Rios Meandricos

8/12/2019 Rios Meandricos

1/267

Analysis and modelling of river meandering

Analyse en modellering van meanderenderivieren


2/267


3/267

Analysis and modelling of river meandering

Analyse en modellering van meanderenderivieren

PROEFSCHRIFTter verkrijging van de graad van doctoraan de Technische Universiteit Delft,

op gezag van de Rector Magnificus prof. dr. ir. J.T. Fokkema,voorzitter van het College voor Promoties,

in het openbaar te verdedigen op maandag 22 september 2008 om 10:00 uur

door

Alessandra CROSATODottore in Ingegneria Civile Idraulica, Universit degli Studi di Padova

geboren te Bolzano, Itali


4/267

Dit proefschrift is goedgekeurd door de promotor:Prof. dr. ir. H.J. de Vriend

Samenstelling promotiecommissie:Rector Magnificus, voorzitter

Prof. dr. ir. H.J. de Vriend, Technische Universiteit Delft, promotorProf. dr. ir. . M.J.F. Stive, Technische Universiteit DelftProf. dr. N.G. Wright, UNESCO-IHE DelftProf. dr. dott. ing. G. Di Silvio, Universit degli Studi di PadovaProf. dr. S. B. Kroonenberg, Technische Universiteit DelftDr. H. Middelkoop, Universiteit UtrechtDr. Herv Piegay, CNRS FranceProf. dr. ir. G.S. Stelling, Technische Universiteit Delft, reservelid

2008 Alessandra Crosato and IOS Press

All rights reserved. No part of this book may be reproduced, stored in a retrieval system, ortransmitted, in any form or by any means, without prior permission from the publisher.

ISBN 978-1-58603-915-8

Key words: river meandering, morphology, planform, bars, bank erosion, bank accretion

Published and distributed by IOS Press under the imprint Delft University Press

PublisherIOS Press

Nieuwe Hemweg 6b1013 BG AmsterdamThe Netherlandstel: +31-20-688 3355fax: +31-20-687 0019email: [email protected] www.iospress.nl

www.dupress.nl

LEGAL NOTICEThe publisher is not responsible fopr the use which might be made of the following information.

PRINTED IN THE NETHERLANDSCover picture: air view of a tributary of the Ob River (Russia), courtesy of Saskia van Vuren


5/267

Acknowledgements

i

cknowledgements

This PhD study has been carried out from 1987 to 2008 at the Department of Civil Engineeringand Geosciences of Delft University of Technology (TU Delft). The study was funded by theIstituto Veneto di Scienze Lettere ed Arti (Venice, Italy) and by Fondazione Ing. Aldo Gini(Padua, Italy) during the first year. WL Delft Hydraulics supported the work until 1991 and fullycovered the costs of the Pilot Flume experiments (1988) as well as my participation at theSummer School on Stability of River and Coastal Forms, in Perugia (1990). In the period 1991-2004 the work was either financed by projects (Studio SICEM S.r.l. and WL Delft Hydraulics)or carried out during my free time. Delft University of Technology co-financed the work in the

period 1988-1990 and fully financed the work in the period 2005-2008 with funds from the WaterResearch Centre Delft.

A large community of scientists and professionals has contributed to this work; therefore I wish tothank a lot of persons, hoping to forget nobody. Given the duration of the work, I find it easier tolist those persons in order of appearance. Moreover, I do not mention any titles or qualificationson purpose, since many of them have now a different title and position with respect to themoment in which they first appeared on the scene.The first persons I want to heartily thank are my parents, Luigi Crosato and Adriana Paccagnella,who gave me the possibility to carry out my studies in civil engineering and supported me formany years.My first husband, Frdric Vellieux, deserves particular thanks. He was able to transfer hisenthusiasm for science and convinced me to become a researcher. Before meeting him, I hadintended to become a project engineer. After so many years, I can say that I managed to do both,

research and projects, and in the last period even teaching river morphodynamics, which is morethan I had ever dreamed of.I thank Giampaolo Di Silvio (University of Padua), who was the first real contributor to thiswork. He gave me the opportunity to do research in the Netherlands, at WL Delft Hydraulics,and to work on the Po River (Italy). As one of the opponents, he finally also contributed to thisPhD thesis.I want to thank also Giovanni Seminara (University of Genoa) and Marco Tubino (University ofTrento), who initiated me in the subject of meandering rivers. With their enthusiasm, theyconveyed me their passion for the subject.

