Hostname: page-component-8448b6f56d-t5pn6 Total loading time: 0 Render date: 2024-04-23T06:38:38.163Z Has data issue: false hasContentIssue false
  • English
  • Français

Numerical and experimental study of the transformation of a solitary wave over a shelf or isolated obstacle

Published online by Cambridge University Press:  21 April 2006

Fernando J. Seabra-Santos ,
Dominique P. Renouard  and
André M. Temperville
Fernando J. Seabra-Santos
Affiliation:
Institut de Mécanique de Grenoble, B.P. 68, 38402 Saint-Martin d'Hères Cedex, France Permanent affiliation: Faculdade de Cienciase Tecnologia Universidade de Coimbra, Portugal.
Dominique P. Renouard
Affiliation:
Institut de Mécanique de Grenoble, B.P. 68, 38402 Saint-Martin d'Hères Cedex, France
André M. Temperville
Affiliation:
Institut de Mécanique de Grenoble, B.P. 68, 38402 Saint-Martin d'Hères Cedex, France
Get access Rights & Permissions [Opens in a new window]

Abstract

In order to model the evolution of a solitary wave near an obstacle or over an uneven bottom, the long-wave equations including curvature effects are introduced to describe the deformation and fission of a barotropic solitary wave passing over a shelf or an obstacle. The numerical results obtained from these equations are shown to be in good agreement with an analytical model derived by Germain (1984) in the framework of a generalized shallow-water theory, and with experimental results collected in a large channel equipped with a wave generator. Given the initial conditions, i.e. amplitude of the incident solitary wave, water depth in the deep region, and height of the shelf or the barrier, it is possible to predict the amplitude and number of the transmitted solitary waves as well as the amplitude of the reflected wave, and to describe the shape of the free surface at any time.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 176 , March 1987 , pp. 117 - 134
Copyright
© 1987 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

Djordjevic, V. D. & Redekopp, L. G. 1978 The fission and disintegration of internal solitary waves moving over two-dimensional topography. J. Phys. Oceanogr. 8, 1016–1024.Google Scholar
Fenton, J. D. & Rienecker, M. M. 1982 A Fourier method for solving nonlinear water-wave problems: application to solitary-wave interactions. J. Fluid Mech. 118, 411–443.Google Scholar
Germain, J. P. 1971a Sur une généralisation de la théorie des mouvements en eau peu profonde. C. R. Acad. Sci. Paris 273A, 1093–1096.Google Scholar
Germain, J. P. 1971b Sur le caractère limité de la théorie des mouvements des liquides parfaits en eau peu profonde. C. R. Acad. Sci. Paris 273A, 1171–1174.Google Scholar
Germain, J. P. 1972 Théorie générale des mouvements d'un fluide parfait pesant en eau peu profonde de profondeur constante. C. R. Acad. Sci. Paris 274A, 997–1000.Google Scholar
Germain, J. P. 1984 Coefficients de réflexion et de transmission en eau peu profonde. Instytut Budownictwa Wodnego, Gdansk. Rozprawy Hydzotechniezne, Rep. No. 46.
Goring, D. C. 1978 Tsunamis – the propagation of long waves onto a shelf. California Institute of Technology, Pasadena, Rep. KHR-38.
Gulli, L. 1975 Etude du passage d'une houle en eau peu profonde sur une barrière verticale immergée. Thèse, Université Scientifique et Médicale de Grenoble.
Kabbaj, A. 1985 Contribution à l'étude du passage des ondes de gravité et de la génération des ondes internes sur un talus, dans le cadre de la théorie de l'eau peu profonde. Thèse. Université Scientifique et Médicale de Grenoble.
McCowan, J. 1894 On the highest wave of permanent type. Phil. Mag. 38, 351.Google Scholar
Madsen, O. S. & Mei, C. C. 1969 The transformation of a solitary wave over an uneven bottom. J. Fluid Mech. 39, 781–791.Google Scholar
Maxworthy, T. 1976 Experiments on collisions between solitary waves. J. Fluid Mech. 76, 177–185.Google Scholar
Mirie, R. M. & Su, C. H. 1982 Collisons between two solitary waves. Part 2. A numerical study. J. Fluid Mech. 115, 475–492.Google Scholar
Renouard, D., Seabra-Santos, F. J. & Temperville, A. 1985 Theoretical and experimental studies of the generation, damping and reflexion of a solitary wave. Dyn. Atmos. Ocean 9, 341–358.Google Scholar
Seabra-Santos, F. J. 1985 Génération, propagation et réflexion des ondes solitaires. Thèse, Université Scientifique et Médicale de Grenoble.
Serre, F. 1953 Contribution à l'étude des écoulements permanents et variables dans les canaux. Houille Blanche, 374–385.
Street, R. L., Burges, S. J. & Whitford, P. W. 1968 The behavior of the solitary waves on a stepped slope. Stanford University Tech. Rep. 93.Google Scholar
Su, C. H. & Gardner, C. S. 1969 Korteweg–de Vries equation generalizations. III. Derivation of the Korteweg–de Vries equation and Burgers equations. J. Math. Phys. 10, 536–539.Google Scholar
Su, C. H. & Mirie, R. M. 1980 On head-on collisions between two solitary waves. J. Fluid Mech. 98, 509–525.Google Scholar