Turbulence in a Gravel-Bed Stream with an Array of Large Gravel Obstacles
Publication: Journal of Hydraulic Engineering
Volume 142, Issue 11
Abstract
This experimental and analytical study investigates the double-averaged (DA) turbulent flow characteristics within an array of large gravel obstacles found atop a porous gravel bed. Analysis of the experimental data reveals that the DA streamwise velocity preserves the logarithmic law above the form-induced sublayer, while a linear law and a third-degree polynomial function apply within the form-induced and interfacial sublayers, respectively. The form-induced shear stress is 70% of the DA Reynolds shear stress (RSS) occurring at the virtual bed level. The DA turbulent kinetic energy (TKE) components, streamwise and vertical, attain their peak values at the obstacle crest level, while they diminish sharply below the virtual bed level. The fluxes of the TKE streamwise and vertical components, however, change their signs slightly below the crest level, indicating a changeover of the dominance of the bursting events. For the TKE budget, the TKE production, diffusion, and pressure energy diffusion rate terms attain their peak values at the crest level, while the TKE dissipation rate has its peak value at the virtual bed level. Third-order moments of velocity fluctuations follow the linear relationship, and their signs change slightly below the crest level. The quadrant analysis suggests that the sweep events are the governing mechanism at the near-bed flow region, while the ejection events become predominant with an increase in vertical distance. The quadrant plots of the form-induced velocity components display a pseudo-elliptical scatter within the interfacial sublayer and a small circular cluster above the form-induced sublayer.
Get full access to this article
View all available purchase options and get full access to this article.
References
Aberle, J., Koll, K., and Dittrich, A. (2008). “Form induced stresses over rough gravel-beds.” Acta Geophys., 56(3), 584–600.
Bigillon, F., Niño, Y., and Garcia, M. H. (2006). “Measurements of turbulence characteristics in an open-channel flow over a transitionally-rough bed using particle image velocimetry.” Exp. Fluids, 41(6), 857–867.
Brayshaw, A. C. (1984). “Characteristics and origin of cluster bedforms in coarse-grained alluvial channels.” Sedimentology of gravels and conglomerates, E. H. Koster and R. J. Steel, eds., Canadian Society of Petroleum Geologists, Calgary, AB, 77–85.
Buffin-Bélanger, T., and Roy, A. G. (1998). “Effects of a pebble cluster on the turbulent structure of a depth-limited flow in a gravel-bed river.” Geomorphology, 25(3–4), 249–267.
Calomino, F., Tafarojnoruz, A., De Marchis, M., Gaudio, R., and Napoli, E. (2015). “Experimental and numerical study on the flow field and friction factor in a pressurized corrugated pipe.” J. Hydraul. Eng., 04015027.
Dey, S. (2014). Fluvial hydrodynamics: Hydrodynamic and sediment transport phenomena, Springer, Berlin.
Dey, S., and Das, R. (2012). “Gravel-bed hydrodynamics: Double-averaging approach.” J. Hydraul. Eng., 707–725.
Dey, S., Sarkar, S., Bose, S. K., Tait, S., and Castro-Orgaz, O. (2011). “Wall-wake flows downstream of a sphere placed on a plane rough-wall.” J. Hydraul. Eng., 1173–1189.
Giménez-Curto, L. A., and Corniero, M. A. (1996). “Oscillating turbulent flow over very rough surfaces.” J. Geophys. Res., 101(C9), 20745–20758.
Giménez-Curto, L. A., and Corniero, M. A. (2002). “Flow characteristics in the interfacial shear layer between a fluid and a granular bed.” J. Geophys. Res., 107(C5), 12-1–12-9.
Giralt, F., and Ferré, J. A. (1993). “Structure and flow patterns in turbulent wakes.” Phys. Fluids, 5(7), 1783–1789.
Goring, D. G., and Nikora, V. I. (2002). “Despiking acoustic Doppler velocimeter data.” J. Hydraul. Eng., 117–126.
Hurther, D., and Lemmin, U. (2000). “Shear stress statistics and wall similarity analysis in turbulent boundary layers using a high-resolution 3-D ADVP.” IEEE J. Ocean. Eng., 25(4), 446–457.
Hussein, H. J., and Martinuzzi, R. J. (1996). “Energy balance for turbulent flow around a surface mounted cube placed in a channel.” Phys. Fluids, 8(3), 764–780.
Hwang, J.-Y., and Yang, K.-S. (2004). “Numerical study of vortical structures around a wall-mounted cubic obstacle in channel flow.” Phys. Fluids, 16(7), 2382–2394.
Lacey, R. W. J., and Roy, A. G. (2007). “A comparative study of the turbulent flow field with and without a pebble cluster in a gravel bed river.” Water Resour. Res., 43(5), W05502.
Lawless, M., and Robert, A. (2001). “Three-dimensional flow structure around small-scale bedforms in a simulated gravel-bed environment.” Earth Surf. Processes Landforms, 26(5), 507–522.
López, F., and García, M. H. (1999). “Wall similarity in turbulent open-channel flow.” J. Eng. Mech., 789–796.
