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The viscous damping of cnoidal waves

Published online by Cambridge University Press:  29 March 2006

Michael de st Q. Isaacson
Affiliation:
Joint Tsunami Research Effort, NOAA, University of Hawaii, Honolulu

Abstract

The viscous damping of cnoidal waves progressing over a smooth horizontal bed is investigated. First approximations are derived for the attenuation of wave height with distance and for the friction coefficient at the bed. Attenuation coefficients are larger than those predicted on the basis of shallow-water sinusoidal wave theory and, unlike the case of sinusoidal waves, they are not independent of wave height. The limiting case of the solitary wave, considered previously by Keulegan (1948), is also discussed.

Type
Research Article
Copyright
© 1976 Cambridge University Press

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References

Biesel, F. 1949 Calcul de l'amortissement d'une houle dans un liquide visqueux de profondeur finie Houille Blanche, 4, 630634.Google Scholar
Eagleson, P. S. 1962 Laminar damping of oscillatory waves. A.S.C.E. J. Hydraul. Div. 88(HY3), 155810.Google Scholar
Hunt, J. N. 1952 Viscous damping of waves over an inclined bed in a channel of finite width Houille Blanche, 7, 836842.Google Scholar
Hunt, J. N. 1964 The viscous damping of gravity waves in shallow water Houille Blanche, 19, 685691.Google Scholar
Isaacson, E. De St Q. & Isaacson, M. DE ST Q. 1975 Dimensional Methods in Engineering and Physics. London: Arnold.
Isaacson, M. De St Q. 1976 Mass transport in the bottom boundary layer of cnoidal waves J. Fluid Mech. 74, 401413.Google Scholar
Keulegan, G. H. 1948 Gradual damping of solitary waves J. Res. Nat. Bur. Stand. 40, 487498.Google Scholar
Laitone, E. V. 1960 The second approximation to cnoidal and solitary waves J. Fluid Mech. 9, 430444.Google Scholar
Longuet-Higgins, M. S. 1975 Integral properties of periodic gravity waves of finite amplitude. Proc. Roy. Soc A 342, 157174.Google Scholar
Lukasik, S. J. & Grosch, C. E. 1963 Discussion of ‘Laminar damping of oscillatory waves’ by P. S. Eagleson. A.S.C.E. J. Hydraul. Div. 89(HY1), 231810.Google Scholar
Treloar, P. D. & Brebner, A. 1970 Energy losses under water action. Proc. 12th Coastal Engng Conf., Wash., pp. 257267.