Nico Struiksma (WL Delft Hydraulics) deserves special thanks. With his creative imagination,impressive personality and wide experience he became the example to follow and made me anenthusiastic river engineer and researcher.Huib de Vriend (WL Delft Hydraulics and TU Delft) was at first an experienced colleague andan exceptionally good supervisor and later became my official PhD supervisor. I want to thankhim especially because he gave me the chance to finish the work at TU Delft in a second phase.Special thanks are due to Matthijs de Vries, who offered me the opportunity to carry out this PhDwork in the first place and became my first official supervisor. My appreciation for his approachto the study and teaching of river morphology has grown especially after I started to teach the


6/267

Acknowledgements

i i

subject myself at UNESCO-IHE. I very much regret that he passed away just two months beforehe could see this thesis.First as a colleague and then as second husband, Erik Mosselman (WL Delft Hydraulics and TUDelft), was and still is, my great inspirator. Lively discussions, covering all types of subjects,characterize our common life. In the field of river morphology, we have been exchanging ideas

and trying new ways throughout all these years, without loosing enthusiasm. This even led to afew works together. I thank him gratefully for his support and contribution to this work.I desire to thank Gary Parker (University of Illinois), for the intriguing discussions, which weinitially pursued by mail (no e-mail, but letters in envelopes) and at specific occasions, such asduring the summer school in Perugia (Italy).The MSc students who contributed to this work deserve a big thank you! They are KhwajaGhulam Murshed (UNESCO-IHE, 1991), Astrid Blom (TU Delft, 1997), Eva Miguel (TU Delft,2006), May Samir Saleh (UNESCO-IHE, 2007), Yasir S.A. Ali (UNESCO-IHE, 2008) andRoxana M. Duran Tapia (UNESCO-IHE, 2008).A number of researchers contributed to the work through their participation in fruitfuldiscussions. They are Arno Talmon (WL Delft Hydraulics and TU Delft), Kees Sloff (WL Delft

Hydraulics and TU Delft), Ronald van Balen (Free University of Amsterdam), Robbert Fokkink(TU Delft), Wim Uijttewaal (TU Delft), Hans van Duivendijk (TU Delft and Royal Haskoning),Jarit de Gijt (TU Delft and Rotterdam Harbour Authority) and Jelle Olthof (TU Delft and RoyalBoskalis Westminster).Also many friends contributed indirectly. They are Irini Katopodi, Nico Kitou, Maximo Peviani,Paolo De Girolamo, Johan Romate, Erica Cecchi, Federico Maggi, Paolo Reggiani, Katia Bilardo,Amparo Serra Piera, Cecilia Iacono and many others. Without this group of friends some darkand cold days would have been even darker and colder.I cannot list all the colleagues at TU Delft and WL Delft Hydraulics. Some of them, however,deserve great thanks, because I could share my everyday life with them. They are Mindert deVries, Pauline Thoolen, Walther van Kesteren, John Cornelisse, Kees Kuijper, Pim van der Salm,

Ilka Tanczos, Thijs van Kessel and many others. They made me feel at home also when being atwork.Finally, I want to thank the opponents Nigel Wright, Herv Piegay, Marcel Stive, SalomonKroonenberg, Hans Middelkoop and Guus Stelling, who spent their time on this thesis and

provided constructive comments.

This work is dedicated to G. Adyabadam, of the institute of Meteorology and Hydrology inMongolia, who, after having raised her family in Mongolia, took up study and research in the

Netherlands. Her example gave me the decisive push to complete this PhD thesis after so manyyears.


