Hostname: page-component-745bb68f8f-cphqk Total loading time: 0 Render date: 2025-02-04T15:05:28.447Z Has data issue: false hasContentIssue false
  • English
  • Français

Free surface waves over a depression

Published online by Cambridge University Press:  17 April 2009

J. W. Choi
J. W. Choi
Affiliation:
Department of Mathematics, Korea University, Seoul, 136–701, Korea, e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Steady waves at the free surface of an incompressible fluid passing over a depression are considered. By studying a KdV equation with negative forcing term, new types of solutions are discovered numerically and a new cut-off value of the Froude number, above which unsymmetric solitary-wave-like wave solutions exist, is also found.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 65 , Issue 2 , April 2002 , pp. 329 - 335
Copyright
Copyright © Australian Mathematical Society 2002

References

[1]Cole, S.L., ‘Transient waves produced by flow past a bump’, Wave Motion 7 (1985), 579–587.CrossRefGoogle Scholar
[2]Forbes, L.K., ‘Two-layer critical flow over a semi-circular obstruction’, J. Eng. Math. 23 (1989), 325–342.Google Scholar
[3]Forbes, L.K. and Schwartz, L.W., ‘Free surface flow over a semi-circular obstruction’, J. Fluid Mech. 144 (1982), 299–314.CrossRefGoogle Scholar
[4]Gong, L. and Shen, S.P., ‘multiple supercritical solitary wave solutions of the statinary forced Dorteweg-de Vires equation and their stability’, SIAM J. Appl. Math. 54 (1994), 1268–1290.CrossRefGoogle Scholar
[5]Shen, S.P., ‘Forced solitary waves and hydraulic falls in two layer flows’, J. Fluid Mech. 234 (1992), 583–612.CrossRefGoogle Scholar
[6]Shen, S.P. and Shen, M.C., ‘On the limit of subcritical free surface flow over an obstruction’, Acta Mech. 82 (1990), 225–230.Google Scholar
[7]Shen, S.P. and Shen, M.C. and Sun, S.M., ‘A model equation for steady surface wave over a bump’, J. Engrg. Math. 23 (1989), 315–323.CrossRefGoogle Scholar
[8]Vanden-Broeck, J.M., ‘Free-surface flow over and obstruction in a channel’, Phys. Fluids 30 (1987), 2315–2317.Google Scholar
[9]Wu, D.M. and Wu, T.Y., ‘Three-dimensional nonlinear long waves due to moving surface pressure’, in Proc. 14th Symp. Naval Hydrodyn. (National Academy of Science, Washington, 1982), pp. 103–125.Google Scholar