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Finite-amplitude river dunes

Published online by Cambridge University Press:  25 September 2008

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
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Abstract

The linear and weakly nonlinear stability of a uniform flow in an infinitely wide open channel with erodible bottom is studied. Under suitable conditions the flow is found to be unstable, leading to the formation of dunes and antidunes. At a linear level, the corresponding regions of existence are presented and compared with experimental data. A weakly nonlinear analysis is then performed in a neighbourhood of the critical conditions for dune and antidune formation. The analysis shows that, for values of the ratio of the shear velocity to the depth-averaged velocity of practical interest, dune bifurcation is supercritical, whereas antidune bifurcation is subcritical. The latter result suggests a possible interpretation of the plane–antidune transition, where plane bed and antidune configurations are observed to coexist for the same values of the flow and the sediment parameters. The supercritical behaviour of the dune bifurcation allows for the prediction of an equilibrium amplitude that successfully compares with the amplitudes measured in laboratory experiments.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 611 , 25 September 2008 , pp. 283 - 306
Copyright
Copyright © Cambridge University Press 2008

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References

REFERENCES

Allen, J. R. L. 1968 Current Ripples: Their Relation to Patterns of Water and Sediment Motion. North-Holland.Google Scholar
ASCE, Task Committee 1963 Friction factors in open channels. J. Hydraul. Div. 89 (HY2), 97–143.CrossRefGoogle Scholar
ASCE, Task Committee 2002 Flow and transport over dunes. J. Hydraul. Engng. ASCE 127, 726–728.Google Scholar
Besio, G., Blondeaux, P. & Vittori, G. 2006 On the formation of sand waves and sand banks. J. Fluid Mech. 557, 1–27.CrossRefGoogle Scholar
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
Best, J. & Kostaschuk, R. 2002 An experimental study of turbulent flow over a low-angle dune. J. Geophys. Res. Earth Surface 107 (C9), 3135–3153.CrossRefGoogle Scholar
Blondeaux, P. 1990 Sand ripples under sea waves. Part 1. Ripple formation. J. Fluid Mech. 218, 1–17.CrossRefGoogle Scholar
Blondeaux, P. & Seminara, G. 1985 A unified bar-bend theory of river meanders. J. Fluid Mech. 157, 449–470.CrossRefGoogle Scholar
Callander, R. A. 1969 Instability and river channels. J. Fluid Mech. 36, 465–480.CrossRefGoogle Scholar
Carling, P. A. & Shvidchenko, A. B. 2002 A consideration of the dune:antidune transition in fine gravel. Sedimentology 49, 1269–1282.CrossRefGoogle Scholar
Carling, P. A., Gölz, E., Orr, H. G. & Radecki-Pawlik, A. 2000 The morphodynamics of fluvial sand dunes in the river Rhine, near Mainz, Germany. I. sedimentology and morphology. Sedimentology 47, 227–252.CrossRefGoogle Scholar
Carling, P. A., Richardson, K. & Ikeda, H. 2005 A flume experiment on the development of subacqueous fine-gravel dunes from a lower-stage plan bed. J. Geophys. Res. Earth Surface 110, F04S05.CrossRefGoogle Scholar
Coleman, S. E. & Fenton, J. D. 2000 Potential-flow instability theory and alluvial stream bed forms. J. Fluid Mech. 418, 101–117.CrossRefGoogle Scholar
Coleman, S. E. & Melville, B. W. 1996 Initiation of bed forms on a flat sand bed. J. Hydraul. Engng ASCE 122, 301–310.CrossRefGoogle Scholar
Coleman, S. E., Nikora, V. I., McLean, S. R., Clunie, T. M., Schlicke, T. & Melville, B. W. 2006 Equilibrium hydrodynamics concept for developing dunes. Phys. Fluids 18, 12.CrossRefGoogle Scholar