7/267

Summary English

i i i

ummary

This thesis examines the morphological changes of non-tidal meandering rivers at the spatialscale of several meanders. With this purpose, a physics-based mathematical model, MIANDRAS,has been developed for the simulation of the medium-term to long-term evolution of meanderingrivers. Application to several real rivers shows that MIANDRAS can properly simulate bothequilibrium river bed topography and planimetric changes. Three models of different complexitycan be obtained by applying different degrees of simplification to the equations. These models,along with experimental tests and field data, constitute the tools for several analyses.At conditions of initiation of meandering, it is found that river bends can migrate upstream anddownstream. This depends on meander wave length and width-to-depth ratio, irrespective ofwhether the parameters are in the subresonant or the superresonant range. Varying lag distances

between flow velocity and bed topography are found to offer an explanation why local channel

migration rates reach a maximum at a certain bend sharpness, in addition to previous explanations based on flow separation.A new method has been developed to calculate the number of bars in a river channel with givenwidth. It predicts successfully whether reducing or enlarging the river width would lead tomeandering or braiding.Channel migration coefficients are demonstrated to depend not only on physical properties of theeroding bank, but also on physical properties of the accreting bank and the numerical scheme.Moreover, they need to account for overbank flows.Model results and a re-examination of experimental observations suggest that intrinsic initiation ofmeandering is not necessarily related to steady bars due to a permanent upstream disturbance. Theymay also be related to a steady bed deformation due to small quickly-varying periodic or random

disturbances, for instance due to the presence of migrating alternate bars. The latter finding stillrequires further confirmation.


8/267

Summary English

i v


9/267

Samenvatting Nederlands

v

amenvatting

Dit proefschrift onderzoekt de morfologische veranderingen van meanderende rivieren zondergetij op de ruimteschaal van enkele meanders. Met dit doel is een op fysica gebaseerd wiskundigmodel, MIANDRAS, ontwikkeld voor het simuleren van de evolutie van meanderende rivierenop middellange en lange termijn. Toepassing op verschillende echte rivieren laat zien datMIANDRAS zowel de evenwichtsbodemligging van de rivier als de veranderingen in plattegrondop juiste wijze kan simuleren. Drie modellen van verschillende complexiteit kunnen wordenverkregen door verschillende graden van vereenvoudiging toe te passen op de vergelijkingen.Deze modellen vormen, samen met experimentele proeven en veldgegevens, de instrumentenvoor verscheidene analyses.Onder omstandigheden van het begin van meanderen wordt gevonden dat rivierbochtenstroomopwaarts en stroomafwaarts kunnen migreren. Dit hangt af van de meandergolflengte en

de breedte-diepteverhouding, ongeacht of de parameters zich bevinden in het subresonante of hetsuperresonante domein. Gevonden wordt dat varirende afstanden van naijling tussenstroomsnelheid en bodemtopografie een verklaring bieden waarom lokale snelheden vangeulmigratie bij een bepaalde bochtscherpte een maximum bereiken, in aanvulling op eerdereverklaringen op basis van loslating van de stroming.Een nieuwe methode is ontwikkeld om het aantal banken te berekenen in een riviergeul metgegeven breedte. Deze voorspelt met succes of verkleining of vergroting van de rivierbreedte zouleiden tot meanderen of vlechten.Aangetoond wordt dat cofficinten van geulmigratie niet alleen afhangen van fysischeeigenschappen van de eroderende oever, maar ook van fysische eigenschappen van de aangroeiendeoever en het numerieke schema. Bovendien moeten zij de invloed verrekenen van stromingen als de

rivier buiten haar oevers treedt.Modelresultaten en een hernieuwde analyse van experimentele waarnemingen suggereren dat hetintrinsieke begin van meanderen niet noodzakelijk gerelateerd is aan stationaire banken als gevolgvan een permanente verstoring bovenstrooms, maar mogelijk ook aan een stationaire vervormingvan de bodem als gevolg van snel varirende periodieke of willekeurige verstoringen, bijvoorbeeldals gevolg van de aanwezigheid van migrerende alternerende banken. Deze laatste bevinding

behoeft nog nadere bevestiging.


