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Mass transport in a turbulent boundary layer under a progressive water wave

Published online by Cambridge University Press:  20 April 2006

S. J. Jacobs
S. J. Jacobs
Affiliation:
Department of Atmospheric and Oceanic Science, and Department of Mechanical Engineering and Applied Mechanics, The University of Michigan, Ann Arbor. MI 48107
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Abstract

The bottom boundary layer under a progressive water wave is studied using Saffman's turbulence model. Saffman's equations are analysed asymptotically for the case Re [Gt ] 1, where Re is a Reynolds number based on a characteristic magnitude of the orbital velocity and a characteristic orbital displacement. Approximate solutions for the mass-transport velocity at the edge of the boundary layer and for the bottom stress are obtained, and Taylor's formula for the rate of energy dissipation is verified. The theoretical results are found to agree well with observations for sufficiently large Reynolds numbers.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 146 , September 1984 , pp. 303 - 312
Copyright
© 1984 Cambridge University Press

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References

Bijker, E. W., Kalwijk, J. P. T. & Pieters, T. 1974 In Proc. 14th Coastal Engng Conf., p. 447. ASCE.
Brebner, A., Askew, J. A. & Law, S. W. 1966 In Proc. 10th Coastal Engng Conf., p. 175. ASCE.
Bush, W. B. & Fendell, F. E. 1972 J. Fluid Mech. 56, 657.
Collins, J. I. 1963 J. Geophys. Res. 68, 6007.
Lamb, H. 1932 Hydrodynamics, 6th edn. Cambridge University Press.
Lighthill, J. 1978 Waves in Fluids. Cambridge University Press.
Longuet-Higgins, M. S. 1953 Phil. Trans. R. Soc. Lond. A 245, 66.
Riedel, H. P., Kamphuis, J. W. & Brebner, A. 1972 In Proc. 13th Coastal Engng Conf., p. 587. ASCE.
Russell, R. C. H. & Osorio, J. D. C. 1958 In Proc. 6th Coastal Engng Conf., p. 171. ASCE.
Saffman, P. G. 1970 Proc. R. Soc. Lond. A 317, 417.
Saffman, P. G. 1974 Stud. Appl. Maths 53, 17.
Saffman, P. G. & Wilcox, D. C. 1974 AIAA J. 12, 541.
Schlichting, H. 1979 Boundary-Layer Theory, 7th edn. McGraw-Hill.
Taylor, G. I. 1919 Phil. Trans. R. Soc. Lond. A 220, 1.