Colombini, M. 2004 Revisiting the linear theory of sand dune formation. J. Fluid Mech. 502, 1–16.CrossRefGoogle Scholar
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
Colombini, M., Seminara, G. & Tubino, M. 1987 Finite-amplitude alternate bars. J. Fluid Mech. 181, 213–232.CrossRefGoogle Scholar
Engelund, F. 1970 Instability of erodible beds. J. Fluid Mech. 42, 225–244.CrossRefGoogle Scholar
Engelund, F. & Fredsøe, J. 1974 Transition from dunes to plane bed in alluvial channels. Series paper 4. Tech. Univ. Denmark, Inst. Hydrodyn. and Hydraulic Engng.Google Scholar
Engelund, F. & Hansen, E. 1967 A Monograph on Sediment Transport in Alluvial Streams. Teknisk Forlag, Copenhagen, Denmark.Google Scholar
Federici, B. & Seminara, G. 2003 On the convective nature of bar instability. J. Fluid Mech. 487, 125–145.CrossRefGoogle Scholar
Fredsøe, J. 1974 On the development of dunes in erodible channels. J. Fluid Mech. 64, 1–16.CrossRefGoogle Scholar
Giri, S. & Shimizu, Y. 2006 Numerical computation of sand dune migration with free surface flow. Water Resour. Res. 42, W10422.CrossRefGoogle Scholar
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 Geol. Survey.CrossRefGoogle Scholar
Ikeda, S., Parker, G. & Saway, K. 1981 Bend theory of river meanders. Part 1. Linear development. J. Fluid Mech. 112, 363–377.CrossRefGoogle Scholar
Ji, Z.-G. & Mendoza, C. 1997 Weakly nonlinear stability analysis for dune formation. J. Hydraul. Engng ASCE 123, 979–985.CrossRefGoogle Scholar
Kennedy, J. F. 1963 The mechanism of dunes and antidunes in erodible-bed channels. J. Fluid Mech. 16, 521–544.CrossRefGoogle Scholar
Lee, H.-Y. & Hsu, I.-S. 1994 Investigation of saltating particle motion. J. Hydraul. Engng ASCE 120, 831–845.CrossRefGoogle Scholar
Meyer-Peter, E. & Müller, R. 1948 Formulas for bed-load transport. In Proc. 2nd Meeting IAHR, pp. 39–64. Stockholm, Sweden.Google Scholar
Parker, G. 1975 Sediment inertia as cause of river antidunes. J. Hydraul. Div. 101, 536–558.Google Scholar
Reynolds, A. J. 1965 Waves on an erodible bed. J. Fluid Mech. 22, 113–133.CrossRefGoogle Scholar
Richards, K. J. 1980 The formation of ripples and dunes on an erodible bed. J. Fluid Mech. 99, 597–618.CrossRefGoogle Scholar
Rouse, H. 1946 Elementary Mechanics of Fluids. Wiley.Google Scholar
Schielen, R., Doelman, A. & de Swart, H. E. 1993 On the nonlinear dynamics of free bars in straight channels. J. Fluid Mech. 252, 325–356.CrossRefGoogle Scholar
Sekine, M. & Kikkawa, H. 1992 Mechanics of saltating grains. J. Hydraul. Engng ASCE 118, 536–558.CrossRefGoogle Scholar
Smith, J. D. 1970 Stability of a sand bed subjected to a shear flow at low Froude number. J. Geophys. Res. 75, 5928–5940.CrossRefGoogle Scholar
Stuart, J. T. 1971 Nonlinear stability theory. Annu. Rev. Fluid Mech. 3, 347–370.CrossRefGoogle Scholar
Sumer, B. M. & Bakioglu, M. 1984 On the formation of ripples on an erodible bed. J. Fluid Mech. 144, 177–190.CrossRefGoogle Scholar
Tjerry, S. & Fredsøe, J. 2005 Calculation of dune morphology. J. Geophys. Res. Earth Surface 110, F04013.CrossRefGoogle Scholar
Van Rijn, L. C. 1984 a Sediment transport, Part ii: Suspended load transport. J. Hydraul. Engng ASCE 110, 1613–1641.CrossRefGoogle Scholar
Van Rijn, L. C. 1984 b Sediment transport, Part iii: Bed forms and alluvial roughness. J. Hydraul. Engng ASCE 110, 1733–1754.CrossRefGoogle Scholar
Vanoni, V. A. & Brooks, N. H. 1957 Laboratory studies of the roughness and suspended load of alluvial streams. Tech. Rep. California Institute of Technology, Pasadena, California.Google Scholar
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
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