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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

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