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Mass transport under standing waves over a sloping beach

Published online by Cambridge University Press:  14 May 2012

Pietro Scandura ,
Enrico Foti  and
Carla Faraci
Pietro Scandura*
Affiliation:
Department of Civil and Environmental Engineering, University of Catania, Viale A. Doria 6, 95125 Catania, Italy
Enrico Foti
Affiliation:
Department of Civil and Environmental Engineering, University of Catania, Viale A. Doria 6, 95125 Catania, Italy
Carla Faraci
Affiliation:
Department of Civil and Environmental Engineering, University of Messina, C.da Di Dio (S. Agata), 98166 Messina, Italy
*
†Email address for correspondence: pscandu@dica.unict.it
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Abstract

This paper deals with the mass transport induced by sea waves propagating over a sloping beach and fully reflected from a wall. It is shown that for moderate slopes the classical recirculation cell structure holds for small Reynolds numbers only. When the Reynolds number is large, the cells interact among themselves giving rise to the merging of the negative cells and the confinement of the positive ones near the bottom. Under such circumstances the fluid moves onshore near the bottom and offshore near the free surface. The seaward decrease of the vorticity produced at the bottom appears to be the reason for the merging phenomenon.

JFM classification

Boundary Layers: Boundary Layers Geophysical and Geological Flows: Coastal engineering Waves/Free-surface Flows: Surface gravity waves
Type
Papers
Information
Journal of Fluid Mechanics , Volume 701 , 25 June 2012 , pp. 460 - 472
Copyright
Copyright © Cambridge University Press 2012

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References

1. Arakawa, A. 1966 Computational design for long-term numerical integration of the equations of fluid motion: two-dimensional incompressible flow. Part 1. J. Comput. Phys. 1 (1), 119–143.CrossRefGoogle Scholar
2. Blondeaux, P., Brocchini, M. & Vittori, G. 2002 Sea waves and mass transport on a sloping beach. Proc. R. Soc. Lond. A 458, 2053–2082.CrossRefGoogle Scholar
3. Carter, T. G., Liu, P. F.-L. & Mei, C. C. 1973 Mass transport by waves and offshore sand bedforms. J. Waterways Harbors Div. ASCE 99, 165–184.Google Scholar
4. Craik, A. D. D. 1982 The drift velocity of water waves. J. Fluid Mech. 116, 187–205.CrossRefGoogle Scholar
5. Dore, B. D. 1976 Double boundary layers in standing surface waves. Pure Appl. Geophys. 114, 629–637.Google Scholar
6. Haddon, E. W. & Riley, N. 1983 A note on the mean circulation in standing waves. Wave Motion 5, 43–48.CrossRefGoogle Scholar
7. Hunt, J. N. & Johns, B. 1963 Currents induced by tides and gravity waves. Tellus 15, 343–351.CrossRefGoogle Scholar
8. Hwung, H. H. & Lin, C. 1990 The mass transport of waves propagating on a sloping bottom. In Proceedings of XXII International Conference Coastal Engineering, pp. 544–556. ASCE.Google Scholar
9. Iskandarani, M. & Liu, P. L.-F. 1991a Mass transport in two-dimensional water waves. J. Fluid Mech. 231, 395–415.CrossRefGoogle Scholar
10. Iskandarani, M. & Liu, P. L.-F. 1991b Mass transport in three-dimensional water waves. J. Fluid Mech. 231, 417–437.CrossRefGoogle Scholar
11. Lau, J. & Travis, B. 1973 Slow varying stokes waves and submarine longhshore bar. J. Geophys. Res. Oceans 78, 4489–4497.CrossRefGoogle Scholar
12. Liu, P. L.-F. 1977 Mass transport in the free surface boundary layers. Coastal Engng 1, 207–219.CrossRefGoogle Scholar
13. Longuet-Higgins, M. S. 1953 Mass transport in water waves. Phil. Trans. R. Soc. Lond. A 345, 535–581.Google Scholar
14. Mei, C. C., Stiassnie, M. & Yue, D. K.-P. 2005a Theory and Applications of Ocean Surface Waves Part 1: Linear Aspects. World Scientific.Google Scholar
15. Mei, C. C., Stiassnie, M. & Yue, D. K.-P. 2005b Theory and Applications of Ocean Surface Waves Part 2: Nonlinear Aspects. World Scientific.Google Scholar
16. Riley, N. 2001 Steady streaming. Annu. Rev. Fluid Mech. 33, 43–65.CrossRefGoogle Scholar
17. Roache, P. J. 1972 Computational Fluid Dynamics. Hermosa Publishers.Google Scholar
18. Stoker, J. J. 1947 Surface waves in water of variable depth. Q. Appl. Maths 5, 1–54.Google Scholar
19. Thom, A. 1928 An investigation of fluid flow in two dimensions. Tech. Rep. 1194. Aerospace Research Center UK.Google Scholar
20. Wen, J. & Liu, P. L.-F. 1994 Mass transport under partially reflected waves in a rectangular channel. J. Fluid Mech. 226, 121–145.Google Scholar