Skip to main content Accessibility help

The transformation of a solitary wave over an uneven bottom

  • O. S. Madsen (a1) and C. C. Mei (a1)


Based on a set of approximate equations for long waves over an uneven bottom, numerical results show that as a solitary wave climbs a slope the rate of amplitude increase depends on the initial amplitude as well as on the slope. Results are also obtained for a solitary wave progressing over a slope onto a shelf. On the shelf a disintegration of the initial wave into a train of solitary waves of decreasing amplitude is found. Experimental evidence is also presented.



Hide All
Byrne, R. J. 1969 J. Geoph. Res. 74, 2590.
Camfield, F. E. & Street, R. L. 1969 Proc. ASCE, J.W.W. and H. Div. 95, 1.
Galvin, C. J. 1968 Trans. Am. Geophy. Union, 49, 206.
Gardner, C. S., Greene, J. M., Kruskal, M. O. & Miura, R. M. 1967 Phys. Rev. Lett. 19, 1095.
Horikawa, K. & Wiegel, R. L. 1959 Univ. Calif. Wave Res. Lab., Ser. 89, Issue 4.
Ippen, A. T. & Kulin, G. 1955 M.I.T. Hydro. Lab. Tech. Rep. no. 15.
Ippen, A. T., Kulin, G. & Raza, M. A. 1955 M.I.T. Hydro. Lab. Tech. Rep. no. 16.
Kishi, T. & Saeki, H. 1966 Proc. 10th Con. Coastal Engng. 1, 322.
Lin, C. C. & Clark, A. 1959 Tsing Hua, J. Chinese Studies, Spec. no. 1, Nat. Sci. 54.
Long, R. R. 1964 J. Fluid Mech. 20, 161.
Mei, C. C. & Leméhauté, B. 1966 J. Geoph. Res. 71, 393.
Peregrine, D. H. 1966 J. Fluid. Mech. 25, 321.
Peregrine, D. H. 1967 J. Fluid Mech. 27, 815.
Street, R. L., Burges, S. J. & Whitford, P. W. 1968 Dept. Civ. Engng., Standford Univ. Tech. Rep. no. 93.
Ursell, F. 1953 Proc. Cam. Phil. Soc. 49, 685.
Whitham, G. B. 1967 Proc. Roy. Soc. A, 299, 6.
Zabusky, N. J. 1967 Nonlinear Partial Differential Equations (edited by W. F. Ames). New York: Academic.
Zabusky, N. J. & Galvin, C. J. 1968 Trans. Am. Geophys. Union, 49, 209.
Zabusky, N. J. & Kruskal, M. D. 1965 Phys. Rev. Lett. 15, 240.
MathJax is a JavaScript display engine for mathematics. For more information see


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed