Meanders are puzzling phenomena because a meandering river seems to contradict the principle of least action. Different approaches to explain this paradox are outlined by adopting a topological view, which allows for a classification of different types of meanders and to discuss the relevant mechanisms in a rather general manner. It is shown that secondary flows of helical type are the features responsible for the increase in the sediment transport when the slope of rivers decreases due to meandering and that the increase in the discharge is due to a partial Beltramisation of the flow and to a reduction in the friction at the boundary of the helical cells. The review article contains 78 references.
Issue Section:
Review Articles
Keywords:
boundary layers,
channel flow,
friction,
geomorphology,
rivers,
sedimentation,
topography (Earth)
1.
Garde
, R. J.
, and Raju
, K. G. R.
, 1977, Mechanics of Sediment Transportation and Alluvial Stream Problems
, Wiley Eastern
, New Dehli
.2.
Hayashi
, T.
, 1971, “Study of the Cause of Meander
,” Trans. JSCE
, 2
(2
), p. 235
.3.
Leopold
, L. B.
, and Langbein
, W. B.
, 1966, “River Meanders
,” Sci. Am.
0036-8733, 217
, pp. 60
–70
.4.
Langbein
, W. B.
, and Leopold
, L. B.
, 1966, “River Meanders—Theory of Minimum Variance
,” U.S. Geol. Survey Prof. Paper 422 H, pp. 1–15.5.
Leopold
, L. B.
, and Wolman
, M. G.
, 1960, “River Meanders
,” Geol. Soc. Am. Bull.
0016-7606, 71
, pp. 769
–794
.6.
Leopold
, L. B.
, and Wolman
, M. G.
, 1957, “River Channel Patterns: Braided, Meandering and Straight
,” U.S. Geol. Survey Prof. Paper 282-B.7.
Edwards
, B. F.
, and Smith
, D. H.
, 2002, “River Meandering Dynamics
,” Phys. Rev. E
1063-651X, 65
, p. 046303
.8.
Schumm
, S. A.
, and Khan
, H. R.
, 1972, “Experimental Study of Channel Patterns
,” Geol. Soc. Am. Bull.
0016-7606, 83
, pp. 1755
–1770
.9.
Schumm
, S. A.
, Khan
, H. R.
, Winkley
, B. R.
, and Robbins
, L. G.
, 1972, “Variability of River Patterns
,” Nature (London), Phys. Sci.
0300-8746, 237
, pp. 75
–76
.10.
Schumm
, S. A.
, 1973, “Geomorphic Thresholds and Complex Response of Drainage Systems
,” Fluvial Geomorphology
, M.
Morisawa
, ed., pp. 299
–310
.11.
Schumm
, S. A.
, and Beathard
, R. M.
, 1976, “Geomorphic Thresholds: An Approach to River Management
,” 3rd Ann. Symp. Waterways, Harbors and Coastal Eng. Div. ASCE
, Vol. 1
, pp. 707
–724
.12.
da Vinci
, L.
, 1986, See the Contribution by Macagno or in Facsimiles Editions of His Work Here Especially: A. Marioni Il Monoscrito H Giunti-Barbèra, Firence and E. Carusi and R. Marcolongo, I Manoscritti di Leonardo da Vinci Publicati Dalla Reale Commissione Vinciana, il Codex Arundel, pp. 1923
–1930
.13.
Larras
, J.
, 1968, “Problèmes D’hydraulique Fluviale
,” Ann. Ponts Chaussees
0003-4304, 138
, pp. 195
–209
.14.
Callander
, R. A.
, 1978, “River Meandering
,” Annu. Rev. Fluid Mech.
0066-4189, 10
, pp. 129
–158
.15.
Toebes
, G. H.
, and Sooky
, A. A.
, 1967, “Hydraulic of Meandering Rivers With Flood Plains
,” J. Wtrwy. and Harb. Div.
0569-8103, 93
, pp. 213
–226
.16.
Chang
, H. H.
, 1983, “Energy Expenditure in Curved Open Channels
,” J. Hydraul. Eng.
0733-9429, 109
, pp. 1012
–1022
.17.
Ervine
, D. A.
, and Ellis
, J.
, 1987, “Experimental and Computational Aspects of Overbank Flood Plain Flow
,” Trans. R. Soc. Edinburgh: Earth Sci.
, 78
, pp. 315
–325
.18.
Willetts
, B. B.
, and Hardwick
, R. I.
