Hostname: page-component-8448b6f56d-c47g7 Total loading time: 0 Render date: 2024-04-24T10:07:56.816Z Has data issue: false hasContentIssue false
  • English
  • Français

The formation of ripples and dunes on an erodible bed

Published online by Cambridge University Press:  19 April 2006

Kelvin J. Richards
Kelvin J. Richards
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW
Get access Rights & Permissions [Opens in a new window]

Abstract

A two-dimensional stability analysis is presented of flow of low Froude number over an erodible bed. Particular regard is given to the modelling of the turbulent flow close to the bed. In contrast to previous theories that use a constant eddy-viscosity approach the present theory predicts the occurrence of two separate modes of instability, with wavelengths related to the roughness of the bed and the depth of the flow. It is postulated that these two modes correspond to the formation of ripples and dunes respectively. The results are strongly dependent on the two parameters z0, the roughness length of the bed, and β, the effect of the local bed slope on the bed-load transport. Using physically plausible estimates for these parameters the results of the analysis are in good agreement with observations for both ripples and dunes.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 99 , Issue 3 , 14 August 1980 , pp. 597 - 618
Copyright
© 1980 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Allen, J. R. L. 1970 Physical Processes of Sedimentation. Elsevier.
Bagnold, R. A. 1954 Proc. Roy. Soc. A 225, 49.
Bagnold, R. A. 1956 Phil. Trans. Roy. Soc. A 249, 235.
Benjamin, T. B. 1959 J. Fluid Mech. 6, 161.
Bradshaw, P., Ferris, P. H. & Atwell, N. P. 1967 J. Fluid Mech. 28, 593.
Engelund, F. 1970 J. Fluid Mech. 42, 225.
Engelund, F. & Fredsoe, J. 1974 Tech. Univ. Denmark, Inst. Hydrodyn. and Hydraulic Engng, Series Paper 4.
Exner, F. M. 1925 Sitzber. Akad. Wiss. (Wien) 3–4, 165.
Fredsoe, J. 1974 J. Fluid Mech. 64, 1.
Fredsoe, J. & Engelund, F. 1975 Tech. Univ. Denmark, Inst. Hydrodyn. and Hydraulic Engng, Series Paper 8.
Jackson, R. G. 1976 J. Fluid Mech. 77, 531.
Kamphuis, J. W. 1974 J. Hydraulic Res. 12, 193.
Keller, H. B. 1968 Numerical Methods for Two-point Boundary Values Problems. Waltham, Mass.: Blaisdell.
Kennedy, J. F. 1963 J. Fluid Mech. 16, 521.
Langhorne, D. N. 1973 Marine Geol. 14, 129.
Liu, H. K. 1957 Proc. A.S.C.E. 83 (HY2), 1197.
Lysne, D. K. 1969 Proc. A.S.C.E. 95 (HY6), 1835.
Meyer-Peter & Müller, R. 1948 Inter. Ass. Hydr. Res., 2nd Meeting, Stockholm.
Miles, J. W. 1957 J. Fluid Mech. 3, 185.
Moss, A. J. 1972 Sedimentology 18, 159.
Nikuradse, J. 1933 V.D.I. - Forschungsheft no. 361.
Owen, P. R. 1964 J. Fluid Mech. 20, 225.
Raudkivi, A. J. 1966 J. Fluid Mech. 26, 507.
Reynolds, A. J. 1976 Nordic Hydrology 7, 161.
Richards, K. J. 1978 Ph.D. thesis, University of Southampton.
Rodi, W. 1978 Univ. Karlsruhe Rep. SFB 80/T/127.
Smith, J. D. 1970 J. Geophys. Res. 75, 5928.
Smith, J. D. & McLean, S. R. 1977 J. Geophys. Res. 82, 1735.
Taylor, P. A. 1977 Boundary-Layer Met. 11, 439.
Taylor, P. A., Richards, K. J. & Nunes, R. A. 1978 In Turbulent Fluxes Through the Sea Surface, Wave Dynamics, and Prediction (ed. A. Favre & K. Hasselman). Plenum.
Townsend, A. A. 1972 J. Fluid Mech. 55, 719.
Williams, P. B. & Kemp, P. H. 1971 Proc. A.S.C.E. 97 (HY4), 505.
Yalin, M. S. 1964 Proc. A.S.C.E. 90 (HY5), 105.