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A unified bar–bend theory of river meanders

Published online by Cambridge University Press:  20 April 2006

P. Blondeaux  and
G. Seminara
P. Blondeaux
Affiliation:
Istituto di Idraulica, Facoltà di Ingegneria, Università di Genova, Genoa, Italy
G. Seminara
Affiliation:
Istituto di Idraulica, Facoltà di Ingegneria, Università di Genova, Genoa, Italy
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Abstract

A two-dimensional model of flow and bed topography in sinuous channels with erodible boundaries is developed and applied in order to investigate the mechanism of meander initiation. By reexamining the problem recently tackled by Ikeda, Parker & Sawai (1981), a previously undiscovered ‘resonance’ phenomenon is detected which occurs when the values of the relevant parameters fall within a neighbourhood of certain critical values. It is suggested that the above resonance controls the bend growth, and it is shown that it is connected in some sense with bar instability. In fact, by performing a linear stability analysis of flow in straight erodible channels, resonant flow in sinuous channels is shown to occur when curvature ‘forces’ a ‘natural’ solution represented by approximately steady perturbations of the alternate bar type. A comparison with experimental observations appears to support the idea that resonance is associated with meander formation.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 157 , August 1985 , pp. 449 - 470
Copyright
© 1985 Cambridge University Press

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References

Adachi S.1967 A theory of stability of streams. Proc. 12th Congr. IAHR, Fort Collins, Colorado, vol. 1, pp. 338–343.
Blondeaux, P. & Seminara G.1983a Bed topography and instabilities in sinuous channels. Proc. ASCE Rivers ‘83, New Orleans, pp. 747–758.
Blondeaux, P. & Seminara G.1983b,c Formazione dei meandri in alvei incoerenti. Giornata di Studio sugli Alvei con Granulometria Grossolana e Incoerente, Napoli, parte i e ii, pp. 141–180.Google Scholar
Callander R. A.1969 Instability and river channels. J. Fluid Mech. 36, 465–480.Google Scholar
Chang H., Simons, D. B. & Woolhiser D. A.1971 Flume experiments on alternate bar formation. J. Waterways, Harbors, Coastal Engng Div. ASCE 97, 155–165.Google Scholar
Chien N.1954 In Proc. ASCE 80, 1954.Google Scholar
De Vriend H. J.1977 A mathematical model of steady flow in curved shallow channels. J. Hydraul. Res. 15, 37–54.Google Scholar
De Vriend, H. J. & Struiksma, N. 1983 Flow and bed deformation in river bends. Proc. ASCE Rivers ‘83, New Orleans, pp. 810–828.
Einstein H. A.1950 The bedload function for sediment transport in open channel flow. US Dept Agric. Tech. Bull. 1026.Google Scholar
Engelund F.1974 Flow and bed topography in channel bends. J. Hydraul. Div. ASCE 100, (HY11), 1631–1648.Google Scholar
Engelund F.1981 The motion of sediment particles on an inclined bed. Tech. Univ. Denmark ISVA Prog. Rep. 53, pp. 15–20.Google Scholar
Engelund, F. & Hansen E.1967 A Monograph on Sediment Transport in Alluvial Streams. Copenhagen: Danish Technical Press.
Engelund, F. & Skovgaard O.1973 On the origin of meandering and braiding in alluvial streams. J. Fluid Mech. 57, 289–302.Google Scholar
FredsÒ J.1978 Meandering and braiding of rivers. J. Fluid Mech. 84, 609–624.Google Scholar
Gottlieb L.1976 Three-dimensional flow pattern and bed topography in meandering channels. ISVA Tech. Univ. Denmark Series Paper 11.Google Scholar
Hansen E.1967 On the formation of meanders as a stability problem. Hydraul. Lab. Tech. Univ. Denmark Basic Res. Prog. Rep. 13, pp. 9–13.Google Scholar
Hasegawa, K. & Yamaoka I.1980 The effect of plane and bed forms of channels upon the meander development. Proc. JSCE 296, 143–152.Google Scholar
Hayashi T.1971 Study on the cause of meandering of rivers. Trans. JSCE 2, 235.Google Scholar
Hayashi, T. & Ozaki S.1976 On dominant wave length in river meanders from the viewpoint of stability theory on beds. Proc. 20th Japanese Conf. Hydraul., pp. 89–96.
Hayashi, T. & Ozaki S.1980 Alluvial bed form analysis - formation of alternating bars and braids. In Application of Stochastic Processes in Sediment Transport (ed. T. Kishi & M. Kuroki); Water Resources Publ., Littleton, Colorado, pp. 7.1–7.40.
Hooke R. L.1974 Shear stress and sediment distribution in a meander bend. Ungi Rep. 30, University of Uppsala, Sweden.Google Scholar
Ikeda S.1984 Prediction of alternate bar wavelength and height. ASCE J. Hydraul. Engng 110, 371–386.Google Scholar
Ikeda S., Hino, M. & Kikkawa H.1976 Theoretical study of the free meandering of rivers. Proc. JSCE 255, 63–73 (in Japanese).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
Kikkawa H., Ikeda, S. & Kitagawa A.1976 Flow and bed topography in curved open channels. J. Hydraul. Div. ASCE 102 (HY9), 1326–1342.Google Scholar
Kinoshita, R. & Miwa H.1974 River channel formation which prevents downstream translation of transverse bars. Shinsabo 94, 12–17 (in Japanese).Google Scholar
Kishi, T. & Kuroki, M. (eds) 1980 Application of Stochastic Processes in Sediment Transport; Water Resources Publ., Littleton, Colorado.
Kitanidis, P. K. & Kennedy J. F.1984 Secondary current and river-meander formation. J. Fluid Mech. 144, 217–229.Google Scholar
Lewin J.1976 Initiation of bed forms and meanders in coarse-grained sediment. Geol. Soc. Am. Bull. 87, 281.Google Scholar
Parker G.1975 Meandering of supraglacial melt streams. Water Resources Res. 11, 551–552.Google Scholar
Parker G.1976 On the cause and characteristic scales of meandering and braiding in rivers. J. Fluid Mech. 76, 457–480.Google Scholar
Parker G.1984 Lateral bed load transport on side slopes. ASCE J. Hydraul. Engng 110, 197–199.Google Scholar
Richardson E. W., Everett, V. & Simons D. B.1967 Resistance to flow in sand channels. Proc. 12th Congr. IAHR, Fort Collins, Colorado, vol. 1, pp. 141–161.
Rozovskii I. L.1957 Flow of Water in Bends of Open Channels. Kiev: Acad. Sci. Ukhranian SSR.
Sukegawa N.1971 Conditions for the occurrence of river meanders. Trans. JSCE 2, 257–261.Google Scholar