, 1993, “Stage Dependency for Overbank Flow in Meandering Channels
,” Proc. Inst. Civ. Eng., Waters. Maritime Energ.
0965-0946, 101
, pp. 45
–54
.19.
Sellin
, R. J. H.
, Ervine
, D. A.
, and Willetts
, B. B.
, 1993, “Behaviour of Meandering Two-Stage Channels
,” Proc. Inst. Civ. Eng., Waters. Maritime Energ.
0965-0946, 101
, pp. 99
–111
.20.
Ervine
, D. A.
, Willetts
, B. B.
, Sellin
, R. H. J.
, and Lorena
, M.
, 1993, “Factors Affecting Conveyance in Meandering Compound Flows
,” J. Hydraul. Eng.
0733-9429, 119
, pp. 1383
–1399
.21.
Shiono
, K.
, Muto
, Y.
, Knight
, D. W.
, and Hyde
, A. F. L.
, 1999, “Energy Losses Due to Secondary Flow and Turbulence in Meandering Channels With Overbank Flows
,” J. Hydraul. Res.
0022-1686, 37
, pp. 641
–663
.22.
Karamisheva
, R. D.
, Lyness
, J. F.
, Myers
, W. R. C.
, and O’Sullivan
, J.
, 2006, “Sediment Discharge Prediction in Meandering Compound Channels
,” J. Hydraul. Res.
0022-1686, 44
, pp. 603
–613
.23.
Wallis
, I. G.
, 1973, “On the Development of River Meanders. Part I Laboratory Experiments
,” Monash Univ. Geophys. Fluid Dyn. Lab., Paper No. 57, 28 pages.24.
Stølum
, H. H.
, 1996, “River Meandering as a Self-Organization Process
,” Science
0036-8075, 271
, pp. 1710
–1713
.25.
Chang
, H. H.
, 1988, Fluvial Processes in River Engineering
, Wiley
, New York
.26.
Yalin
, M. S.
, 1992, River Mechanics
, Pergamon
, Oxford
.27.
28.
Ferreira da Silva
, A. M.
, 2006, “On Why and How Do River Meander
,” J. Hydraul. Res.
0022-1686, 44
, pp. 579
–590
.29.
Onishi
, Y.
, Jain
, S. C.
, and Kennedy
, J. F.
, 1976, “Effects of Meandering in Alluvial Streams
,” J. Hydr. Div.
0044-796X, 102
, pp. 899
–917
.30.
Prandtl
, L.
, 1926, “Über die Ausgebildete Turbulenz
,” Verhandlung D.2. Internationaler Kongress fur, Technische Mechanik
, Zürich.31.
Gyr
, A.
, and Hoyer
, K.
, 2006, Sediment Transport: A Geophysical Phenomenon
, Springer
, Dordrecht
.32.
Einstein
, A.
, 1954, “The Cause of the Formation of Meanders in the Course of Rivers and the So-Called Bear’s Law
,” Ideas and Opinions
, Bonanza
, New York
, 249
–253
.33.
Martinez-Frias
, J.
, Hochberg
, D.
, and Rull
, F.
, 2006, “A Review of the Contributions of Albert Einstein to Earth Sciences—In Commemoration of the World Year of Physics
,” Naturwiss.
0028-1042, 93
, pp. 66
–71
.34.
Ferguson
, R. I.
, 1976, “Meander Irregularity and Wavelength Estimation
,” J. Hydrol.
0022-1694, 26
, pp. 315
–333
.35.
Howard
, A. D.
, and Knutson
, T. R.
, 1984, “Sufficient Conditions for River Meandering: A Simulation Approach
,” Water Resour. Res.
0043-1397, 20
, pp. 1659
–1667
.36.
Scheidegger
, E. A.
, 1967, “A Thermodynamic Analogy for Meander Systems
,” Water Resour. Res.
0043-1397, 3
, pp. 1041
–1046
.37.
von Schelling
, H.
, 1951, “Most Frequent Particle Path in a Plane
,” Trans., Am. Geophys. Union
0002-8606, 32
, pp. 222
–226
.38.
von Schelling
, H.
, 1964, "Most Frequent Random Walks
,” Gen. Elec. Co. Report No. 64GL92, Schenectady, NY.39.
Surkan
, A. J.
, and van Kan
, J.
, 1969, “Constrained Random Walk Meander Generation
,” Water Resour. Res.
0043-1397, 5
, pp. 1343
–1352
.40.
