Double-Averaged Open-Channel Flows with Small Relative Submergence
Publication: Journal of Hydraulic Engineering
Volume 133, Issue 8
Abstract
We investigate the turbulent structure of shallow open channel flows where the flow depth is too small (compared with the roughness height) to form a logarithmic layer but large enough to develop an outer layer where the flow is not directly influenced by the roughness elements. Since the log layer is not present, the displacement height , which defines the position of the zero plane, and the shear velocity cannot be found by fitting the velocity data to the log law. However, these parameters are still very important because they are used for scaling flow statistics for the outer and roughness layers. In this paper we propose an alternative procedure for evaluating in laboratory conditions, where is found from additional experiments with the fully developed log layer. We also point out the appropriate procedure for evaluating the shear velocity for flows with low submergence. These procedures are applied to our own laboratory flume experiments with uniform sphere roughness, where velocities were measured using Particle Image Velocimetry. Results were interpreted within the framework of the double-averaged Navier–Stokes equations and include mean velocities, turbulence intensities, Reynolds stresses, and form-induced normal and shear stresses. The data collapse well and show that in flows without a developed log layer the structure of turbulence in the outer layer remains similar to that of flows with a log layer. This means that even though the roughness layer in the experiments reported herein was sufficiently high to prevent the development of the log layer, influence of the bed roughness did not spread further up into the outer layer. Furthermore, the results show that flow statistics do not depend on relative submergence except for the form-induced stresses which increase when relative submergence decreases.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
This investigation was carried out as part of an experimental program funded by the United Kingdom Engineering and Physical Sciences Research Council (Grant No. EPSRC-GBGR/R51865/01).
References
Campbell, L. J. (2005). “Double-averaged open channel flow over regular rough beds.” Ph.D. thesis, Aberdeen Univ., Aberdeen, U.K.
Dittrich, A., and Koll, K. (1997). “Velocity field and resistance of flow over rough surface with large and small relative submergence.” J. Sediment Res., 12(3), 21–33.
Ferro, V., and Baiamonte, G. (1994). “Flow velocity profiles in gravel-bed rivers.” J. Hydraul. Eng., 120(1), 60–80.
Finnigan, J. J. (1985). “Turbulent transport in flexible plant canopies.” The forest–Atmosphere interactions, B. A. Hutchinson and B. B. Hicks, eds., Reidel, 443–480.
Gimenez-Curto, L. A., and Corniero Lera, M. A. (1996). “Oscillating turbulent flow over very rough surfaces.” J. Geophys. Res., 101(C9), 20745–20758.
Graf, W. H., and Altinakar, M. S. (1998). Fluvial hydraulics, Wiley, New York.
Jarvela, J. (2005). “Effect of submerged flexible vegetation on flow structure and resistance.” J. Hydrol., 307, 233–241.
Jimenez, J. (2004). “Turbulent flow over rough walls.” Annu. Rev. Fluid Mech., 36, 173–196.
Katul, G., Wiberg, P., Albertson, J., and Hornberger, G. (2002). “A mixing layer theory for flow resistance in shallow streams.” Water Resour. Res., 38(11), 1250–1257.
Kironoto, B. A., and Graf, W. H. (1994). “Turbulence characteristics in rough uniform open-channel flow.” Proc. Inst. Civ. Eng., Waters. Maritime Energ., 106, 333–344.
Landau, L. D., and Lifshitz, E. M. (1944). Mechanics of continuous media, 1st Russian Ed., Gostekhisdat, Moscow, USSR.
McLean, S. R., Wolfe, S. R., and Nelson, J. M. (1999). “Spatially averaged flow over a wavy boundary revisited.” J. Geophys. Res., 104(C7), 15,743–15,753.
Monin, A. S., and Yaglom, A. M. (1971). Statistical fluid mechanics: Mechanics of turbulence, Vol. 1, MIT Press, Cambridge, Mass.
Nakagawa, H., Tsujimoto, T., and Shimizu, Y. (1991). “Turbulent flow with small relative submergence.” Lecture notes in Earth sciences, 33–44.
Nezu, I., and Nakagawa, H. (1993). Turbulence in open channel flows, Balkema, Rotterdam, The Netherlands.
Nikora, V. (2004). “Spatial averaging concept for rough-bed open-channel and overland flows.” Proc. 6th Int. Conf. on Hydro-Science and Engineering (CD-ROM), Brisbane, Australia.
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., 130(10), 1036–1042.
Nikora, V., Koll, K., McLean, S., Dittrich, A., and Aberle, J. (2002). “Zero-plane displacement for rough-bed open-channel flows.” Proc., Int. Conf. on Fluvial Hydraulics River Flow 2002, Louvain-la-Neuve, Belgium, 83–92.
Nikora, V., Goring, D., McEwan, I., and Griffiths, G. (2001). “Spatially averaged open-channel flow over rough bed.” J. Hydraul. Eng., 127(2), 123–133.
Pope, S. B. (2000). Turbulent flows, Cambridge University Press, Cambridge, U.K.
Raupach, M. R., Antonia, R. A., and Rajagopalan, S. (1991). “Rough wall turbulent boundary layers.” Appl. Mech. Rev., 44(1), 1–25.
Raupach, M. R., and Shaw, R. H. (1982). “Averaging procedures for flow within vegetation canopies.” Boundary-Layer Meteorol., 22, 79–90.
Tani, I. (1987). “Turbulent boundary layer development over rough surfaces.” Perspectives in turbulence studies, H. U. Meier and P. Bradshaw, eds., Springer, Berlin, 223–249.
Thom, A. S. (1971). “Momentum absorption by vegetation.” Q. J. R. Meteorol. Soc., 97, 414–428.
Townsend, A. A. (1976). The structure of turbulent shear flow, Cambridge University Press, Cambridge, U.K.
Wilson, N. R., and Shaw, R. H. (1977). “A higher order closure model for canopy flow.” J. Appl. Meteorol., 16, 1197–1205.
Zanke, U. C. E. (2003). “On the influence of turbulence on the initiation of sediment motion.” J. Sediment Res., 18(1), 1–15.
Information & Authors
Information
Published In
Copyright
© 2007 ASCE.
History
Received: Jan 13, 2006
Accepted: Dec 28, 2006
Published online: Aug 1, 2007
Published in print: Aug 2007
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.