10/267

Samenvatting Nederlands

v i


11/267

Sommario Italiano

v i i

ommario

Questa tesi esamina i cambiamenti morfologici dei fiumi a meandri senza marea alla scalaspaziale di molti meandri. A questo scopo, nellambito del lavoro stato sviluppato un modellomatematico, basato sulla descrizione fisica dei fenomeni, per la simulazione dellevoluzione diquesti fiumi sul medio-lungo termine, MIANDRAS. La sua applicazione a un certo numero difiumi mostra che MIANDRAS in grado di simulare in modo soddisfacente la topografia diequilibrio del letto e i cambiamenti planimetrici dei fiumi a meandri. Inoltre, applicando diversilivelli di semplificazione alle equazioni si possono ottenere tre modelli di diversa complessit.Questi modelli, insieme a test sperimentali di laboratorio e a dati raccolti sul campo, costituisconogli strumenti di molte delle analisi effettuate.Alle condizioni iniziali di formazione dei meandri si trovato che i tornanti del fiume possonomigrare sia verso valle che verso monte. Ci dipende dalla lunghezza donda dei meandri e dal

rapporto tra larghezza e profondit del canale principale ed indipendente dal fatto che il sistemafluviale si trovi entro il dominio di sotto-risonanza o di super-risonaza. Si inoltre scoperto che lavariazione del ritardo spaziale tra la velocit della corrente e la topografia del letto in grado dispiegare perch la velocit di migrazione trasversale del fiume raggiunge un massimo ad un certovalore di intensit della curvatura. Questa spiegazione si aggiunge alle spiegazioni precedenti basate sulla separazione del flusso di corrente. stato sviluppato un nuovo metodo per calcolare il numero di barre in un canale fluviale dilarghezza conosciuta. Questo metodo in grado di predire se aumentare o diminuire la larghezzadel fiume porta ad un fiume a meandri o a configurazione intrecciata.Si dimostrato che i coefficienti usati per pesare la migrazione laterale del fiume dipendono nonsolamente dalle caratteristiche fisiche della sponda in erosione, ma anche dalle caratteristiche della

sponda in accrescimento e dallo schema numerico del modello. Essi inoltre devono tener conto delmoto della corrente sulle golene.I risultati del modello e il riesame di osservazioni sperimentali suggeriscono che la formazioneiniziale dei meandri intrinseca al sistema. Essa infatti non sembra necessariamente legata alla presenza di barre stazionarie causate da un disturbo a monte permanente, ma anche a unadeformazione del letto stazionaria causata da piccoli disturbi che variano velocemente nel tempo, periodici o completamente casuali, come per esempio quelli originati dalla presenza di barrealternate migranti. Questultima scoperta richiede ulteriori conferme.


12/267

Sommario Italiano

v i i i


13/267

Contents

i x

CONTENTS

1 INTRODUCTION ............................................................................................................................... 1 1.1 R ATIONALE .................................................................................................................................... 1 1.2 BACKGROUND OF THE STUDY ........................................................................................................ 4 1.3 OBJECTIVES ................................................................................................................................... 6 1.4 GENERAL APPROACH ..................................................................................................................... 6

2 MEANDERING RIVERS................................................................................................................... 9 2.1 I NTRODUCTION .............................................................................................................................. 9 2.2 MEANDERING AND OTHER PLANFORMS OF ALLUVIAL RIVERS ........................................................ 9 2.3 PLANIMETRIC CHARACTERISTICS OF MEANDERING RIVERS .......................................................... 12

2.3.1 Channel sinuosity ................................................................................................................... 12 2.3.2 Size of meanders ..................................................................................................................... 13 2.3.3 Size of the meander belt.......................................................................................................... 14 2.3.4 Bend sharpness....................................................................................................................... 152.3.5 River width.............................................................................................................................. 15

2.4 BED TOPOGRAPHY ....................................................................................................................... 16 2.5 DISCHARGES ................................................................................................................................ 18 2.6 SEDIMENT .................................................................................................................................... 19 2.7 BEND FLOW ................................................................................................................................. 19 2.8 CHANNEL MIGRATION .................................................................................................................. 21

2.8.1 General description ................................................................................................................ 21 2.8.2 Bank erosion........................................................................................................................... 23 2.8.3 Bank accretion........................................................................................................................ 25

