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Bend theory of river meanders. Part 2. Nonlinear deformation of finite-amplitude bends

Published online by Cambridge University Press:  20 April 2006

Gary Parker ,
Kenji Sawai  and
Syunsuke Ikeda
Gary Parker
Affiliation:
St Anthony Falls Hydraulic Laboratory, University of Minnesota, Minneapolis, Minnesota, 55414, USA
Kenji Sawai
Affiliation:
Disaster Prevention Research Institute, Kyoto University, Uji, Japan
Syunsuke Ikeda
Affiliation:
Department of Foundation Engineering, Saitama University, Saitama, Japan
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Abstract

Meander bends typically show certain systematic deviations from simple Cartesian sinusoidal forms. Bends tend to be round and full, or ‘fat’, often to the point of possessing double-valued plan-forms, as Langbein & Leopold (1966) have noted. Bends also tend to be characteristically skewed in such a fashion that their direction of migration can be determined directly from an aerial photograph of the planform; the water margin of the downstream accreting half of a point bar describes a convex planform, whereas the upstream eroding side has a concave shape.

In the present paper a generalized nonlinear equation of bend migration is treated based on the analysis of Part 1 (Ikeda, Parker & Sawai 1981). An expansion technique reminiscent of the Stokes expansion for water waves is developed to perform a nonlinear stability analysis. This analysis provides an explanation of skewing and fattening, and also indicates that lateral and downstream migration rates should increase as bend amplitude develops. These results agree qualitatively with field observations.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 115 , February 1982 , pp. 303 - 314
Copyright
© 1982 Cambridge University Press

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References

Ikeda, S., Parker, G. & Sawai, K. 1981 Bend theory of river meanders. Part I. Linear development. J. Fluid Mech. 112, 363–377.Google Scholar
Kinoshita, R. 1961 An investigation of channel deformation of the Ishikari River. Publication no. 36, Natural Resources Division, Ministry of Science and Technology of Japan, 139 pp. (in Japanese).
Langbein, W. B. & Leopold, L. B. 1966 River meanders - theory of minimum variance. U.S. Geological Survey Professional Paper 422H.
Narai, S. 1975 On the trajectory of fluvial meanders. Proceedings of 30th Annual Meeting of the Japan Society of Civil Engineers, pp. 362–363 (in Japanese).
Whitham, G. B. 1974 Linear and Nonlinear Waves. John Wiley.