Bed Waves Generated by Internal Waves in Alluvial Channels
Publication: Journal of Hydraulic Engineering
Volume 115, Issue 6
Abstract
A theory has been developed to explain the generation of dunes and ripples on an erodible bed in open channel flow. The flow is conceived as a stratified flow both with respect to the velocity distribution and the density distribution of the sediment‐fluid mixture. The free internal waves that may occur in such a flow are assumed to be the triggering mechanism for the generation of dunes and ripples on an initially flat bottom. The effectiveness of the theory is demonstrated by comparing the calculated free waves with the peaks in the bed‐wave spectrum as measured at small times after starting the flow in a channel with an initially flat bed. The theory shows that dunes are generated by internal waves corresponding with the steady free‐surface waves. Ripples are due to free internal waves that only occur in flows with sediment transport. The theory has been demonstrated for bedload transport. However, an extension to any other transport mode is straightforward.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Abbott, J. E., and Francis, J. R. D., (1977). “Saltation and suspension trajectories of solid grains in a water stream.” Proc., Royal Soc. 284, A 1321, London, U.K.,
2.
Anderson, A. G. (1953). “The characteristics of sediment waves formed by flow in open channels.” Proc., Third Midwestern Conf. in Fluid Mech., Minneapolis, Minn., 379–395.
3.
Bagnold, R. A. (1973). “The nature of saltation and of bed‐load transport in water.” Proc., Royal Soc., A 332, London, U.K.
4.
Coles, D. (1956). “The law of the wake in the turbulent boundary layer.” J. Fluid Mech., 191–226.
5.
Einstein, H. A. (1950). “The bed‐load function for sediment transportation in open channel flow.” Tech. Bulletin No. 1026, U.S. Dept. of Agric, Washington, D.C., Sept.
6.
Engelund, F. (1970). “Instability of erodible beds.” J. Fluid Mech., 42, 225–244.
7.
Engelund, F., and Fredsøe, J. (1982). “Sediment ripples and dunes.” Ann. Rev. Fluid Mech., 14, 13–37.
8.
Fernandez Luque, R., and Beek, R. van, (1976). “Erosion and transport of bed‐load sediment.” J. Hydr. Res., 14(2).
9.
Francis, J. R. D. (1973). “Experiments on the motion of solitary grains along the bed of a water‐stream.” Proc., Royal Soc., A332, London, U.K.
10.
Fredsøe, J. (1974). “On the development of dunes in erodible channels.” J. Fluid Mech., 64, 1–16.
11.
Graf, W. H. (1971). Hydraulics of sediment transport, McGraw‐Hill Book Co., Inc., New York, N.Y.
12.
Jain, S. C., and Kennedy, J. F. (1971). “The growth of sand waves.” Proc., Int. Symp. on Stochastic Hydraulics, Pittsburgh Univ. Press., Pittsburgh, Penn., 449–471.
13.
Jain, S. C., and Kennedy, J. F., (1974). “The spectral evolution of sedimentary bed forms.” J. Fluid Mech., 63(part 2)301–314.
14.
Jong, B. de (1983). “The formation of dunes in open channel flow on an initially flattened erodible bed.” B. Mutlu Sumer and A. Müller, eds., Proc., Euromech 156: Mechanics of Sediment Transport, July 12‐14, A. A. Balkema, Rotterdam, The Netherlands.
15.
Jong, B. de (1986). “The interaction of suspended flow with the bed shape in an open erodible channel.” W. Bechteler, ed., Proc., Euromech 192: Transport of Suspended Solids in Open Channels, June 11—15, A. A. Balkema, Rotterdam, The Netherlands.
16.
Jong, B. de (1987). “The generation of ripples and dunes in open erodible channelflow with only bed‐load transport.” Preprints, Third Int. Symp. on Stratified Flows, California Inst. of Tech., Pasadena, Calif., Feb. 3–5.
17.
Kennedy, J. F. (1963). “The mechanics of dunes and antidunes in erodible‐bed channels.” J. Fluid Mech., 16, 521–544.
18.
Lighthill, J. (1978). Waves in fluids. Cambridge Univ. Press, Cambridge, U.K.
19.
Liu, H.‐K. (1957). “Mechanics of sediment‐ripple formation.” J. Hydr. Engrg., ASCE, 83(2).
20.
Phillips, O. M. (1977). The dynamics of the upper ocean. Cambridge Univ. Press, Cambridge, U.K.
21.
Raudkivi, A. J. (1966). “Bed forms in alluvial channels.” J. Fluid Mech., 26, 507–514.
22.
Reynolds, A. J. (1976). “A decade's investigation of the stability of erodible stream beds.” Nordic Hydrology 7, 161.
23.
Richards, K. J., (1980). “The formation of ripples and dunes on an erodible bed.” J. Fluid Mech., 99(part 3), 597–618.
24.
Rijn, L. C. van, (1984). “Sediment transport, part I: Bed load transport.” J. Hydr. Engrg., ASCE, 110(10), 1431–1456.
25.
Sawyer, J. S. (1960). “Numerical calculation of the displacements of a stratified airstream crossing a ridge of small height.” Quart. J. Roy. Met. Soc., 86, 326–345.
26.
Scorer, R. S. (1949). “Theory of waves in the lee of mountains.” Quart. J. Roy. Met. Soc., 75, 417–428.
27.
Shirasuna, A. S. (1973). “Formation of sand waves.” Proc., 15th Congr. Int. Assoc. Hydraulic Res. 1, Paper Al5, 107–114.
28.
Stoker, J. J. (1957). Water waves, Interscience, New York, N.Y.
29.
Turner, J. S. (1973). Boyancy effects in fluids. Cambridge Univ. Press., Cambridge, U.K.
30.
Vanoni, V. A., and Nomicos, G. N., (1959). “Resistance properties of sediment laden streams.” Proc., Amer. Soc. Civ. Eng., 85.
31.
Whitham, G. B. (1974). Linear and nonlinear waves. Wiley, New York, N.Y.
Information & Authors
Information
Published In
Copyright
Copyright © 1989 ASCE.
History
Published online: Jun 1, 1989
Published in print: Jun 1989
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.