2.9 CUTOFFS ...................................................................................................................................... 28 3 FACTORS CONTROLLING RIVER MEANDERING ................................................................ 31

3.1 I NTRODUCTION ............................................................................................................................ 31 3.2 PLANFORM CLASSIFICATIONS ...................................................................................................... 31 3.3 FLOW STRENGTH .......................................................................................................................... 37 3.4 SEDIMENT SUPPLY ....................................................................................................................... 38 3.5 BANK ERODIBILITY ...................................................................................................................... 39 3.6 R IPARIAN VEGETATION ................................................................................................................ 40 3.7 FREQUENCY OF FLOODS ............................................................................................................... 44 3.8 ACTIVE TECTONICS ...................................................................................................................... 44

4 STATE OF THE ART IN MEANDER MIGRATION MODELLING......................................... 47 4.1 I NTRODUCTION ............................................................................................................................ 47 4.2 MODELLING OF FLOW FIELD AND BED TOPOGRAPHY IN CURVED CHANNELS ................................ 47 4.3 MODELLING OF BANK EROSION AND BANK RETREAT ................................................................... 51

4.3.1 Fluvial entrainment ................................................................................................................ 52

4.3.2 Bank failure ............................................................................................................................ 53 4.3.3 Effects of eroded bank material.............................................................................................. 57 4.4 MODELLING OF BANK ACCRETION AND BANK ADVANCE ............................................................. 58 4.5 MODELLING OF CUT -OFFS ............................................................................................................ 61 4.6 MODELLING OF MEANDER MIGRATION ........................................................................................ 63

4.6.1 Introduction ............................................................................................................................ 63 4.6.2 History .................................................................................................................................... 64 4.6.3 Computation of lateral channel migration ............................................................................. 65 4.6.4 Meander migration models including cutoffs ......................................................................... 67


14/267

Contents

x

5 THE MEANDER MIGRATION MODEL MIANDRAS ............................................................... 69 5.1 I NTRODUCTION ............................................................................................................................ 69 5.2 MATHEMATICAL DESCRIPTION OF FLOW VELOCITY AND DEPTH .................................................. 70

5.2.1 Basic equations....................................................................................................................... 70 5.2.2 Simplification of the equations ............................................................................................... 77 5.2.3 Zero-order equations: unperturbed system ............................................................................ 80 5.2.4 First-order equations: perturbed system................................................................................ 81 5.2.5 Near-bank velocity and water depth excesses ........................................................................ 82 5.2.6 Axi-symmetric solution of the equations ................................................................................. 84 5.2.7 Steady-state equations ............................................................................................................ 86 5.2.8 Time adaptation of transverse bed deformation ..................................................................... 88

5.3 MATHEMATICAL DESCRIPTION OF BANK RETREAT AND ADVANCE ............................................... 92 5.4 SIMULATION OF CUTOFFS ............................................................................................................. 93 5.5 COMPUTATION OF THE RIVER CORRIDOR WIDTH .......................................................................... 94

6 STRAIGHT FLUME EXPERIMENT ON BAR FORMATION .................................................. 97 6.1 I NTRODUCTION ............................................................................................................................ 97 6.2 EXPERIMENTAL SET UP ................................................................................................................ 97 6.3 TEST T1 ..................................................................................................................................... 100 6.4 TEST T2 ..................................................................................................................................... 103

7 ANALYSES OF MODEL BEHAVIOUR...................................................................................... 107 7.1 I NTRODUCTION .......................................................................................................................... 107 7.2 NEAR -BANK FLOW VELOCITY AND DEPTH OSCILLATION ............................................................ 107

7.2.1 Theoretical analysis.............................................................................................................. 107 7.2.2 Comparison with experimental data..................................................................................... 114

7.3 FLOW VELOCITY LAG ................................................................................................................. 116 7.3.1 Theoretical analysis.............................................................................................................. 116 7.3.2 Comparison with experimental data..................................................................................... 118

7.4 I NITIATION OF MEANDERING ...................................................................................................... 118 7.4.1 Historical background .......................................................................................................... 118 7.4.2 Initiation of meandering in MIANDRAS............................................................................... 120

