Hostname: page-component-7c8c6479df-hgkh8 Total loading time: 0 Render date: 2024-03-28T22:30:44.368Z Has data issue: false hasContentIssue false

Steady streaming and sediment transport at the bottom of sea waves

Published online by Cambridge University Press:  16 March 2012

Paolo Blondeaux*
Affiliation:
Department of Civil, Environmental and Architectural Engineering, University of Genoa, via Montallegro 1, 16145 Genova, Italy
Giovanna Vittori
Affiliation:
Department of Civil, Environmental and Architectural Engineering, University of Genoa, via Montallegro 1, 16145 Genova, Italy
Antonello Bruschi
Affiliation:
Istituto Superiore per la Ricerca e la Protezione Ambientale - ISPRA, via Curtatone 3, 00185 Rome, Italy
Francesco Lalli
Affiliation:
Istituto Superiore per la Ricerca e la Protezione Ambientale - ISPRA, via Curtatone 3, 00185 Rome, Italy
Valeria Pesarino
Affiliation:
Istituto Superiore per la Ricerca e la Protezione Ambientale - ISPRA, via Curtatone 3, 00185 Rome, Italy
*
Email address for correspondence: blx@dicat.unige.it

Abstract

The flow and sediment transport in the boundary layer at the sea bottom due to the passage of surface waves are determined by considering small values of the wave steepness and of the ratio between the thickness of the boundary layer and the local water depth. Both the velocity field and the sediment transport rate are determined up to the second order of approximation thus evaluating both the steady streaming and the net (wave-averaged) flux of sediment induced by nonlinear effects. The flow regime is assumed to be turbulent and a two-equation turbulence model is used to close the problem. The bed load is evaluated by means of an empirical relationship as function of the bed shear stress. The suspended load is determined by computing the sediment flux, once the sediment concentration is determined by solving an appropriate advection–diffusion equation. The decay of the wave amplitude, which is due to the energy dissipation taking place in the boundary layer, is taken into account. The steady streaming and the sediment transport rate at the bottom of sea waves turn out to be different from those which are observed in a wave tunnel (U-tube), because of the dependence on the streamwise coordinate of the former flow. In particular, in the range of the parameters presently investigated, the sediment transport rate at the bottom of sea waves is found to be always onshore directed while, in a water tunnel (U-tube), the sediment transport rate can be onshore or offshore directed.

