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The mechanics of dunes and antidunes in erodible-bed channels

Published online by Cambridge University Press:  28 March 2006

John F. Kennedy
John F. Kennedy
Affiliation:
W. M. Keck Laboratory of Hydraulics and Water Resources, California Institute of Technology
Now at Hydrodynamics Laboratory, Department of Civil Engineering, Massachusctts Institute of Technology.
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Abstract

An analytic model of free-surface flow over an erodible bed is developed and used to investigate the stability of the fluid-bed interface and the characteristics of the bed features. The model is based on the potential flow over a two-dimensional, moving, wavy bed with a sinusoidal profile of varying amplitude, and a sediment transport relation in which the transport rate is proportional to a power of the fluid velocity at the level of the bed. By assuming that the dominant wavelength is that for which the rate of amplitude growth is the greatest, expressions are obtained for the wavelength and velocity of the bed features. In addition, conditions for the occurrence of the different configurations, dunes, flat bed, and antidunes, are found from the model. The predicted wavelengths of antidunes and ranges of wavelengths of dunes, and the predicted conditions for change of bed configuration are found to be in good agreement with experimental data. Finally, brief consideration is given to the factors involved in determining the maximum heights of the bed features and surface waves.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 16 , Issue 4 , August 1963 , pp. 521 - 544
Copyright
© 1963 Cambridge University Press

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References

Anderson, Alvin, G. 1953 The characteristics of sediment waves formed by flow in open channels. Proc. third Mid-Western Conf. on Fluid Mech. University of Minnesota, pp. 379–95.
Barton, J. R. & Lin, P.-N. 1955 A study of sediment transport in alluvial channels. Rep. no. 55JRB2, Civil Engineering Dep., Colorado A. and M. College. Ft. Collins, Colorado.
Brooke Benjamin, T. 1957 Wave formation in laminar flow down an inclined plate. J. Fluid Mech., 2, 554–74.Google Scholar
Brooke Benjamin, T. 1959 Shearing flow over a wavy boundary. J. Fluid Mech., 6, 161–205.Google Scholar
Brooks, N. H. 1954 Laboratory studies of the mechanics of streams flowing over a movable bed of fine sand. Doctoral Thesis, California Istitute of Technology.
Colby, B. R. 1957 Relationship of unmeasured sediment discharge to mean velocity. Trans. Amer. Geophys. Un., 38, 708–17.Google Scholar
Colby, B. R. 1961 Effect of depth of flow on discharge of bed material. Geological Survey Water-Supply Paper 1498-D. U.S. Government Printing Office.
Fuchs, R. A. 1952 On the theory of short-crested oscillatory waves. Gravity Waves, Nat. Bureau of Standards Circular, no. 521, pp. 187–200. U.S. Government Printing Office.
Gilbert, G. K. 1914 The transportation of debris by running water. Geological Survey Water-Supply Paper, no. 86. U.S. Government Printing Office.
Kármán, Th. Von 1947 Sand ripples in the desert. Technion Year Book, 1947. (Also in Collected Works of T. von Kármán, vol.IV, pp. 352-6. London: Butterworths 1956.)
Kennedy, J. F. 1961a Stationary waves and antidunes in alluvial channels. Rep. no. KH-R-2, W. M. Keck Laboratory of Hydraulics and Water Resources, California Institute of Technology.
Kennedy, J. F. 1961b Further laboratory studies of the roughness and suspended load of alluvial streams. Rep. no. KH-R-3, W. M. Keck Laboratory of Hydraulics and Water Resources, California Institute of Technology.
Laursen, E. M. 1958 The total sediment load of streams. Proc. Am. Soc. Civ. Engrs, J. Hyd. Div., 84, HY1, pp. 1530–1 to 1530–36.Google Scholar
Michell, J. H. 1893 The highest waves in water. Phil. Mag., 36, 430–7.Google Scholar
Milne-Thomson, L. M. 1960 Theoretical Hydrodynamics. New York: MacMillan.
Plate, E. J. O. F. 1957 Laboratory studies on the beginning of sediment ripple formation in an alluvial channel. Masters Thesis, Colorado State University.
Simons, D. B., Richardson, E.V. & Albertson, M. L. 1961 Flume studies using medium sand (0.45 mm). Geological Survey Water-Supply Paper, no. 1498-A. U.S. Government Printing Office.
Simons, D. B. & Richardson, E. V. 1961 Forms of bed roughness in alluvial channels. Proc. Am. Soc. Civ. Engrs, J. of Hyd. Div., 87, HY3, 87–106.Google Scholar
Sundborg, A. 1957 The river Klarälven; a study in fluvial processes. Bull. no. 52, Institution of Hydraulics, Royal Institute of Technology, Stockholm.
Tison, L. H. 1949 Origine des ondes de sable et des bancs de sable sous I'action des courants. Trans. Int. Ass. for Hyd. Structures Research, Third Meeting, Grenoble.
Tsubaki, T., Kawasumi, T. & Yasutomi, T. 1953 On the influence of sand ripples upon the sediment transport in open channels. Rep. Res. Inst. for Appl. Mech., Kyushu University, 2, 241–56.Google Scholar
Vanoni, V. A. & Brooks, N. H. 1957 Laboratory studies of the roughness and suspended load of alluvial streams. Rep. no. E-68, Sedimentation Laboratory, California Institute of Technology.