The instability of sand ripples under partially standing surface waves

Physics of Fluids

Volumn 9, Issue 6, 1997, Pages 1606-1620

  Mei, Chiang C ^a   Yu, Jie ^a  

^a Massachusetts Institute of Technology Cambridge   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

INSTABILITY; RIPPLES; WAVES;

EID: 0030859478     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.869281     Document Type: Article

References (41)

1. R. A. Bagnold, "Motion of waves in shallow water: Interaction of waves and sand bottom," Proc. R. Soc. London Ser. A 187, 1 (1946).
2. T. G. Carter, L-F. P. Liu, and C. C. Mei, "Mass transport by waves and offshore sand bedforms," J. Waterways, Harbors, Coastal Eng. Div. ASCE X 165, (1973).
3. A. Kaneko and H. Honji, "Double structures of steady streaming in the oscillatory viscous flow over a wavy wall," J. Fluid Mech. 93, 727 (1979).
4. J. F. A. Sleath and A. C. Ellis, "Ripple geometry in oscillatory flow," University of Cambridge, Department of Engineering Report No. A/Hydraul/TR2, 1978.
5. J. F. A. Sleath, Seabed Mechanics (Wiley, New York, 1984).
6. M. S. Longuet-Higgins, "Oscillatory flow over steep ripples," J. Fluid Mech. 107, 1 (1981).
7. W. H. Lyne, "Unsteady viscous flow over a wavy wall," J. Fluid Mech. 50, 33 (1971).
8. J. F. A. Sleath, "Mass transport over a rough bed," J. Marine Res. 32, 13 (1974).
9. G. Vittori, "Nonlinear viscous oscillatory flow over a small amplitude wavy wall," J. Hydraul. Res. 27, 267 (1989).
10. J. T. Stuart, "Unsteady boundary layers," in Laminar Boundary Layers (Oxford University Press, Oxford, 1963), pp. 349-409.
11. T. Hara and C. C. Mei, "Oscillating flows over periodic ripples," J. Fluid Mech. 211, 183 (1990).
12. J. F. A. Sleath, "A contribution to the study of vortex ripples," J. Hydraul. Res. 13, 315 (1975).
13. S. Sato, N. Mimura, and A. Watanabe, "Oscillatory boundary lalyer flow over ripple beds," Proceedings of the 19th Conference on Coastal Engineering, 1984, pp. 2293-2309.
14. T. K. Shum, "A numerical study of vortex dynamics over rigid ripples," Ph.D. thesis, MIT, Department of Civil Engineering, Cambridge, MA. 1988.
15. P. Blondeaux and G. Vittori, "Vorticity dynamics in an oscillatory flow over a rippled bed," J. Fluid Mech. 226, 257 (1991).
16. P. Blondeaux and G. Vittori, "A route to chaos in an oscillatory flow: Feigenbaum scenario," Phys. Fluids A 3, 2492 (1991b).
17. N. Matsunaga and H. Honji, "Formation mechanism of brick-pattern ripples," Rep. Res. Inst. Appl. Mech. Kyushu Univ. 28, 27 (1980).
18. T. Hara and C. C. Mei, "Centrifugal instability of an oscillatory flow over periodic ripples," J. Fluid Mech. 227, 1 (1990).
19. P. Blondeaux. "Sand ripples under sea waves part 1. Ripple formation," J. Fluid Mech. 218, 1 (1990).
20. G. Vittori and P. Blondeaux. "Sand ripples under sea waves. Part 2: Finite-amplitude development," J. Fluid Mech. 248, 19 (1990).
21. G. Vittori and P. Blondeaux, "Mass transport under sea waves propagating over a rippled bed," J. Fluid Mech. 314, 247 (1996).
22. P. Blondeaux, E. Foti, and G. Vittori, "Sand ripples under sea waves part 4. Wave-current ripples." to appear in J. Fluid Mech.
23. G. Vittori and P. Blondeaux, "Sand ripples under sea waves. Part 3: Brick-pattern ripples formation," J. Fluid Mech. 239, 23 (1992).
24. J. N. Hunt and B. Johns, "Current induced by tides and gravity waves," Tellus 15, 343 (1963).
25. C. C. Mei, The Applied Dynamics of Ocean Surface Waves (World Scientific, Singapore, 1989).
26. A. J. Grass and R. N. M. Ayoub, "Bed load transport of fine sand by laminar and turbulent flow," in Proceedings of the 18th Coastal Engineering Conference, edited by B. L. Edge, 1982, pp. 1589-1599.
27. J. F. A. Skath, "Measurements of bed load in oscillatory flow," J. Waterway Port Coastal Ocean Eng. Div. ASCE, 104, 291 (1978).
28. G. Kalkanis, "Transportation of bed material due to wave action," U.S. Army Corps of Engineers, CERC, Tech. Memo No. 2, 1964, pp. 38.
29. M. M. Abou-Seida, "Bed load function due to wave action," University of California, Berkeley, Hydraulic Engineering Laboratory, Report No. HEL-2-11, 1965, pp. 78.
30. H. A. Einstein, "A basic description of sediment transport on beaches," in Waves on Beaches and Resulting Sediment Transport, edited by R. E. Meyer (Academic Press, New York, 1972), pp. 53-93.
31. J. Fredsøe, "On the development of dunes on erodible channels," J. Fluid Mech. 64, 1 (1974).
32. J. B. Herbich, H. D. Murphy, and B. Van Weele, "Scour of flat sand beaches due to wave action in front of sea walls," Coastal Engineering, Santa Barbara Specialty Conference, ASCE. 1967, pp. 705-727.
33. M. Manohar, "Mechanics of bottom sediment movement due to wave action," U.S. Army Beach Erosion Board Technical Memo, 1955, p. 75.
34. J. F. A. Sleath, "On rolling-grain ripples," J. Hydraul. Res. 14, 69 (1976).
35. P. Blondeaux, J. F. A. Sleath, and G. Vittori, "Experimental data on sand ripples in an oscillatory flow," Report No. 01/88, Institute Hydraulics, University of Genova, 1988.
36. J. F. Kennedy and M. Falcon, "Wave-generated sediment ripples," MIT Hydrodynamics Lab Report, 1965, p. 86.
37. K. Horikawa and A. Watanabe, "A study on sand movement due to wave action," Coastal Eng. Jpn. 10, 39 (1967).
38. A. D. Heathershaw, "Seabed-wave resonance and sand bar growth," Nature 296, 343 (1982).
39. A. G. Davies and A. D. Heathershaw, "Surface wave propagation over sinusoidally varying topography," J. Fluid Mech. 144, 419 (1984).
40. C. C. Mei, "Resonance reflection of surface water waves by periodic sandbars," J. Fluid Mech. 152, 315 (1985).
41. C. C. Mei and C. M. Chian, "Dispersion of small suspended particles in a wave boundary layer," J. Phys. Oceanogr. 24, 2479 (1994).