Type
Papers
Copyright
Copyright © Cambridge University Press 2012

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Amoudry, L., Hsu, T. J. & Liu, P. L. F. 2008 Two-phase model for sand transport in sheet flow regime. J. Geophys. Res. 113, C03011.Google Scholar
2. Blondeaux, P. 1987 Turbulent boundary layer at the bottom of gravity waves. J. Hydraul. Res. 25 (4), 447464.CrossRefGoogle Scholar
3. Blondeaux, P. & Colombini, M. 1985 Pulsitile turbulent pipe flow. In 5th International Symposium on Turbulent Shear Flows Ithaca (NY) (ed. J. L. Lumley, B. E. Launder, N. C. Reynolds & J. A. Whitelaw).Google Scholar
4. Blondeaux, P. & Vittori, G. 1991a Vorticity dynamics in an oscillatory flow over a rippled bed. J. Fluid Mech. 226, 257289.CrossRefGoogle Scholar
5. Blondeaux, P. & Vittori, G. 1991b A route to chaos in an oscillatory flow: Feigenbaum scenario. Phys. Fluids A 3, 24922495.CrossRefGoogle Scholar
6. Blondeaux, P. & Vittori, G. 1994 Wall imperfections as a triggering mechanism for Stokes-layer transition. J. Fluid Mech. 264, 107135.CrossRefGoogle Scholar
7. Blondeaux, P. & Vittori, G. 1999 Boundary layer and sediment dynamics under sea waves. Adv. Coast. Ocean Engng 4, 133190.CrossRefGoogle Scholar
8. Blondeaux, P., Vittori, G. & Foti, E. 2000 Migrating sea ripples. Eur. J. Mech. (B/Fluids) 19, 285301.CrossRefGoogle Scholar
9. Brebner, A., Askew, J. A. & Law, S. W. 1966 The effect of roughness of the mass transport of progressive gravity waves. In Proceedings of the 10th International Conference on Coastal Engineering, Tokyo (Japan), ASCE, 175–184.Google Scholar
10. Carstensen, S., Sumer, B. M. & Fredsoe, J. 2010 Coherent structures in wave boundary layers. Part 1. Oscillatory motion. J. Fluid Mech. 646, 169206.CrossRefGoogle Scholar
11. Cavallaro, L., Scandura, P. & Foti, E. 2011 Turbulence-induced steady streaming in an oscillatory boundary layer: on the reliability of turbulence closure models. Coastal Engineering 58, 290304.CrossRefGoogle Scholar
12. Chowdhury, S. A., Sato, M. & Ueno, A. 1997 Numerical model of the turbulent wave boundary layer induced by finite amplitude water waves. Appl. Ocean Res. 19, 201209.CrossRefGoogle Scholar
13. Collins, J. I. 1963 Inception of turbulence at the bed under periodic gravity waves. J. Geophys. Res. 68, 60076014.CrossRefGoogle Scholar
14. Costamagna, P., Vittori, G. & Blondeaux, P. 2003 Coherent structures in oscillatory boundary layers. J. Fluid Mech. 474, 133.CrossRefGoogle Scholar
15. Dong, P. & Zhang, K. 2002 Intense near-bed sediment motions in waves and currents. Coastal Engineering 45, 7587.CrossRefGoogle Scholar
16. Van Dore, B. D. 1982 On the second approximation to mass transport in the bottom boundary layer. Coastal Engineering 6, 93120.CrossRefGoogle Scholar
17. Foti, E. & Blondeaux, P. 1995 Sea ripple formation: the turbulent boundary layer case. Coastal Engineering 25 (3-4), 227236.CrossRefGoogle Scholar
18. Foti, E. & Scandura, P. 2004 A low Reynolds number k- model validated for flows over smooth and rough wall. Coastal Engineering 51, 173184.CrossRefGoogle Scholar
19. Fredsoe, J. & Deigaard, R. 1992 Mechanics of Coastal Sediment Transport. Advance Series on Ocean Engineering, vol. 3 , World Scientific.CrossRefGoogle Scholar
20. Garcia, M. H. & Parker, G. 1991 Entrainment of bed sediment into suspension. J. Hydraul. Engng 117 (4), 414435.CrossRefGoogle Scholar
21. Gonzalez-Rodriguez, D. & Madsen, O. S. 2011 Boundary layer hydrodynamics and bed load sediment transport in oscillating water tunnels. J. Fluid Mech. 667, 4884.CrossRefGoogle Scholar