Lu, S. S., and Willmarth, W. W. (1973). “Measurements of the structure of the Reynolds stress in a turbulent boundary layer.” J. Fluid Mech., 60(3), 481–511.
Manes, C., Pokrajac, D., McEwan, I., and Nikora, V. (2009). “Turbulence structure of open channel flows over permeable and impermeable beds: A comparative study.” Phys. Fluids, 21(12), 125109.
Mignot, E., Barthelemy, E., and Hurther, D. (2009a). “Double-averaging analysis and local flow characterization of near-bed turbulence in gravel-bed channel flows.” J. Fluid Mech., 618, 279–303.
Mignot, E., Barthelemy, E., and Hurther, D. (2008). “Turbulent kinetic energy budget in a gravel-bed channel flow.” Acta Geophys., 56(3), 601–613.
Mignot, E., Hurther, D., and Barthelemy, E. (2009b). “On the structure of shear stress and turbulent kinetic energy flux across the roughness layer of a gravel-bed channel flow.” J. Fluid Mech., 638, 423–452.
Mignot, E., Hurther, D., and Barthelemy, E. (2011). “Discussion of ‘Double-averaging turbulence characteristics in flows over a gravel bed’ by S. Sarkar and S. Dey.” J. Hydraul. Res., 49(5), 703–704.
Morris, H. M. (1955). “Flow in rough conduits.” Trans. ASCE, 120, 373–705.
Nakagawa, H., and Nezu, I. (1977). “Prediction of the contributions to the Reynolds stress from bursting events in open-channel flows.” J. Fluid Mech., 80(1), 99–128.
Nakagawa, H., Nezu, I., and Ueda, H. (1975). “Turbulence of open channel flow over smooth and rough beds.” Proc. Jpn. Soc. Civ. Eng., 241, 155–168.
Nezu, I., and Nakagawa, H. (1993). Turbulence in open-channel flows, Balkema, Rotterdam, Netherlands.
Nikora, V., et al. (2007a). “Double-averaging concept for rough-bed open-channel and overland flows: Applications.” J. Hydraul. Eng., 884–895.
Nikora, V., Goring, D., McEwan, I., and Griffiths, G. (2001). “Spatially averaged open-channel flow over rough bed.” J. Hydraul. Eng., 123–133.
Nikora, V., Koll, K., McEwan, I., McLean, S., and Dittrich, A. (2004). “Velocity distribution in the roughness layer of rough-bed flows.” J. Hydraul. Eng., 1036–1042.
Nikora, V., McEwan, I., McLean, S., Coleman, S., Pokrajac, D., and Walters, R. (2007b). “Double-averaging concept for rough-bed open-channel and overland flows: Theoretical background.” J. Hydraul. Eng., 873–883.
Papanicolaou, A. N., Diplas, P., Dancey, C. L., and Balakrishnan, M. (2001). “Surface roughness effects in near-bed turbulence: Implications to sediment entrainment.” J. Eng. Mech., 211–218.
Papanicolaou, A. N., Kramer, C. M., Tsakiris, A. G., Stoesser, T., Bomminayuni, S., and Chen, Z. (2012). “Effects of a fully submerged boulder within a boulder array on the mean and turbulent flow fields: Implications to bedload transport.” Acta Geophys., 60(6), 1502–1546.
Papanicolaou, A. N., and Tsakiris, A. G. (2015). “Boulder effects on turbulence and bedload transport.” Proc., Conf. Gravel Bed Rivers, Wiley, Kyoto, Japan.
Pokrajac, D., Campbell, L. J., Nikora, V., Manes, C., and McEwan, I. (2007). “Quadrant analysis of persistent spatial velocity perturbations over square-bar roughness.” Exp. Fluids, 42(3), 413–423.
Raupach, M. R. (1981). “Conditional statistics of Reynolds stress in rough-wall and smooth-wall turbulent boundary layers.” J. Fluid Mech., 108, 363–382.
Sarkar, S., and Dey, S. (2010). “Double-averaging turbulence characteristics in flows over a gravel-bed.” J. Hydraul. Res., 48(6), 801–809.
Sarkar, S., and Dey, S. (2015). “Turbulent length scales and anisotropy downstream of a wall mounted sphere.” J. Hydraul. Res., 53(5), 649–658.
Tsakiris, A. G., Papanicolaou, A. N., Hajimirzaie, S. M., and Buchholz, J. H. J. (2014). “Influence of collective boulder array on the surrounding time-averaged and turbulent flow fields.” J. Mt. Sci., 11(6), 1420–1428.
Uchida, T., and Fukuoka, S. (2012). “Bottom velocity computation method by depth integrated model without shallow water assumption.” J. Jpn. Soc. Civ. Eng. Ser. B1, 68(4), I_1225–I_1230 (in Japanese).
Yager, E. M., Kirchner, J. W., and Dietrich, W. E. (2007). “Calculating bed load transport in steep boulder bed channels.” Water Resour. Res., 43(7), W07418.
Information & Authors
Information
Published In
Copyright
© 2016 American Society of Civil Engineers.
History
Received: Feb 22, 2016
Accepted: Apr 8, 2016
Published online: Jul 13, 2016
Published in print: Nov 1, 2016
Discussion open until: Dec 13, 2016
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.