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Sand ripples under sea waves Part 3. Brick-pattern ripple formation

Published online by Cambridge University Press:  26 April 2006

G. Vittori  and
P. Blondeaux
G. Vittori
Affiliation:
Hydraulic Institute, University of Genoa, Via Montallegro, 1, 16145 Genoa, Italy
P. Blondeaux
Affiliation:
Hydraulic Institute, University of Genoa, Via Montallegro, 1, 16145 Genoa, Italy
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Abstract

An oscillatory flow over a cohesionless bottom can produce regular three-dimensional bedforms known as brick-pattern ripples characterized by crests perpendicular to the direction of fluid oscillations joined by equally spaced bridges shifted by half a wavelength between adjacent sequences (a photo of brick-pattern ripples is shown in Sleath 1984, p. 141). In the present paper brick-pattern ripple formation is explained on the basis of a weakly nonlinear stability analysis of a flat cohesionless bottom subject to an oscillatory flow in which three-dimensional perturbations are considered. It is shown that brick-pattern ripples are generated by the simultaneous growth of two-dimensional and three-dimensional perturbations which interact with each other, according to a mechanism similar to that described by Craik (1971) in a different context, forming a resonant triad. A comparison between the present theoretical finding and experimental data by Sleath & Ellis (1978), concerning the region of existence of brick-pattern ripples in the parameter space and their geometrical characteristics, supports the validity of the present approach.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 239 , June 1992 , pp. 23 - 45
Copyright
© 1992 Cambridge University Press

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References

Allen, J. R. L.: 1984 Developments in Sedimentology. Elsevier.
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.: 1990 Sand ripples under sea waves. Part 1. Ripple formation. J. Fluid Mech. 218, 1–17.Google Scholar
Blondeaux, P. & Seminara, G., 1985 A unified bar–bend theory of river meanders. J. Fluid Mech. 157, 449–470.Google Scholar
Blondeaux, P., Sleath, J. F. A. & Vittori, G. 1988 Experimental data on sand ripples in an oscillatory flow. Rep. 01/88. Hydraulic Institute, University of Genoa.
Colombini, M., Seminara, G. & Tubino, M., 1987 Finite-amplitude alternate bars. J. Fluid Mech. 181, 213–232.Google Scholar
Craik, A. D. D.: 1971 Non-linear resonant instability in boundary layers. J. Fluid Mech. 50, 393–413.Google Scholar
Craik, A. D. D.: 1985 Wave Interactions and Fluid Flows. Cambridge University Press.
Fredsøe, J.: 1974 On the developments of dunes on erodible channels. J. Fluid Mech. 64, 1–16.Google Scholar
Grass, J. A. & Ayoub, N. M., 1982 Bed load transport of fine sand by laminar and turbulent flow. In Proc. 18th Coastal Eng. Conf. (ed. B. L. Edge) pp. 1589–1599.
Hara, T. & Mei, C. C., 1990 Centrifugal instability of an oscillatory flow over periodic ripples. J. Fluid Mech. 217, 1–32.Google Scholar
Horikawa, K. & Watanabe, A., 1968 Laboratory study on oscillatory boundary layer flow. Coastal Eng. Japan 11, 13–28.Google Scholar
Parker, G.: 1976 On the cause and characteristic scales of meandering and braiding in rivers. J. Fluid Mech. 76, 457–480.Google Scholar
Richards, K. J.: 1980 The formation of ripples and dunes on an erodible bed. J. Fluid Mech. 99, 597–618.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
Sleath, J. F. A.: 1984 Sea Bed Mechanics. Wiley.
Sleath, J. F. A. & Ellis, A. C. 1978 Ripple geometry in oscillatory flow. CUED/A – Hydraulics/TR 2, University of Cambridge, Engineering Department.
Smith, F. T. & Stewart, P. A., 1987 The resonant-triad nonlinear interaction in boundary-layer transition. J. Fluid Mech. 179, 227–252.Google Scholar
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
Sumer, M. & Bakioglu, M., 1984 On the formation of ripples on an erodible bed. J. Fluid Mech. 144, 177–190.Google Scholar
Vittori, G.: 1992 Flow field induced by sea waves over brick-pattern ripples. J. Hydraul. Engng ASCE (to appear).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
Weiland, J. & Wilhelmsson, H., 1977 Coherent Nonlinear Interaction of Waves in Plasmas. Pergamon.