Hostname: page-component-cd9895bd7-7cvxr Total loading time: 0 Render date: 2024-12-18T18:38:16.596Z Has data issue: false hasContentIssue false
  • English
  • Français

Nonlinear theory of open-channel steady flow past a solid surface of finite-wave-group shape

Published online by Cambridge University Press:  28 March 2006

M. S. Howe
M. S. Howe
Affiliation:
Imperial College, London
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper deals with a detailed application of the Whitham theory of finite amplitude wave propagation to open-channel steady flow of water of infinite depth past a slowly modulated wavy wall. A numerical procedure first used by Garabedian & Lieberstein (1958) for the solution of ‘stably-posed’ elliptic Cauchy problems is employed to obtain a map of the wave pattern on the free surface of the water. The appearance of a ‘shock’ in this solution is discussed in terms of previous analytical and experimental results.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 30 , Issue 3 , 29 November 1967 , pp. 497 - 512
Copyright
© 1967 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

Benjamin, T. B. & Feir, J. E. 1967 J. Fluid Mech. 27, 417.
Garabedian, P. R. & Lieberstein, H. M. 1958 J. Aero. Sci. 25, 109.
Lamb, H. 1932 Hydrodynamics, 6th ed. Cambridge University Press.
Lieberstein, H. M. 1959 MRC Technical Summary Rept. no. 81. Madison, Wisconsin.
Lighthill, M. J. 1965 J.I.M.A. 1, 269.
Lighthill, M. J. (organiser) 1967 A Discussion on nonlinear theory of wave propagation in dispersive systems. Proc. Roy. Soc. A 299, 1–145.Google Scholar
Whitham, G. B. 1965a Proc. Roy. Soc. A 283, 238.
Whitham, G. B. 1965a J. Fluid Mech. 22, 273.
Whitham, G. B. 1967 J. Fluid Mech. 27, 399.