7.5 MEANDERING AND BRAIDING .................................................................................................... 124 7.5.1 Introduction .......................................................................................................................... 124 7.5.2 Previous work....................................................................................................................... 124 7.5.3 A new predictor .................................................................................................................... 126

7.6 POINT BAR SHIFT AND MEANDER GROWTH ................................................................................. 132 7.6.1 General case......................................................................................................................... 132 7.6.2 Non-damped system with negligible spiral flow................................................................... 135 7.6.3 Effects of damping ................................................................................................................ 136 7.6.4 Effects of helical flow ........................................................................................................... 139 7.6.5 Combined effects................................................................................................................... 140

7.7 COMPARISON WITH OTHER CLASSES OF MEANDER MIGRATION MODELS .................................... 142 7.7.1 No-lag kinematic model........................................................................................................ 142 7.7.2 Ikeda-type model................................................................................................................... 143

7.7.3 MIANDRAS........................................................................................................................... 143 7.7.4 Longitudinal profile of near-bank water depth..................................................................... 144 7.7.5 Initiation and further developments of meanders ................................................................. 145

8 NUMERICAL ASPECTS ............................................................................................................... 149 8.1 NUMERICAL IMPLEMENTATION .................................................................................................. 149

8.1.1 Basic equations..................................................................................................................... 149 8.1.2 Numerical scheme................................................................................................................. 152 8.1.3 Model calibration ................................................................................................................. 156 8.1.4 Computation of the channel centreline curvature................................................................. 159


15/267

Contents

x i

8.1.5 Regridding ............................................................................................................................ 160 8.2 STABILITY OF COMPUTATIONS : TIME STEP VS . SPACE STEP ........................................................ 161 8.3 EFFECTS OF SMOOTHING AND REGRIDDING IN MEANDER MIGRATION MODELS .......................... 162 8.4 EFFECTS OF BOUNDARY CONDITIONS ......................................................................................... 167

8.4.1 Steady-state computations .................................................................................................... 167 8.4.2 Computations with time adaptation...................................................................................... 171

9 FIELD APPLICATIONS................................................................................................................ 179 9.1 I NTRODUCTION .......................................................................................................................... 179 9.2 LOCAL MIGRATION RATES AND CHANNEL CURVATURE .............................................................. 185 9.3 VARIATION OF AVERAGE MIGRATION RATES WITH INCREASING RIVER SINUOSITY ..................... 191 9.4 PREDICTION OF PRESENT MORPHOLOGICAL TRENDS OF THE R IVER GEUL (THE NETHERLANDS ) 194

9.4.1 General description .............................................................................................................. 194 9.4.2 Approach .............................................................................................................................. 197 9.4.3 Results................................................................................................................................... 198 9.4.4 Conclusions .......................................................................................................................... 200

9.5 PREDICTION OF PLANFORM CHANGES OF THE R IVER DHALESWARI (BANGLADESH ).................. 200 9.5.1 General description .............................................................................................................. 200 9.5.2 Approach .............................................................................................................................. 201 9.5.3 Results................................................................................................................................... 202 9.5.4 Conclusions .......................................................................................................................... 205

9.6 PREDICTION OF PLANFORM CHANGES OF THE R IVER ALLIER (FRANCE )..................................... 206 9.6.1 General description .............................................................................................................. 206 9.6.2 Approach .............................................................................................................................. 208 9.6.3 Results................................................................................................................................... 211 9.6.4 Conclusions .......................................................................................................................... 213

