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Sand ripples under sea waves Part 2. Finite-amplitude development

Published online by Cambridge University Press:  26 April 2006

G. Vittori  and
P. Blondeaux
G. Vittori
Affiliation:
Istituto di Idraulica. Università di Genova, Via Montallagero, 1. 16145 Genova, Italy
P. Blondeaux
Affiliation:
Istituto di Idraulica. Università di Genova, Via Montallagero, 1. 16145 Genova, Italy
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Abstract

In the present paper we formulate a theory to predict the time development of sand ripples characterized by small but finite amplitude under the action of surface gravity waves. The theory is based on a weakly nonlinear stability analysis of a flat sandy bottom subject to viscous oscillatory flow. The parameters of the problem (namely the Reynolds number of the flow and the Reynolds and Froude numbers of sediments) are assumed to fall within a neighbourhood of the critical conditions determined in Blondeaux (1990). The analysis can predict the actual ripple height, wavelength and profile when flow separation is absent, i.e. for the case of rolling-grain ripples. Assuming Sleath's (1984) criterion for separation, the values of the relevant parameters at which transition from rolling-grain ripples to vortex ripples occurs are predicted. A comparison between theoretical findings and experimental data supports the validity of the present theory.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 218 , September 1990 , pp. 19 - 39
Copyright
© 1990 Cambridge University Press

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References

Blondeaux, P.: 1987 Turbulent boundary layer of the bottom of gravity waves. J. Hydraul. Res. 25, 447–464.Google Scholar
Blondeaux, P.: 1990 Sand ripples under sea waves. Part 1. Ripple formation. J. Fluid Mech. 218, 1–17, (referred to herein as I).Google Scholar
Blondeaux, P. & Colombini, M., 1988 Two-dimensional vortical structures in transitional unsteady boundary layers. Euromech 235, Patras, May-June.Google Scholar
Blondeaux, P. & Seminara, G., 1979 Transizione incipiente al fondo di un'onda di gravita. Rendiconte 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.
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
Horikawa, K. & Watanabe, A., 1968 Laboratory study on oscillatory boundary layer flow. Coastal Engng Japan 11, 13–28.Google Scholar
Jonsson, I. G.: 1963 Measurements in the turbulent wave boundary layer. Proc. 10th Congr. Intl Assoc. Hydraul. Res., London, vol. 1, pp. 85–92.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
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.
Stuart, J. T.: 1971 Non linear stability theory. Ann. Rev. Fluid Mech. 3, 347–370.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.
Vittori, G.: 1989 Non-linear viscous oscillatory flow over a small amplitude wavy wall. J. Hydraul. Res. 27, 267–280.Google Scholar
Vittori, G.: 1990 Formation and non-linear development of ripples at the bottom of gravity waves. Ph.D thesis, Genoa University (in Italian).