Hostname: page-component-745bb68f8f-l4dxg Total loading time: 0 Render date: 2025-02-12T01:19:44.530Z Has data issue: false hasContentIssue false
  • English
  • Français

Run-up of solitary waves

Published online by Cambridge University Press:  20 April 2006

G. Pedersen  and
B. Gjevik
G. Pedersen
Affiliation:
Department of Mechanics, University of Oslo, P.O. Box 1053, Blindern, Oslo 3, Norway
B. Gjevik
Affiliation:
Department of Mechanics, University of Oslo, P.O. Box 1053, Blindern, Oslo 3, Norway
Get access Rights & Permissions [Opens in a new window]

Abstract

A numerical model based on a Lagrangian description has been developed for studying run-up of long water waves governed by a set of Boussinesq equations. The performance of the numerical scheme has been tested by comparing with analytical solutions and experimental data. Simulations of the run-up of solitary waves on relatively steep planes (inclination angle > 20°) show surface displacements and run-up heights in good agreement with experiments. For waves with relatively large amplitude the simulations reveal the development of a breaking bore during the backwash. Results for run-up heights in converging and diverging channels are also presented.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 135 , October 1983 , pp. 283 - 299
Copyright
© 1983 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Arntsen, ø. A. 1978 Theoretical and experimental study of wave run-up on relatively steep slopes. Cand.real. thesis, University of Oslo.
Carrier, G. F. 1966 Gravity waves on water of variable depth J. Fluid Mech. 24, 641–659.Google Scholar
Carrier, G. F. & Greeenspan, H. P. 1958 Water waves of finite amplitude on a sloping beach J. Fluid Mech. 4, 97–109.Google Scholar
Chang, P., Melville, W. K. & Miles, J. W. 1979 On the evolution of a solitary wave in a gradually varying channel J. Fluid Mech. 95, 401–414.Google Scholar
Gjevik, B. & Pedersen, G. 1981 Run-up of long waves on an inclined plane. Preprint Ser. no. 2, Dept of Maths, University of Oslo.Google Scholar
Hall, J. V. & Watts, G. M. 1953 Laboratory investigation of the vertical rise of solitary waves on impermeable slopes. U. S. Army, Corps of Engrs, Beach Erosion Board, Tech. Memo no. 33.Google Scholar
Helal Badawi, S. 1981 Etude théorique de la réflexion des ondes de gravité de grande longueur d'onde relative sur les plages. Thesis, L'Université scientifique et médicale, Grenoble.
Hibberd, S. & Peregrine, D. H. 1979 Surf and run-up on a beach: a uniform bore. J. Fluid Mech. 95, 323–345.Google Scholar
Kishi, T. & Saeki, H. 1967 The shoaling, breaking and run-up of the solitary wave on impermeable rough slopes. In Proc. 10th Conf. Coastal Engng, Tokyo, 1966. ASCE, New York.
Langsholt, M. 1981 Experimental study of wave run-up. Cand.real. thesis, University of Oslo.
Mesinger, F. & Arakawa, A. 1976 Numerical methods used in atmospheric models. GARP Pub. Ser. no. 17, WMO-ICSU, Geneva.Google Scholar
Meyer, R. E. & Taylor, A. D. 1972 Run-up on beaches. In Waves on Beaches and Resulting Sediment Transport (ed. R. E. Meyer), pp. 357–411. Academic.
Miles, J. W. 1979 On the Korteweg-de Vries equation for a gradually varying channel J. Fluid Mech. 91, 181–190.Google Scholar
Pedersen, G. 1981 Run-up of solitary waves in channel. Cand.real. thesis. University of Oslo.
Peregrine, D. H. 1968 Long waves in a uniform channel of arbitrary cross-section J. Fluid Mech. 32, 353–365.Google Scholar
Peters, A. S. 1966 Rotational and irrotational solitary waves in a channel with arbitrary cross-section Communs Pure Appl. Maths 19, 445–471.Google Scholar
Shuto, N. 1967 Run-up of long waves on a sloping beach Coastal Engng in Japan 10, 23–38.Google Scholar
Spielvogel, L. Q. 1976 Single wave run-up on sloping beaches J. Fluid Mech. 74, 685–694.Google Scholar
Wiegel, R. L. 1964 Oceanographical Engineering. Prentice-Hall.