10 CONCLUSIONS AND RECOMMENDATIONS......................................................................... 215 10.1 SCOPE AND MODELLING APPROACH ........................................................................................... 215 10.2 I NITIATION OF MEANDERING ...................................................................................................... 215 10.3 MEANDER WAVE LENGTH .......................................................................................................... 217 10.4 CONDITIONS FOR MEANDERING ................................................................................................. 217 10.5 LAG DISTANCE BETWEEN FLOW VELOCITY AND BED TOPOGRAPHY ............................................ 217 10.6 POINT BAR LOCATION WITH RESPECT TO THE BEND APEX .......................................................... 218 10.7 EFFECTS OF BEND SHARPNESS ON LOCAL MIGRATION RATES ..................................................... 219 10.8 AVERAGE MIGRATION SPEED AND GROWTH OF RIVER MEANDERS ............................................. 220 10.9 NUMBER OF BARS IN A CHANNEL CROSS -SECTION ..................................................................... 220 10.10 MODEL APPLICABILITY .......................................................................................................... 221 10.11 NUMERICAL EFFECTS ............................................................................................................ 222 10.12 ASSUMPTION THAT BED SLOPE EQUALS VALLEY SLOPE DIVIDED BY SINUOSITY .................... 222 10.13 M IGRATION COEFFICIENTS .................................................................................................... 223 10.14 R ECOMMENDATIONS FOR FUTURE RESEARCH ON BANK ACCRETION ...................................... 224

REFERENCES...........................................................................................................................................227

LIST OF MAIN SYMBOLS......................................................................................................................247

CURRICULUM VITAE............................................................................................................................251


16/267

Contents

x i i


17/267

Introduction

1

1 Introduction

1 1 Rationale

The planimetric evolution of meandering rivers, characterized by the progressive growth and shiftof river bends and by the occurrence of bend short cuts, is one of the primary river planform

phenomena. It is not only scientifically interesting and relevant to natural rivers, it is also an issuein river training and reservoir geology. Despite significant scientific progress in recent decades,an established practice applying simple and easy-to-use morphological models to predict large-scale river planimetric changes is still lacking. Such models are key to progress in theunderstanding of this planform phenomenon and these are necessary tools to interpret and upscaleresults from more complex models, which are bound to cover only relatively small river reaches.

This thesis examines non-tidal meandering rivers, with special emphasis on their large-scale

medium- to long-term planimetric changes. This spatio-temporal scale is referred to as theengineering scale. The aim is to increase the understanding of the fundamental processes ofriver planform evolution by filling in several knowledge gaps in this field. The work includes thedevelopment of a numerical model for the simulation of the medium- to long-term evolution ofmeandering rivers, MIANDRAS. Together with experimental and field data, this modelconstitutes the main tool for the analyses carried out.

Why concentrate on meandering rivers?

Because meandering is the most common riverplanform style in populated areas

Meandering rivers have single-thread channels with high sinuosity and almost constant width.They could be regarded as a particular type of braided rivers [Murray & Paola, 1994], in whichthe multiple-thread channel has reduced to single-thread. Why focus on this particular type ofriver? The reasons are manifold.

First of all, natural meandering rivers are mainly found in large fertile valleys, the most valuablezones for agriculture and human settlement, which are often under demographic and economic pressure. The result is that the river floodplains are progressively occupied by settlements andindustry [Muhar et al., 2005]. This makes flood control and the control of bank erosion andmeander migration of essential importance. In many European countries, as for instance the

Netherlands, Italy and France, after a long period in which single municipalities could decidewhere to plan settlements without any basin-wide coordination, it is now recognized that reducingthe active river bed by occupying the floodplains and raising levees is not sustainable on the long-


18/267

Introduction

2

term. Ever further encroachment of floodplains leads to even higher flood levels, but leveescannot be raised indefinitely. Therefore, a new land-use policy allowing more space for the riveris required. The most recent management approaches [Silva et al., 2004; Ercolini, 2004]introduced the concept of river corridor or streamway with the slogan: free space to the river[Malavoi et al., 1998 and Malavoi et al., 2002]. The river corridor is an artificially maintained,

regularly flooded, alluvial belt where the river is allowed to erode its banks, in a controllednatural state. Uncontrolled bank erosion could affect valuable land, whereas free meanderingcould affect river navigability. For these reasons, the knowledge of bank erosion processes,meander evolution and cut-offs is of essential importance for the design of such corridors [Pigayet al., 2005; Larsen et al., 2006]. Besides, natural gradients in water depth, flow velocity andsediment composition, due to the presence of oxbow lakes, pools, point bars and vertical eroding

banks, have proved to be of great importance for the river corridor ecology [Ward & Stanford,1995]. A deep knowledge of river morphodynamic processes is therefore needed for both designand maintenance of river corridors, as well as for the assessment of the long-term impact ofimportant river training works, such as the fixing of a river bend or the creation of an artificialcut-off.

