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Three-dimensional river bed forms

Published online by Cambridge University Press:  07 February 2012

M. Colombini  and
A. Stocchino
M. Colombini*
Affiliation:
Dipartimento di Ingegneria delle Costruzioni, dell’Ambiente e del Territorio, Università degli Studi di Genova, via Montallegro 1, 16145 Genova, Italy
A. Stocchino
Affiliation:
Dipartimento di Ingegneria delle Costruzioni, dell’Ambiente e del Territorio, Università degli Studi di Genova, via Montallegro 1, 16145 Genova, Italy
*
†Email address for correspondence: [email protected]
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Abstract

The linear stability of a uniform flow in an infinitely wide erodible channel is investigated with respect to disturbances of the bed that are periodic in both the transverse and the longitudinal directions. A rotational flow and sediment transport model, originally developed to study the formation of two-dimensional dunes and antidunes, is straightforwardly extended to cover variations in the lateral direction. Sediment is assumed to be transported as bed load, disregarding the role of suspension. Following a standard linearization procedure, a dispersion relationship is obtained that expresses the growth rate and the celerity of the sand wave as a function of the streamwise and spanwise wavenumbers and of the relevant flow and sediment parameters. Regions of instabilities in the space of the parameters are found, which can be associated with bed forms of different kinds, spanning from dunes and antidunes to alternate bars. Therefore, the present theory allows for a unified view of the formation of two- and three-dimensional bed forms in rivers in terms of the relevant flow and sediment parameters.

JFM classification

Geophysical and Geological Flows: River dynamics Geophysical and Geological Flows: Sediment transport
Type
Papers
Information
Journal of Fluid Mechanics , Volume 695 , 25 March 2012 , pp. 63 - 80
Copyright
Copyright © Cambridge University Press 2012

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References

1. Allen, J. R. L. 1982 Sedimentary Structures: Their Character and Physical Basis – Vol. 1. Elsevier.Google Scholar
2. ASCE, Task Committee, 1963 Friction factors in open channels. J. Hydraul. Div. ASCE 89 (HY2), 97–143.Google Scholar
3. Besio, G., Blondeaux, P. & Vittori, G. 2006 On the formation of sand waves and sand banks. J. Fluid Mech. 557, 1–27.CrossRefGoogle Scholar
4. Best, J. 2005 The fluid dynamics of river dunes: a review and some future research directions. J. Geophys. Res. – Earth Surface 110, F04S02.CrossRefGoogle Scholar
5. Blondeaux, P. & Seminara, G. 1985 A unified bar-bend theory of river meanders. J. Fluid Mech. 157, 449–470.CrossRefGoogle Scholar
6. Blondeaux, P. & Vittori, G. 2011 Dunes and alternate bars in tidal channels. J. Fluid Mech. 670, 558–580.CrossRefGoogle Scholar
7. Callander, R. A. 1969 Instability and river channels. J. Fluid Mech. 36, 465–480.CrossRefGoogle Scholar
8. Camporeale, C. & Ridolfi, L. 2011 Modal versus nonmodal linear stability analysis of river dunes. Phys. Fluids 23 (10), 104102.CrossRefGoogle Scholar
9. Colombini, M. 2004 Revisiting the linear theory of sand dune formation. J. Fluid Mech. 502, 1–16.CrossRefGoogle Scholar
10. Colombini, M., Seminara, G. & Tubino, M. 1987 Finite-amplitude alternate bars. J. Fluid Mech. 181, 213–232.CrossRefGoogle Scholar
11. Colombini, M. & Stocchino, A. 2005 Coupling or decoupling bed and flow dynamics: fast and slow sediment waves at high Froude numbers. Phys. Fluids 17 (3), 9.CrossRefGoogle Scholar
12. Colombini, M. & Stocchino, A. 2008 Finite-amplitude river dunes. J. Fluid Mech. 611, 283–306.CrossRefGoogle Scholar
13. Colombini, M. & Stocchino, A. 2011 Ripple and dune formation in rivers. J. Fluid Mech. 673, 121–131.CrossRefGoogle Scholar
14. Devauchelle, O., Malverti, L., Lajeunesse, È., Lagrèe, P.-Y., Josserand, C. & Nguyen Thu-Lam, K.-D. 2010 Stability of bedform in laminar flows with free-surface: from bars to ripples. J. Fluid Mech. 642, 329–348.CrossRefGoogle Scholar
15. Einstein, H. A. & Shen, H. W. 1964 A study on meandering in straight alluvial channels. J. Geophys. Res. 69, 5239–5247.CrossRefGoogle Scholar
16. Engelund, F. 1970 Instability of erodible beds. J. Fluid Mech. 42, 225–244.CrossRefGoogle Scholar
17. Engelund, F. 1974 The development of oblique dunes. Prog. Rep. 1–2. Technical University of Denmark, Institute of Hydrodynamics and Hydraulic Engineering.Google Scholar
18. Engelund, F. 1981 The motion of sediment particles on an inclined bed. ISVA Prog. 53. Technical University of Denmark, Institute of Hydrodynamics and Hydraulic Engineering.Google Scholar
19. Engelund, F. & Fredsøe, J. 1974 Transition from dunes to plane bed in alluvial channels. Series paper 4. Technical University of Denmark, Institute of Hydrodynamics and Hydraulic Engineering.Google Scholar
20. Fredsøe, J. 1974 a The development of oblique dunes. Prog. Rep. 3–4. Technical University of Denmark, Institute of Hydrodynamics and Hydraulic Engineering.Google Scholar
21. Fredsøe, J. 1974b On the development of dunes in erodible channels. J. Fluid Mech. 64, 1–16.CrossRefGoogle Scholar
22. Gradowczyk, M. H. 1968 Wave propagation and boundary instability in erodible-bed channels. J. Fluid Mech. 33, 93–112.CrossRefGoogle Scholar
23. Guy, H. P., Simons, D. B. & Richardson, E. V. 1966 Summary of alluvial channel data from flume experiments 1956–61. Prof. paper 462-I. US Geological Survey.CrossRefGoogle Scholar
24. Hall, P. 2006 Nonlinear evolution equations and the braiding of weakly transporting flows over gravel beds. Stud. Appl. Maths 117, 27–69.CrossRefGoogle Scholar
25. Idier, D. & Astruc, D. 2003 Analytical and numerical modelling of sandbanks dynamics. J. Geophys. Res. – Oceans 108, 3060–3074.CrossRefGoogle Scholar
26. Jaeggi, M. 1984 Formation and effects of alternate bars. J. Hydraul. Engng. ASCE 110, 142–156.CrossRefGoogle Scholar
27. Kennedy, J. F. 1963 The mechanism of dunes and antidunes in erodible-bed channels. J. Fluid Mech. 16, 521–544.CrossRefGoogle Scholar
28. Lajeunesse, E., Malverti, L., Lancien, P., Armstrong, L., Métivier, F., Coleman, S., Smith, C. E., Davies, T., Cantelli, A. & Parker, G. 2010 Fluvial and submarine morphodynamics of laminar and near-laminar flows: a synthesis. Sedimentology 57, 1–26.CrossRefGoogle Scholar
29. Meyer-Peter, E. & Müller, R. 1948 Formulas for bed-load transport. In Proceedings of 2nd IAHR Meeting, pp. 39–64. Stockholm, Sweden.Google Scholar
30. Muramoto, Y. & Fujita, Y. 1978 The classification of meso-scale river bed configuration and the criterion of its formation. In Proceedings of 22nd Japanese Conference on Hydraulics, Japan, pp. 275–282.Google Scholar
31. Reynolds, A. J. 1976 A decade’s investigation of the stability of erodible stream beds. Nord. Hydrol. 7, 161–183.CrossRefGoogle Scholar
32. Roos, P. C., Hulscher, S. J. M. H., Knaapen, M. A. F. & Van Damme, R. M. J. 2004 The cross-sectional shape of tidal sandbanks: modelling and observations. J. Geophys. Res. – Earth Surface 109, F02003.Google Scholar
33. Seminara, G. 2010 Fluvial sedimentary patterns. Annu. Rev. Fluid Mech. 42, 43–66.CrossRefGoogle Scholar
34. Seminara, G., Solari, L. & Parker, G. 2002 Bed load at low Shield stress on arbitrarily sloping beds: failure of the Bagnold hypothesis. Water Resour. Res. 38, W000681.CrossRefGoogle Scholar
35. Sukegawa, N. 1971 Study on meandering of streams in straight channels. Tech. Rep. Bureau of Resources, Department of Science & Technology, Japan.Google Scholar
36. Tubino, M., Repetto, R. & Zolezzi, G. 1999 Free bars in rivers. J. Hydraul. Res. 32, 759–775.CrossRefGoogle Scholar
37. Wong, M. & Parker, G. 2006 Reanalysis and correction of bed-load relation of Meyer–Peter and Müller using their own database. J. Hydraul. Engng. ASCE 132, 1159–1168.CrossRefGoogle Scholar