22. Hassan, W. N. M. & Ribberink, J. S. 2005 Transport processes of uniform and mixed sands in oscillatory sheet flow. Coast. Engng 52, 745770.CrossRefGoogle Scholar
23. Hassan, W. N. M. & Ribberink, J. S. 2010 Modelling of sand transport under wave-generated sheet flows with a RANS diffusion model. Coastal Engineering 57 (1), 1929.CrossRefGoogle Scholar
24. Hayashi, T. & Ohashi, M. 1981 A dynamical and visual study on the oscillatory turbulent boundary layer. In 3rd International Symposium on Turbulent Shear Flows, Davis (CA), pp. 1833. Springer.Google Scholar
25. Hino, M., Kashiwayanagi, M., Nakayama, A. & Hara, T. 1983 Experiments on the turbulence statistics and the structure of a reciprocating oscillatory flow. J. Fluid Mech. 131, 363400.CrossRefGoogle Scholar
26. Hsu, T. J., Jenkins, J. T. & Liu, P. L. F. 2004 On two-phase sediment trasnport: sheet flow of massive particles. Proc. R. Soc. Lond. A 460, 22232250.CrossRefGoogle Scholar
27. Hsu, T. W. & Ou, S. H. 1994 On the mass transport of water waves. Ocean Engng 21 (2), 195206.CrossRefGoogle Scholar
28. Isaacson, M. de St. Q. 1976 The secons approximation to mass transport in cnoidal waves. J. Fluid Mech. 78, 445457.CrossRefGoogle Scholar
29. Jacobs, S. J. 1984 Mass transport in a turbulent boundary layer under a progressive water wave. J. Fluid Mech. 146, 303312.CrossRefGoogle Scholar
30. Jensen, B. L., Summer, B. M. & Fredsoe, J. 1989 Turbulent oscillatory boundary layers at high Reynolds numbers. J. Fluid Mech. 206, 265297.CrossRefGoogle Scholar
31. Jonsson, I. J. 1963 Measurements in the turbulent wave boundary layer. In Proceedings 10th IAHR Congress, London (UK), vol. 1, 85–92.Google Scholar
32. Jonsson, I. J. 1966 Wave boundary layers and friction factors. In Proceedings of the 10th International Conference Coastal Engineering, Tokyo (Japan), ASCE, 127–148.Google Scholar
33. Jonsson, I. J. & Carlsen, N. A. 1976 Experimental and theoretical investigations in an oscillatory rough turbulent boundary layer. J. Hydraul. Res. 14, 4560.CrossRefGoogle Scholar
34. Justesen, P. A. 1988 Prediction of turbulent oscillatory flow over rough beds. Coastal Engineering 12, 257284.CrossRefGoogle Scholar
35. Kajiura, K. 1968 A model of the bottom boundary layer in water waves. Bull. Earthq. Res. Inst. 46, 75123.Google Scholar
36. Longuet-Higgins, M. S. 1953 Mass transport in water waves. Phil. Trans. R. Soc. Lond. A 245, 535581.Google Scholar
37. Longuet-Higgins, M. S. 1958 The mechanism of the boundary layer near the bottom in a progressive wave. In Proceedings of the 6th International Conference on Coastal Engineering, Berkeley (CA), ASCE, 184–193.Google Scholar
38. Mazzuoli, M., Vittori, G. & Blondeaux, P. 2011 Turbulent spots in oscillatory boundary layers. J. Fluid Mech. 685, 365376.CrossRefGoogle Scholar
39. Mei, C. C. 1989 The Applied Dynamics of Ocean Surface Waves. Advanced Series on Ocean Engineering, vol. 1 , World Scientific.Google Scholar
40. Mellor, G. 2001 One dimensional, ocean surface layer modelling: a problem and a solution. J. Phys. Oceanogr. 31, 790809.2.0.CO;2>CrossRefGoogle Scholar
41. Mellor, G. L. 2002 Oscillatory bottom boundary layers. J. Phys. Oceanogr. 32, 30753088.2.0.CO;2>CrossRefGoogle Scholar
42. Mellor, G. L. & Yamada, T. 1982 Development of a turbulence closure model for geophysical fluid problems. Rev. Geophys. Space Phys. 20, 851875.CrossRefGoogle Scholar
43. Parker, G. 1978 Self-formed straight rivers with equilibrium banks and mobile beds. Part 1. The sand–silt river. J. Fluid Mech. 89, 109125.CrossRefGoogle Scholar