Liverpool
, T. B.
, and Edwards
, S. F.
, 1995, “The Dynamics of a Meandering River
,” Phys. Rev. Lett.
0031-9007, 75
, pp. 3016
–3019
.41.
Holmes
, D.
, and Lumley
, J. L.
, and Berkooz
, G.
, 1996, Turbulence, Coherent Structures, Dynamical Systems and Symmetry
, Cambridge University Press
, Cambridge
.42.
Townsend
, A. A.
, 1976, The Structure of Turbulent Shear Flow
, 2nd ed., Cambridge University Press
, Cambridge
.43.
Parker
, G.
, 1976, “On the Cause and Characteristic Scales of Meandering and Braiding in Rivers
,” J. Fluid Mech.
0022-1120, 76
, pp. 457
–483
.44.
Leopold
, L. B.
, 1982, “Water Surface Topography in River Channels and Implications for Meander Development
,” Gravel-Bed Rivers
, R. D.
Hey
, J. C.
Bathurst
, and C. R.
Thorne
, eds., Wiley
, Chichester
, pp. 359
–388
.45.
Boussinesq
, J.
, 1868, “Mémoire sur l’influence des Frottements dans les Mouvements Réguliers des Fluids
,” J. Math. Pures Appl.
0021-7824, 13
, pp. 377
–424
.46.
Thomson
, J.
, 1876, “On the Origin of Windings of Rivers in Alluvial Plains With Remarks on the Flow of Water Round Bends in Pipes
,” Proc. R. Soc. London
0370-1662, 25
, pp. 5
–8
.47.
Fredsøe
, J.
, 1978, “Meandering and Braiding of Rivers
,” J. Fluid Mech.
0022-1120, 84
, pp. 609
–624
.48.
Ikeda
, S.
, Parker
, G.
, and Sawai
, K.
, 1981, “Bend Theory of River Meanders. Part 1. Linear Development
,” J. Fluid Mech.
0022-1120, 112
, pp. 363
–377
.49.
Parker
, G.
, Sawai
, K.
, and Ikeda
, S.
, 1982, “Bend Theory of River Meanders. Part 2. Nonlinear Deformation of Finite-Amplitude Bends
,” J. Fluid Mech.
0022-1120, 115
, pp. 303
–314
.50.
Blondeaux
, P.
, and Seminara
, G.
, 1985, “A Unified Bar-Bend Theory of River Meanders
,” J. Fluid Mech.
0022-1120, 157
, pp. 449
–470
.51.
Tubino
, M.
, and Seminara
, G.
, 1990, “Free-Forced Interactions in Developing Meanders and Suppression of Free Bars
,” J. Fluid Mech.
0022-1120, 214
, pp. 131
–159
.52.
Seminara
, G.
, and Tubino
, M.
, 1992, “Weakly Nonlinear Theory of Regular Meanders
,” J. Fluid Mech.
0022-1120, 244
, pp. 257
–288
.53.
Seminara
, G.
, Solezzi
, G.
, Tubino
, M.
, and Zardi
, D.
, 2001, “Downstream and Upstream Influence in River Meandering. Part 2. Planimetric Development
,” J. Fluid Mech.
0022-1120, 438
, pp. 213
–230
.54.
Kennedy
, J. F.
, 1969, “The Formation of Sediment Ripples, Dunes and Antidunes
,” Annu. Rev. Fluid Mech.
0066-4189, 1
, pp. 147
–168
.55.
Kitanidis
, P. K.
, and Kennedy
, J. F.
, 1984, “Secondary Current and River-Meander Formation
,” J. Fluid Mech.
0022-1120, 144
, pp. 217
–229
.56.
Parker
, G.
, and Andrews
, E. D.
, 1986, “On the Time Development of Meander Bends
,” J. Fluid Mech.
0022-1120, 162
, pp. 139
–156
.57.
Siebert
, W.
, 1975, “Experimentelle Untersuchungen zum Mechanismus Einer Kanalströmung Beim Übergang von Einer Geraden Strecke in Einen Kreisbogen
,” Leitmotiv Wasser
, W.
Buck
and H. H.
Bernhart
, eds., University of Karlsruhe
, pp. 373
–391
.58.
Siebert
, W.
, and Götz
, W.
, 1975, “A Study on the Deformation of Secondary Flow in Models of Rectangular Meandering Channels
,” Proceedings of the 16th Congress IAHR
, Vol. 2
, pp. 141
–149
.59.