A second reason to focus on meandering rivers is that human interventions have mademeandering the most common river planform style in developed areas. For example, the DanubeRiver downstream of Vienna used to be braided, but is now limited to a single-thread meanderingchannel. Like the Danube, most piedmont rivers are increasingly assuming a meandering

planform. Damming, canalisation and the widely practiced extraction of sand and gravel fromriver beds are the major causes of the transformation [Cencetti et al., 2004; Surian & Rinaldi,2003; Pigay et al., 2000 and 2006]. In Europe, this phenomenon is enhanced even further by therecent depopulation of rural and mountain areas, which favoured new forest growth anddiminished the sediment supply to the rivers, causing river incision [Pigay & Salvador, 1997;Libault & Pigay, 2002].

Finally, parks and restoration projects are preferably designed with single-thread sinuous riversand models are developed for re-meandering of canalised streams [Abad & Garcia, 2006].Sociological aspects also play a role in turning braided into meandering rivers. The publicappears to prefer meandering to braiding [Parker, 2004; Pigay et al., 2006] and, for this reason, asinuous single-thread channel is often imposed in river restoration works. In the USA, some riverrestoration projects are reported to have failed, because newly restored meandering rivers soon re-transformed in braided systems [Kondolf & Railsback, 2001]. This shows once more theimportance of understanding why rivers meander and under which conditions.


19/267

Introduction

3

The main tool used for the analyses carried out in this study is the mathematical and numericalmeander migration model MIANDRAS. This is a one-line model based on a quasi-2D descriptionof the flow field and channel-bed topography along with a bank erosion-accretion equation. Itwas developed in the earlier phases of this study [Crosato, 1987, 1989, 1990].

Why use a relatively simple model like MIANDRAS asthe main tool to examine river meandering?

Why? Lets discuss.

At the start of the third millennium, models simulating river morphodynamics have reached ahigh level of complexity. Models such as Delft3D [Lesser et al., 2004], MIKE21

[www.dhigroup.com] and SSIIM [Olsen, 2003] can simulate water flow and sediment transport intwo and three dimensions, while also computing the bed level changes. They describe manycomplex mechanisms, such as the spiral flow in river bends and graded sediment transport, butthese are coupled to crude bank erosion formulations. Physics-based bank erosion models have

been included in two-dimensional models, such as RIPA [Mosselman, 1992] and MRIPA(modified RIPA) [Darby & Thorne, 1996a], but these models do not treat the processes of theaccreting bank with the same degree of complexity. MIANDRAS has a better balance betweenwater flow, sediment and river bank dynamics. Besides, all available multi-dimensional modelsdo not include the process of bank advance, which results from the stabilization and verticalgrowth of near-bank deposits and is governed by riparian vegetation and soil consolidation. Bankadvance is one of the basic processes of river meandering, together with bank retreat. This

omission strongly restricts the usefulness of these models for the study of the planimetric changesof meandering rivers.

The present study focuses on large-scale medium- to long-term topographic changes ofmeandering rivers, i.e. the changes of several meanders occurring in the time-span of decades orcenturies. For this type of study, models that are more complex do not perform any better and donot necessarily decrease the uncertainties. MIANDRAS has proved to be particularly suitable foranalysing the behaviour of meandering rivers at large spatial and temporal scales. Its simplifiedmathematical description allows finding analytical solutions for some specific conditions, such asinitiation of meandering, equilibrium bed topography and point bar position, which providesinformation on the way processes are reproduced by the model. Numerical analyses can therefore

be coupled to mathematical analyses. More complex models make the analysis of some large-scale phenomena either impossible, by lack of appropriate equations describing bank erosion andaccretion, or more difficult.

When compared to MIANDRAS, many of the most recent meander migration models still containmore simplified descriptions of the underlying physical processes [e.g. Lancaster, 1998; Abad &Garcia, 2005; Coulthard & van de Wiel, 2006]. The most sophisticated ones [e.g. