Lagrangian drift near a wavy boundary in a viscous oscillating flow

Journal of Fluid Mechanics

Volumn 630, Issue , 2009, Pages 391-411

  Larrieu, E ^a   Hinch, E J ^b   Charru, Francois ^a  

^a IMFT   (France)

^b UNIVERSITY OF CAMBRIDGE   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

LAGRANGE MULTIPLIERS;

ARTIFICIAL RIPPLES; COUETTE FLOWS; LAGRANGIAN; MEAN FLOW; SAND RIPPLE; SELF-FORMED; STEADY STREAMING;

OSCILLATING FLOW;

BOUNDARY CONDITION; COUETTE FLOW; DRIFT BEHAVIOR; EXPERIMENTAL STUDY; FORMATION MECHANISM; LAGRANGIAN ANALYSIS; OSCILLATING FLOW; QUANTITATIVE ANALYSIS; RIPPLE; STEADY FLOW; VISCOUS FLOW;

EID: 67651102782     PISSN: 00221120     EISSN: 14697645     Source Type: Journal    
DOI: 10.1017/S002211200900682X     Document Type: Article

References (40)

1. BAGNOLD, R. 1946 Motion of waves in shallow water. interaction between waves and sand bottoms. Proc. R. Soc. Lond. A 187, 1-18.
2. BATCHELOR, G. K. 1967 An introduction to fluid dynamics. Cambridge University Press.
3. BENJAMIN, T. B. 1959 Shearing flow over a wavy boundary. J. Fluid Mech. 6, 161-205.
4. BLONDEAUX, P. 1990 Sand ripples under sea waves. Part 1. Ripple formation. J. Fluid Mech. 218, 1-17.
5. CHARRU, F. 2006 Selection of the ripple length on a granular bed sheared by a liquid flow. Phys. Fluids 18, 121508.
6. CHARRU, F. & HINCH, E. J. 2006a Ripple formation on a particle bed sheared by a viscous liquid. Part 1. Steady flow. J. Fluid Mech. 550, 111-121.
7. CHARRU, F. & HINCH, E. J. 2006b Ripple formation on a particle bed sheared by a viscous liquid. Part 2. Oscillating flow. J. Fluid Mech. 550, 123-137.
8. CHARRU, F., LARRIEU, E., DUPONT, J.-B. & ZENIT, R. 2007 Motion of a particle near a rough wall in a viscous shear flow. J. Fluid Mech. 570, 431-453.
9. CHARRU, F. & MOUILLERON-ARNOULD, H. 2002 Instability of a bed of particles sheared by a viscous flow. J. Fluid Mech. 452, 303-323.
10. CHARRU, F. & MOUILLERON-ARNOULD, H. & Eiff, O. 2004 Erosion and deposition of particles on a bed sheared by a viscous flow. J. Fluid Mech. 519, 55-80.
11. CRAIK, A. D. D. 1982 The drift velocity of water waves. J. Fluid Mech. 116, 187-205.
12. DU TOIT, S. G., & SLEATH, J. F. A. 1981 Velocity measurements close to rippled beds in oscillatory flow. J. Fluid Mech. 112 71-96.
13. HARA, T. & MEI, C. C. 1990 Oscillating flows over periodic ripples. J. Fluid Mech. 211, 183-209.
14. HARA, T. & MEI, C. C. & SHUM, K. T. 1992 Oscillating flows over periodic ripples of finite slope. Phys. Fluids A 4, 1373-1384.
15. KANEKO, A. & HONJI, H. 1979 Double structures of steady streaming in the oscillatory viscous flow over a wavy wall. J. Fluid Mech. 93 (4), 727-736.
16. LIGHTHILL, J. 1978 Acoustic streaming. J. Sound Vib. 61 391-418.
17. LONGUET-HIGGINS, M. S. 1953 Mass transport in water waves. Phil. Trans. R. Soc. Lond. A 245, 535-581.
18. LONGUET-HIGGINS, M. S. 1981 Oscillating flow over steep sand ripples. J. Fluid Mech. 107, 1-35.
19. LYNE, W. H. 1971 Unsteady viscous flow over a wavy wall. J. Fluid Mech. 50, 33-48.
20. MARIN, F. 2004 Eddy viscosity and Eulerian drift over rippled beds in waves. Coastal Engng 50, 139-159.
21. MEI, C. C. & YU, J. 1997 The instability of sand ripples under partially standing surface waves. Phys. Fluids 9, 1609-1620.
22. OURMI_GRERES, Y. & CHAPLIN, J. R. 2004 Visualizations of the disturbed-laminar wave-induced flow above a rippled bed. Exp. Fluids 36, 908-918.
23. OURMI_GRERES, Y. & MOUAZ_ACE, D. 2007 Wave-induced boundary layer flows over a flat and rippled bed. J. Hydraul. Res. 45, 239-253.
24. RAYLEIGH, L. 1883 On the circulation of air observed in Kundt's tubes and some allied acoustical problems. Phil. Trans. R. Soc. Lond. A 175, 1-21.
25. RILEY, N. 1965 Oscillating viscous flows. Mathematika 12 161-175.
26. RILEY, N. 2001 Steady streaming. Annu. Rev. Fluid Mech. 33, 43-65.
27. ROUSSEAUX, G., YOSHIKAWA, H., STEGNER, A. & WESFREID, J. E. 2004 Dynamics of transient eddy above rolling-grain ripples. Phys. Fluids 16, 1049-1058.
28. SCANDURA, P. 2007 Steady streaming in a turbulent oscillating boundary layer. J. Fluid Mech. 571, 265-280.
29. SCHAFLINGER, U., ACRIVOS, A. & STIBI, H. 1995 An experimental study of viscous resuspension in a pressure-driven plane channel flow. Intl J. Multiphase Flow 21, 693-704.
30. SCHLICHTING, H. 1932 Berechnung ebener periodischer Grenzschichtstrmungen Phys. Z. 33, 327-335.
31. SHUM, K. T. 1995 A numerical study of the wave-induced solute transport above a rippled bed. J. Fluid Mech. 299, 267-288.
32. SLEATH, J. F. A. 1974 Mass transport over a rough bed. J. Mar. Sci. 32, 13-24.
33. SLEATH, J. F. A. 1976 On rolling-grain ripples. J. Hydraul. Res. 14, 69-81.
34. STOKES, G. G. 1847 On the theory of oscillatory waves. Camb. Trans. 8, 441-473.
35. STUART, J. T. 1963 Unsteady boundary layers. In Laminary Boundary Layers (ed. L. Rosenhead), pp. 349-408. Oxford University Press.
36. UNLUATA, U. & MEI, C. C. 1970 Mass transport in water waves J. Geophys. Res. 75, 7611-7618.
37. VITTORI, G. 1989 Non-linear viscous oscillatory flow over a wavy wall. J. Hydraul. Res. 27, 267-280.
38. VITTORI, G. & BLONDEAUX, P. 1990 Sand ripples under sea waves. Part 2. Finite-amplitude development. J. Fluid Mech. 218, 19-39.
39. WALLNER, J. & SCHAFLINGER, U. 1998 Viscous resuspension of a sediment caused by oscillating stratified flows. Acta Mech. 127 147-153.
40. ZOUESHTIAGH, F., THOMAS, P. J., THOMY, V. & MERLEN, A. 2008 Micrometric granular ripple patterns in a capillary tube. Phys. Rev. Lett. 100, 054501.