng 112, 302310.
Lopez, F. & Garcia, M. H. 2001 Mean flow and turbulence structure of open-channel flow through non-emergent vegetation. J. Hydraul. Engng 127 (5), 392402.
Lu, S. S. & Willmarth, W. W. 1973 Measurements of the structure of the Reynolds stress in a turbulent boundary layer. J. Fluid Mech. 60, 481511.
Luchik, T. S. & Tiederman, W. G. 1987 Timescale and structure of ejections and bursts in turbulent channel flows. J. Fluid Mech. 174, 529552.
Mignot, E., Barthélemy, E. & Hurther, D. 2008 Turbulent kinetic energy budget in a gravel-bed channel flow. Acta Geophys. 56 (3), 601613.
Mignot, E., Barthélemy, E. & Hurther, D. 2009 Double averaging analysis and local flow characterization of near bed turbulence in gravel-bed channel flows. J. Fluid Mech. 618, 279303.
Nakagawa, H. & Nezu, I. 1977 Prediction of the contribution to Reynolds stress from bursting events in open-channel flows. J. Fluid Mech. 80 (1), 99128.
Nezu, I. & Nakagawa, H. 1993 Turbulence in open channel flows. IAHR Monograph. Balkema, Rotterdam.
Nikora, V., Goring, D., McEwan, I. & Griffiths, G. 2001 Spatially averaged open-channel flow over rough bed. J. Hydraul. Engng 127 (2), 123133.
Nikora, V., McEwan, I., McLean, S., Coleman, S., Pokrajac, D. & Walters, R. 2007 Double-averaging concept for rough-bed open-channel and overland flows: theoretical background. J. Hydraul. Engng 133 (8), 873883.
Perry, A. E., Schofield, W. H. & Joubert, P. N. 1969 Subelement form-drag parameterization in rough-bed flows. J. Fluid Mech. 37, 383413.
Pokrajac, D., Campbell, L. J., Nikora, V., Manes, C. & McEwan, I. 2007 Quadrant analysis of persistent spatial velocity perturbations over square-bar roughness. Exp. Fluids 42, 413423.
Pokrajac, D., McEwan, I. & Nikora, V. 2008 Spatially averaged turbulent stress and its partitioning. Exp. Fluids 45, 7383.
Raupach, M. R., Antonia, R. A. & Rajagopalan, S. 1981 Conditional statistics of Reynolds stress in rough wall and smooth wall turbulent boundary layers. J. Fluid Mech. 108, 363382.
Raupach, M. R., Antonia, R. A. & Rajagopalan, S. 1991 Rough-wall turbulent boundary layers. Appl. Mech. Rev. 44 (1), 125.
Robinson, S. K. 1991 Coherent motions in the turbulent boundary layer. Annu. Rev. Fluid Mech. 23, 601639.
Roth, M. 2000 Review of atmospheric turbulence over cities. Quart. J. R. Meteorol. Soc. 146, 941990.
Schlichting, H. 1936 Experimental investigation of surface roughness. In Proc. Soc. Mech. Eng. NACA TM 823, USA.
Song, T., Graf, W. H. & Lemmin, U. 1994 Uniform flow in open channels with movable gravel bed. J. Hydraul. Res. 32 (6), 861876.
Sumer, B. M. & Deiggard, R. 1981 Particle motions near the bottom in turbulent flow in an open channel. Part 2. J. Fluid Mech. 109, 311337.
Yue, W., Meneveau, C., Parlange, M. B., Zhu, W., Van Hout, R. & Katz, J. 2007 A comparative quadrant analysis of turbulence in a plant canopy. Water Ressour. Res. 43 (5).
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On the structure of shear stress and turbulent kinetic energy flux across the roughness layer of a gravel-bed channel flow



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