Görtler
, H.
, 1954, “Über Eine Dreidimensionale Instabilität Laminarer Grenzschichten an Konkaven Wänden
,” Nachr. Ges. Wiss. Göttingen N.F.
, 2
(1
), pp. 1
–26
, 1940.60.
Leeder
, M. R.
, and Bridge
, P. H.
, 1975, “Flow Separation in Meander Bends
,” Nature (London)
0028-0836, 253
, pp. 338
–339
.61.
Ferguson
, R. J.
, Parsons
, D. R.
, Lane
, S. N.
, and Hardy
, R. J.
, 2003, “Flow in Meander Bends With Recirculation at the Inner Bank
,” Water Resour. Res.
0043-1397, 39
, pp. 1322
–1334
.62.
Studerus
, X.
, 1982, “Sekundärströmungen in Offenen Gerinnen Über Rauhen Längsstreifen
,” Ph.D. thesis Swiss Federal Institute of Technology Zurich.63.
Ascanio
, M. F.
, and Kennedy
, J. F.
, 1983, “Flow in Alluvial-River Curves
,” J. Fluid Mech.
0022-1120, 133
, pp. 1
–16
.64.
Zimmermann
, C.
, and Kennedy
, J. F.
, 1978, “Transvers Bed Slopes in Curved Alluvial Streams
,” J. Hydr. Div.
0044-796X, 104
, pp. 33
–48
.65.
Zimmermann
, C.
, 1974, “Sohlenausbildung, Reibungsfaktoren und Sedimenttransport in Gleichförmig Gekrümmten und Geraden Gerinnen
,” Ph.D. thesis, Institute of Hydromechanics, University of Karlruhe.66.
Bathurst
, J. C.
, Thorne
, C. R.
, and Hey
, R. D.
, 1979, “Secondary Flow and Shear Stress at River Bends
,” J. Hydr. Div.
0044-796X, 105
, pp. 1277
–1295
.67.
Darby
, S. E.
, and Delbono
, I.
, 2002, “A Model of Equilibrium Topography for Meander Bends With Erodible Banks
,” Earth Surf. Processes Landforms
0197-9337, 27
, pp. 1057
–1085
.68.
Eaton
, B. C.
, Church
, M.
, and Davies
, T. R. H.
, 2006, “A Computational Model for Meander Initiation in Bed-Load Dominated Streams
,” Earth Surf. Processes Landforms
0197-9337, 31
, pp. 875
–891
.69.
Lighthill
, M. J.
, 1963, Laminar Boundary Layers
, L.
Rosenhead
, ed., Oxford University Press
, Oxford
, pp. 48
–88
.70.
Müller
, A.
, 1990, “Quadrant Analysis and Instantaneous Momentum Transport—A Critical Review
,” Structure of Turbulence and Drag Reduction
, A.
Gyr
, ed., Springer Berlin
, Heidelberg
, pp. 137
–144
.71.
Engelund
, F.
, 1974, “Flow and Bed Topography in Channel Bends
,” J. Hydr. Div.
0044-796X, 100
, pp. 1631
–1648
.72.
Gessner
, F. B.
, 1973, “The Origin of Secondary Flow in Turbulent Flow Along a Corner
,” J. Fluid Mech.
0022-1120, 58
, pp. 1
–25
.73.
Tsinober
, A.
, 2001, An Informal Introduction to Turbulence
, Kluwer Academic Publishers
.74.
Tsinober
, A.
, 2003, “Nonlocality in Turbulence
,” Sedimentation and Sediment Transport
, A.
Gyr
and W.
Kinzelbach
, eds., Kluwer Academic Publishers
.75.
Kraichnan
, R. H.
, 1973, “Helical Turbulence and Absolute Equilibrium
,” J. Fluid Mech.
0022-1120, 59
, pp. 745
–752
.76.
André
, J. C.
, and Lesieur
, M.
, 1977, “Influence of Helicity on the Evolution of Isotropic Turbulence at High Reynolds Number
,” J. Fluid Mech.
0022-1120, 81
, pp. 187
–207
.77.
Shtilman
, L.
, and Polifke
, W.
, 1990, “Reduction of Nonlinearity and Energy Cascade in Helical and Nonhelical Turbulent Flows
,” Topological Fluid Mechanics
, H. K.
Moffatt
and A.
Tsinober
, eds., Cambridge University Press
, Cambridge
, pp. 598
–606
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