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Weakly nonlinear theory of regular meanders

Published online by Cambridge University Press:  26 April 2006

G. Seminara  and
M. Tubino
G. Seminara
Affiliation:
Istituto di Idraulica. Università di Genova, Via Montallegro 1. 16145 Genova, Italy
M. Tubino
Affiliation:
Istituto di Idraulica. Università di Genova, Via Montallegro 1. 16145 Genova, Italy
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Abstract

Flow and bed topography in a regular sequence of meanders is shown to be strongly influenced by nonlinear effects within a fairly wide range of aspect ratios of the channel and meander wavenumbers. This finding is associated with the behaviour of meanders as nonlinear resonators in a neighbourhood of the resonance conditions discovered by Blondeaux & Seminara (1985). A weakly nonlinear approach valid for relatively small measures of channel curvature and within a neighbourhood of the resonant conditions displays all the typical features of nonlinear resonators, including non-uniqueness of the channel response. The nonlinear structure of forced bars close to resonance is also shown to be related to that of nonlinear free steady bars spatially developing in a straight channel from a non-uniform initial condition. Finally we show how to reconcile the intrinsic nonlinearity of the near-resonant channel response with traditional bend stability theories. Some comparison with a systematic set of experimental observations of Colombini, Tubino & Whiting (1990) provides qualitative support for the present theory but also suggests that strongly nonlinear effects may play a non-negligible role for fairly small values of channel curvature. The main implication of this work is the clear need to revisit the literature on the modelling of flow and bed topography in river meanders, which is mostly based on linear theories.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 244 , November 1992 , pp. 257 - 288
Copyright
© 1992 Cambridge University Press

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References

Blondeaux, P. & Seminara G. 1985 A unified bar-bend theory of river meanders. J. Fluid Mech. 157, 449–470.Google Scholar
Chien N. 1956 The present status of research on sediment transport. Trans. ASCE 121, 833–868.Google Scholar
Coddington, E. A. & Levinson N. 1955 Theory of Ordinary Differential Equations. McGraw-Hill.
Colombini M., Seminara, G. & Tubino M. 1987 Finite-amplitude alternate bars. J. Fluid Mech. 181, 213–232 (referred to herein as CST).Google Scholar
Colombini, M. & Tubino, M. 1990 Finite amplitude free-bars: a fully nonlinear spectral solution. Sand Transport in Rivers, Estuaries and the Sea (ed. R. Soulsby & R. Bettes). Proc. Euromech 262 Colloquium, Wallingford, UK, 26–29 June, pp. 163–169. Balkema.
Colombini M., Tubino, M. & Whiting P. 1990 Topographic expression of bars in meandering channels. In Dynamics of Gravel-Bed Rivers (ed. P. Billi, R. D. Hey C. R. Thorne & P. Tacconi), pp. 457–474. Wiley & Sons.
Engelund F. 1974 Flow and bed topography in channel bends. J. Hydraul. Div. ASCE 100 (HY11), 1631–1648.Google Scholar
Engelund, F. & Hansen E. 1967 A Monograph on Sediment Transport in Alluvial Streams. Copenhagen: Danish Technical Press.
Ferguson R. I. 1975 Meander irregularity and wavelength estimation. J. Hydrol. 26, 315–333.Google Scholar
Hasegawa K. 1989 Studies on qualitative and quantitative prediction of meander channel shift. In River Meandering (ed. S. Ikeda & G. Parker). AGU Water Resources Monograph, vol. 12, pp. 215–235.
Ikeda S. 1982 Lateral bedload transport on sides slopes. J. Hydraul. Engng ASCE 108, 1369–1373.Google Scholar
Ikeda S., Parker, G. & Sawai K. 1981 Bend theory of river meanders. Part 1. Linear development. J. Fluid Mech. 112, 363–377.Google Scholar
Johannesson, H. & Parker G. 1989 Linear theory of river meanders. In River Meandering (ed. S. Ikeda & G. Parker). AGU Water Resources Monograph, vol. 12, pp. 181–213.
Kalkwijk, J. P. Th. & Vriend H. J. DE 1980 Computation of the flow in shallow river bends. J. Hydraul. Res. 18, 327–342.Google Scholar
Kinoshita R. 1961 Investigation of channel deformation in Ishikari River. Rep. Bureau of Resources, Dept. Science & Technology, Japan, pp. 1–174.Google Scholar
Langbein, W. B. & Leopold L. B. 1966 River meanders-theory of minimum variance. USGS Professional Paper 422H, pp. 1–15.Google Scholar
Mosselman E. 1989 Theoretical investigation on discharge-induced river bank erosion. Commun. Hydraul., Delft University of Technology Rep. 3–89.Google Scholar
Nanson, G. C. & Hickin E. J. 1983 Channel migration and incision on the Beatton river. J. Hydraul. Engng ASCE 109, 327–337.Google Scholar
Odgaard J. A. 1989 River-meander model. I: Development. J. Hydraul. Engng ASCE 115, 1433–1450.Google Scholar
Olesen K. W. 1983 Alternate bars and meandering of alluvial rivers. Commun. Hydraul., Delft University of Technology Rep. 7–83.Google Scholar
Parker G. 1978 Self-formed straight rivers with equilibrium banks and mobile bed. Part 1. The gravel river. J. Fluid Mech. 89, 127–146.Google Scholar
Parker G. 1984 Discussion of: ‘Lateral bedload transport on side slopes’ by S. Ikeda. J. Hydraul. Engng ASCE 110, 197–199.Google Scholar
Parker G., Diplas, P. & Akiyama J. 1983 Meander bends of high amplitude. J. Hydraul. Engng ASCE 109, 1323–1337.Google Scholar
Rozovskii I. L. 1957 Flow of Water in Bends of Open Channels. Kiev: Acad. Sci. Ukhranian SSR.
Seminara G. 1989 River bars and nonlinear dynamics. Proc. IAHR Workshop on Fluvial Hydraulics of Mountain Regions, Trent, Italy, 3–6 October.
Seminara, G. & Tubino M. 1985 Further results on the effect of transport in suspension on flow in weakly meandering channels. In Colloq on The Dynamics of Alluvial Rivers, pp. 67–112. Hydraulic Institute, Genoa University.
Seminara, G. & Tubino M. 1989 Alternate bars and meandering: free, forced and mixed interactions. In River Meandering (ed. S. Ikeda & G. Parker). AGU Water Resources Monograph, vol. 12, pp. 267–320.
Seminara, G. & Tubino M. 1991 Discussion of: ‘River-meander model. I: Development’. By J. A. Odgaard, J. Hydraul. Engng ASCE 117, 1088–1091.Google Scholar
Struiksma, N. & Crosato A. 1989 Analysis of a 2-D bed topography model for rivers. In River Meandering, (ed. S. Ikeda & G. Parker). AGU Water Resources Monograph, vol. 12, pp. 153–180.
Struiksma N., Olesen K. W., Flokstra, C. & Vriend H. J. de 1985 Bed deformation in curved alluvial channels. J. Hydraul. Res. 23, 57–79.Google Scholar
Thompson, J. M. T. & Stewart H. B. 1986 Nonlinear Dynamics and Chaos. Wiley & Sons.
Tubino, M. & Seminara G. 1990 Free-forced interactions in developing meanders and suppression of free bars. J. Fluid Mech. 214, 131–159 (referred to herein as TS).Google Scholar