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Mass transport in the bottom boundary layer of cnoidal waves

Published online by Cambridge University Press:  29 March 2006

M. De St Q. Isaacson
M. De St Q. Isaacson
Affiliation:
Joint Tsunami Research Effort, NOAA, University of Hawaii, Honolulu
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Abstract

This study deals with the mass-transport velocity within the bottom boundary layer of cnoidal waves progressing over a smooth horizontal bed. Mass-transport velocity distributions through the boundary layer are derived and compared with that predicted by Longuet-Higgins (1953) for sinusoidal waves. The mass transport at the outer edge of the boundary layer is compared with various theoretical results for an inviscid fluid based on cnoidal wave theory and also with previous experimental results. The effect of the viscous boundary layer is to establish uniquely the bottom mass transport and this is appreciably greater than the somewhat arbitrary prediction for an inviscid fluid.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 74 , Issue 3 , 6 April 1976 , pp. 401 - 413
Copyright
© 1976 Cambridge University Press

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References

Abramowitz, M. & Stegun, I. A. 1965 Handbook of Mathematical Functions. Dover.
Allen, J. & Gibson, D. H. 1959 Experiments on the displacement of water by waves of various heights and frequencies Proc. Inst. Civ. Engng, 13, 363–386.Google Scholar
Batchelor, G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.
Brebner, A. & Collins, J. I. 1961 Onset of turbulence at the bed under periodic gravity waves Trans. Eng. Inst. Can. 5, 55–62.Google Scholar
Collins, J. I. 1963 Inception of turbulence at the bed under periodic gravity waves J. Geophys. Res. 68, 6007–6014.Google Scholar
Isaacson, E. De St Q. & Isaacson, M. DE ST Q. 1975 Dimensional Methods in Engineering and Physics. London: Arnold.
Laitone, E. V. 1960 The second approximation to cnoidal and solitary waves J. Fluid Mech. 9, 430–444.Google Scholar
Le Méhauté, B. 1968 Mass transport in cnoidal waves J. Geophys. Res. 73, 5973–5979.Google Scholar
Longuet-Higgins, M. S. 1953 Mass transport in water waves. Phil. Trans A 245, 535–581.Google Scholar
Longuet-Higgins, M. S. 1958 The mechanics of the boundary-layer near the bottom in a progressive wave. [Appendix to a paper by R. C. H. Russell & J. D. C. Osorio.] Proc. 6th Int. Conf. Coastal Engng, Miami, pp. 184–193.
Sleath, J. F. A. 1974 Stability of laminar flow at seabed. A.S.C.E. J. Waterways, Harbors Coastal Engng Div. 100 (WW2), 105–810.Google Scholar
Spielvogel, E. R. & Spielvogel, L. Q. 1974 Bottom drift due to periodic shallow water waves J. Geophys. Res. 79, 2752–2754.Google Scholar
Stokes, G. G. 1847 On the theory of oscillatory waves Trans. Camb. Phil. Soc. 8, 441–455. (See also Math. Phys. Papers, 1, 197–810, 314–810, 1880. Cambridge University Press.)Google Scholar