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Sand ripples under sea waves Part 1. Ripple formation

Published online by Cambridge University Press:  26 April 2006

P. Blondeaux
P. Blondeaux
Affiliation:
Istituto di Idraulica. Università di Genova, Via Montallegro, 1, 16145 Genova, Italy
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Abstract

In the present paper we formulate a predictive theory of the formation of sand ripples under sea waves. The theory is based on a linear stability analysis of a flat sandy bottom subject to a viscous oscillatory flow. The conditions for decay or amplification of a bottom perturbation are determined along with the wavelength of the most unstable component as a function of the Reynolds number of the flow and of the Froude and Reynolds numbers of the sediments. A comparison between theoretical findings and experimental data supports the validity of the present theory. An analytical solution for viscous oscillatory flow over a small-amplitude wavy bottom is determined for arbitrary values of the ratio r between the amplitude of fluid displacement and the wavelength of bottom waviness. Previous works by Lyne (1971) and Sleath (1976), who considered small or large values of r, are thus extended.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 218 , September 1990 , pp. 1 - 17
Copyright
© 1990 Cambridge University Press

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References

Bagnold, R. A.: 1946 Motion of waves in shallow water. Interaction of waves and sand bottoms. Proc. R. Soc. Lond. A 187, 1–15.Google Scholar
Blondeaux, P.: 1987 Turbulent boundary layer at the bottom of gravity waves. J. Hydraul. Res. 25, 447–464.Google Scholar
Blondeaux, P. & Seminara, G., 1979 Transizione incipiente al fondo di un'onda di gravità. Rendiconti Accad. Naz. Lincei 67, 407–417.Google Scholar
Blondeaux, P., Sleath, J. F. A. & Vittori, G. 1988 Experimental data on sand ripples in an oscillatory flow. Rep. 01/88. Inst. Hydraulics, University of Genoa.
Engelund, F.: 1974 Flow and bed topography in channel bends. J. Hydraul. Div. ASCE 100 (HY11), 1631–1648.Google Scholar
Fredsøe, J.: 1974 On the development of dunes on erodible channels. J. Fluid Mech. 64, 1–16.Google Scholar
Grass, J. A. & Ayoub, N. M., 1982 Bed load transport of time sand by laminar and turbulent flow. In Proc. 18th Coastal Engineering Conference (ed. B. L. Edge), pp. 1589–1599.
Horikawa, K. & Watanabe, A., 1967 A study of sand movement due to wave action. Coastal Engng Japan 10, 39–57.Google Scholar
Hino, M., Sawamoto, M. & Takasu, S., 1976 Experiments on transition to turbulence in an oscillatory pipe flow. J. Fluid Mech. 75, 193–207.Google Scholar
Kaneko, A.: 1981 Oscillation sand ripples in viscous fluids. Proc. Japan. Soc. Civil Engrs 307, 113–124.Google Scholar
Kaneko, A. & Honji, H., 1979 Double structures of steady streaming in the oscillatory viscous flow over a wavy wall. J. Fluid Mech. 93, 727–736.Google Scholar
Kennedy, J. F. & Falcon, M., 1965 Wave-generated sediment ripples. MIT Hydrodyn. Lab. Rep. 86.Google Scholar
Li, H.: 1954 Stability of oscillatory laminar flow along a wall. US Army, Beach Erosion Board, Tech. Memo 47.Google Scholar
Lofquist, K. E. B.: 1978 Sand ripples growth in an oscillatory-flow water tunnel. US Army Corps of Engng Coastal Engng Res. Center Tech. Paper 78–5.Google Scholar
Lyne, W. H.: 1971 Unsteady viscous flow over wavy wall. J. Fluid Mech. 50, 33–48.Google Scholar
Manohar, M.: 1955 Mechanics of bottom sediment movement due to wave action. US Army, Beach Erosion Board Tech. Memo 75.Google Scholar
Merkly, P. & Thomann, H., 1975 Transition to turbulence in oscillatory pipe flow. J. Fluid Mech. 68, 567–575.Google Scholar
Seminara, G. & Hall, P., 1976 The centrifugal instability of a Stokes layer theory. Proc. R. Soc. Lond. A 350, 299–316.Google Scholar
Sergeev, S. I.: 1966 Fluid oscillations in pipes at moderate Reynolds number. Fluid Dyn. 1, 21–22.Google Scholar
Sleath, J. F. A.: 1976 On rolling-grain ripples. J. Hydraul. Res. 14, 69–81.Google Scholar
Sleath, J. F. A.: 1978 Measurements of bed load in oscillatory flow. J. Waterway Port Coastal Ocean Engng Div., ASCE 104 (WW3), 291–307.Google Scholar
Sleath, J. F. A.: 1984 Sea Bed Mechanics. Wiley.
Stokes, A. G.: 1851 On the effect of the internal friction of fluids on the motion of pendulums. Trans. Camb. Phil. Soc. 9, 20–21.Google Scholar
Tromans, P.: 1976 The stability of oscillating pipe flow. Abstract of lecture given at Euromech 73: Oscillatory Flows in Ducts, Aix-en-Provence, April 13–15.
Uda, T. & Hino, M., 1975 A solution of oscillatory viscous flow over a wavy wall. Proc. Japan. Soc. Civil Engrs 237, 27–36.Google Scholar
Vittori, G.: 1988 Non-linear viscous oscillatory flow over a small amplitude wavy wall. J. Hydraul. Res. 27, 267–280.Google Scholar
Vittori, G. & Blondeaux, P., 1990 Sand ripples under sea waves. Part 2. Finite-amplitude development. J. Fluid Mech. 218, 19–39.Google Scholar
Yalin, M. S. & Russel, R. C. H. 1962 Similarity in sediment transport due to waves. Proc. 8th Conf. Coastal Engng Mexico (ed. J. W. Johnson), pp. 151–167.