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Mass transport under sea waves propagating over a rippled bed

  • G. Vittori (a1) and P. Blondeaux (a2)
Abstract

Mass transport under a progressive sea wave propagating over a rippled bed is investigated. Wave amplitudes a* of the same order of magnitude as that of the boundary layer thickness δ* and of the ripple wavelength l* are considered. All the above quantities are assumed to be much smaller than the wavelength L* of the sea wave and much larger than the amplitude 2ε* of the ripples. The analysis is carried out up to the second order in the wave slope a*/L* and in the parameter ε** which is a measure of ripple steepness. Because of these assumptions, the slow damping of wave amplitude in the direction of wave propagation is taken into account. Attention is focused on the bottom boundary layer where an order (ε**)2 correction of the steady velocity components described by Longuet-Higgins (1953) is found. This correction persists at the outer edge of the bottom boundary layer and affects the solution in the entire water column.

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References
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Blondeaux, P. 1990 Sand ripples under sea waves. Part 1. Ripple formation. J. Fluid Mech. 218, 117.

Blondeaux, P. & Vittori, G. 1991 Vorticity dynamics in an oscillatory flow over a rippled bed. J. Fluid Mech. 226, 257289.

Dore, B. D.1974The mass transport velocity due to interacting wave trains. Meccanica9, 172178.

Haddon, E. W. & Riley, N.1983A note on the mean circulation in standing waves. Wave Motion5, 4338.

Hara, T. & Mei, C. C. 1989 Oscillating flows over periodic ripples. J. Fluid Mech. 211, 183209.

Liu, A. K. & Davis, S. H. 1977 Viscous attenuation of mean drift in water waves. J. Fluid Mech. 81, 6384.

Longuet-Higgins, M. S. 1981 Oscillating flow over steep sand ripples. J. Fluid Mech. 107, 135.

Mei, C. C. & Liu, P. L. F.1993Surface waves and coastal dynamics. Ann. Rev. Fluid Mech.25, 215240.

Rayleigh, Lord1983On the circulation of air observed in Kundt's tubes and some allied acoustical problems. Phil. Trans. R. Soc. Lond. A 175, 121.

Riley, N.1984Progressive surface waves on a liquid of non-uniform depth. Wave Motion6, 1522.

Sleath, J. F. A.1976On rolling-grain ripples. J. Hydraul. Res.14, 6981.

Vittori, G.1989Nonlinear viscous oscillatory flow over a small amplitude wavy wall. J. Hydraul. Res.27, 267280.

Wen, J. & Liu, P. L. F. 1994 Mass transport under partially reflected waves in a rectangular channel. J. Fluid Mech. 266, 121145.

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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
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