Spatially Averaged Open-Channel Flow over Rough Bed
Publication: Journal of Hydraulic Engineering
Volume 127, Issue 2
Abstract
In this paper it is suggested that the double-averaged (in temporal and in spatial domains) momentum equations should be used as a natural basis for the hydraulics of rough-bed open-channel flows, especially with small relative submergence. The relationships for the vertical distribution of the total stress for the simplest case of 2D, steady, uniform, spatially averaged flow over a rough bed with flat free surface are derived. These relationships explicitly include the form-induced stresses and form drag as components of the total stress. Using this approach, we define three types of rough-bed flows: (1) Flow with high relative submergence; (2) flow with small relative submergence; and (3) flow over a partially inundated rough bed. The relationships for the double-averaged velocity distribution and hydraulic resistance for all three flow types are derived and compared with measurements where possible. The double-averaged turbulent and form-induced intensities and stresses for the case of regular spherical-segment-type roughness show the dominant role of the double-averaged turbulence stresses and form drag in momentum transfer in the near-bed region.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Bathurst, J. C. ( 1985a). “Theoretical aspects of flow resistance.” Gravel-bed rivers, R. D. Hey, J. C. Bathurst, and C. R. Thorne, eds., Wiley, New York, 83–108.
2.
Bathurst, J. C. (1985b). “Flow resistance estimation in mountain rivers.”J. Hydr. Engrg., ASCE, 111(4), 625–643.
3.
Bathurst, J. C. ( 1994). “At-a-site mountain river flow resistance variation.” Proc., Hydr. Engrg. '94, ASCE, New York, 682–686.
4.
Bathurst, J. C., Simmons, D. B., and Li, R.-M. (1981). “Resistance equation for large-scale roughness.”J. Hydr. Div., ASCE, 107(12), 1593–1613.
5.
Bray, D. I. ( 1985). “Flow resistance in gravel-bed rivers.” Gravel-bed rivers, R. D. Hey, J. C. Bathurst, and C. R. Thorne, eds., Wiley, New York, 109–132.
6.
Day, T. J. ( 1978). “Aspects of flow resistance in steep channels having coarse particulate beds.” Research in fluvial geomorphology, R. Davidson-Arnott and W. Nickling, eds., University of Guelph, Ont., 45–58.
7.
Dittrich, A., and Koll, K. ( 1997). “Velocity field and resistance of flow over rough surface with large and small relative submergence.” Int. J. Sediment Res., 12(3), 21–33.
8.
Finnigan, J. J. ( 1985). “Turbulent transport in flexible plant canopies.” The forest-atmosphere interactions, B. A. Hutchinson and B. B. Hicks, eds., Reidel, Dordrecht, The Netherlands, 443–480.
9.
Gimenez-Curto, L. A., and Corniero Lera, M. A. ( 1996). “Oscillating turbulent flow over very rough surfaces.” J. Geophys. Res., 101(C9), 20745–20758.
10.
Graf, W. H., and Altinakar, M. S. ( 1998). Fluvial hydraulics, Wiley, New York.
11.
Griffiths, G. A. (1981). “Flow resistance in coarse gravel bed rivers.”J. Hydr. Div., ASCE, 107(7), 899–918.
12.
Grinvald, D. I., and Nikora, V. I. ( 1988). River turbulence, Hydrometeoizdat, Leningrad, Russia (in Russian).
13.
Izakson, A. ( 1937). “Formula for the velocity distribution near a wall.” J. Experimental and Theoretical Phys. (Zh. Eksp. Teor. Fiz.), 7, 919–924 (in Russian).
14.
Kironoto, B. A., and Graf, W. H. ( 1994). “Turbulence characteristics in rough uniform open-channel flow.” Proc., Instn. Civ. Engrg. Water, Maritime, and Energy, 106, 333–344.
15.
Kraus, N. C., Lohrmann, A., and Cabrera, R. (1994). “New acoustic meter for measuring 3D laboratory flows.”J. Hydr. Engrg., ASCE, 120(3), 406–412.
16.
