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Waves in meandering streams

Published online by Cambridge University Press:  20 April 2006

Chia-Shun Yih
Chia-Shun Yih
Affiliation:
The University of Michigan, Ann Arbor, Michigan 48109
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Abstract

Free-surface and internal stationary waves in a meandering stream are treated, and analytical solutions given. It is shown that for each category there is an infinite number of Froude numbers, depending on the wavenumber of the meander, at which resonance occurs, and the amplitude of one of the wave components becomes infinite, according to the linear theory. These critical Froude numbers are interpreted physically. Furthermore, variable depth is treated for the case of free-surface waves, and in this treatment it is shown, incidentally, how the eigenvalues of a singular differential equation can be found under the requirement that the eigenfunction be non-singular.

Finally, an attempt is made to explain the self-induced, non-stationary waves in water flowing between corrugated vertical walls, found by Binnie (1960), by an instability mechanism proposed by Yih (1976). There is strong evidence that this mechanism is at work, at least when a sloshing mode is involved in the wave-triad interaction.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 130 , May 1983 , pp. 109 - 121
Copyright
© 1983 Cambridge University Press

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References

Benjamin, T. B. 1967 Instability of periodic wave trains in nonlinear dispersive systems Proc. R. Soc. Lond. A299, 59–75.Google Scholar
Benjamin, T. B. & Feir, J. E. 1967 The disintegration of wave trains on deep water J. Fluid Mech. 27, 417–130.Google Scholar
Binnie, A. M. 1960 Self-induced waves in a conduit with corregated walls. I. Experiments with water in an open horizontal channel with vertically corrugated sides Proc. R. Soc. Lond. A259, 18–27.Google Scholar
Ipen, A. T. et al. 1951 High velocity flow in open channels. (A Symposium.) Paper no. 2434 Trans. ASCE 116, 265–400.Google Scholar
Jahke, E. & Emde, F. 1945 Tables of Functions, Dover.
Phillips, O. M. 1960 On the dynamics of unsteady gravity waves of finite amplitude. Part 1. The elementary interactions J. Fluid Mech. 9, 193–217.Google Scholar
Phillips, O. M. 1961 On the dynamics of unsteady gravity waves of finite amplitude. Part 2. Local properties of a random wave field J. Fluid Mech. 11, 143–155.Google Scholar
Yih, C.-S. 1976 Instability of surface and internal waves Adv. Appl. Mech. 16, 369–419.Google Scholar
Yih, C.-S. 1982 Binnie waves. Paper presented to the 14th Symp. on Naval Hydrodynamics, Ann Arbor, Michigan, August 1982.