44. Quevedo, E., Blondeaux, P., Losada, M. & Vittori, G. 2008 Turbulent steady streming under sea waves. In Proceedings of the 31st International Conference on Coastal Engineering, Hannover (Germany). World Scientific.Google Scholar
45. Ribberink, J. S. & Al-Salem, A. A. 1994 Sediment transport in oscillatory boundary layers in cases of rippled beds and sheet flows. J. Geophys. Res. 99 (C6), 1270712727.CrossRefGoogle Scholar
46. Ribberink, J. S. & Al-Salem, A. A. 1995 Sheet flow and suspension of sand in oscillatory boundary layers. Coastal Engineering 25, 205225.CrossRefGoogle Scholar
47. Ribberink, J. S. & Chen, Z. 1993 Sediment transport of fine sand under asymmetric oscillatory flow. Rep. H840, part VII, Delft Hydraulics.Google Scholar
48. Russel, R. C. H & Osorio, J. D. C. 1958 An experimental investigation of drift profiles in a closed channel. In Proceedings of the 6th International Conference on Coastal Engineering, Berkeley (CA), ASCE, 184–193.Google Scholar
49. Saffman, P. G. 1970 A model for inhomogeneous turbulent flow. Proc. R. Soc. Lond. A 317, 417433.Google Scholar
50. Saffman, P. G. & Wilcox, P. C. 1974 Turbulence model predictions for turbulent boundary layers. AIAA J. 12, 541546.CrossRefGoogle Scholar
51. Scandura, P. 2007 Steady streaming in a turbulent oscillating boundary layer. J. Fluid Mech. 571, 265280.CrossRefGoogle Scholar
52. Schretlen, J. J. L. M., Ribberink, J. S. & O’Donoghue, T. 2010 Boundary layer flow and sand transport under full scale surface waves. In Proceedings of the 32nd International Conference on Coastal Engineering, Shangai 2010 (ed. Smith, J. M. & Lynett, P. ). Coastal Engineering Research Council.Google Scholar
53. Sleath, J. F. A. 1972 A second approximation to mass transport by water waves. J. Mar. Res. 30 (3), 295304.Google Scholar
54. Trowbridge, J. & Madsen, O. S. 1984a Turbulent wave boundary layers. 1. Model formulation and first-order solution. J. Geophys. Res. 89 (C5), 79897997.CrossRefGoogle Scholar
55. Trowbridge, J. & Madsen, O. S. 1984b Turbulent wave boundary layers. 2. Second-order theory and mass-transport. J. Geophys. Res. 89 (C5), 79998007.CrossRefGoogle Scholar
56. Van der Werf, J. J., Schretlen, J. J. L. M., Ribberink, J. S. & O’Donoghue, T. 2009 Database of full-scale laboratory experiments on wave-driven sand transport processes. Coastal Engineering 56 (7), 726732.CrossRefGoogle Scholar
57. Van Doorn, T. 1981 Experimental investigation of near-bottom velocities in water waves with and without a current. Rep. MI. 423 Delft Hydraulics Lab.Google Scholar
58. Van Rijn, L. 1991Sediment transport in combined waves and currents. In Proceedings Euromech 262 Colloquium Sand Transport in Rivers, Estuaries and the Sea, Wallingford (UK) (ed. R. Soulsby & R. Bettess). A.A. Balkema.Google Scholar
59. Vittori, G. 2003 Sediment suspension due to waves. J. Geophys. Res. Oceans 108 (C6), 3173 4-1/4-17.CrossRefGoogle Scholar
60. Vittori, G. & Blondeaux, P. 1996 Mass transport under sea waves propagating over a rippled bed. J. Fluid Mech. 314, 247265.CrossRefGoogle Scholar
61. Vittori, G. & Verzicco, R. 1998 Direct simulation of transition in an oscillatory boundary layer. J. Fluid Mech. 371, 207232.CrossRefGoogle Scholar
62. Zyserman, J. A. & Fredsoe, J. 1994a Data analysis of bed concentration of suspended sediment. Hydraul. Engng 120 (9), 10211042.CrossRefGoogle Scholar
63. Zyserman, J. A. & Fredsoe, J. 1994 b Bed concentration of suspended sediment and total load transport in asymmetric oscillatory flow. In Book of Abstracts Overall Workshop, MAST, 1994, Gregynog, Wales (ed. M. Stive).Google Scholar