Lawrence, D. S. L. ( 1997). “Macroscale surface roughness and frictional resistance in overland flow.” Earth Surface Processes and Landforms, 22, 365–382.
17.
Lindsey, R. K., Kohler, M. A., and Paulhus, J. L. H. ( 1975). Hydrology for engineers, McGraw-Hill, New York.
18.
Lohrmann, A., Cabrera, R., and Kraus, N. C. ( 1994). “Acoustic-Doppler velocimeter (ADV) for laboratory use.” Proc., Symp. on Fundamentals and Advancements in Hydr. Measurements and Experimentation, C. A. Pugh, ed., ASCE, New York, 351–365.
19.
Lopez, F., and Garcia, M. ( 1996). “Turbulence structure in cobble-bed open-channel flow.” Hydr. Engrg. Ser. No. 52, University of Illinois at Urbana-Champaign, Ill., 139.
20.
Millikan, C. B. ( 1939). “A critical discussion of turbulent flows in channels and circula tubes.” Proc., 5th Int. Congr. Appl. Mech., 386–392.
21.
Monin, A. S., and Yaglom, A. M. ( 1971). Statistical fluid mechanics: Mechanics of turbulence, Vol. 1, MIT Press, Cambridge, Mass.
22.
Nezu, I., and Nakagawa, H. ( 1993). Turbulence in open-channel flows, Balkema, Rotterdam, The Netherlands.
23.
Nikitin, I. K. ( 1963). Turbulent channel flow and processes in the near-bed region, Ukraine Acad. Sci., Kiev, Ukraine (in Russian).
24.
Nikitin, I. K. ( 1980). Complex turbulent flows and heat and mass transfer processes, Ukraine Acad. Sci., Kiev, Ukraine (in Russian).
25.
Nikora, V. I., and Goring, D. G. (1998). “ADV measurements of turbulence: Can we improve their interpretation?”J. Hydr. Engrg., ASCE, 124(6), 630–634.
26.
Nikora, V. I., Goring, D. G., and Biggs, B. J. F. ( 1998a). “On gravel-bed roughness characterisation.” Water Resour. Res., 34(3), 517–527.
27.
Nikora, V. I., Goring, D. G., and Biggs, B. J. F. ( 1998b). “Silverstream eco-hydraulics flume: Hydraulic design and tests.” NZ J. of Marine and Freshwater Res., 32, 607–620.
28.
Nikora, V. I., and Smart, G. M. (1997). “Turbulence characteristics of New Zealand gravel-bed rivers.”J. Hydr. Engrg., ASCE, 123(9), 764–773.
29.
Raupach, M. R., Antonia, R. A., and Rajagopalan, S. ( 1991). “Rough-wall turbulent boundary layers.” Appl. Mech. Rev., 44(1), 1–25.
30.
Raupach, M. R., and Shaw, R. H. ( 1982). “Averaging procedures for flow within vegetation canopies.” Boundary-Layer Meteorology, 22, 79–90.
31.
Shimizu, Y., Tsujimoto, T., and Nakagawa, H. ( 1990). “Experiment and macroscopic modelling of flow in highly permeable porous medium under free-surface flow.” J. Hydrosci. and Hydr. Engrg., 8(1), 69–78.
32.
Smith, J. D., and McLean, S. R. ( 1977). “Spatially averaged flow over a wavy surface.” J. Geophys. Res., 83(12), 1735–1746.
33.
Song, T., and Graf, W. H. ( 1994). “Nonuniform open-channel flow over a rough bed.” J. Hydrosci. and Hydr. Engrg., 12(1), 1–25.
34.
Townsend, A. A. ( 1998). The structure of turbulent shear flows, Cambridge University Press, London.
35.
Wilson, N. R., and Shaw, R. H. ( 1977). “A higher order closure model for canopy flow.” J. Appl. Meteorology, 16, 1197–1205.
Information & Authors
Information
Published In
Journal of Hydraulic Engineering
Volume 127 • Issue 2 • February 2001
Pages: 123 - 133
History
Received: Jun 7, 1999
Published online: Feb 1, 2001
Published in print: Feb 2001
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.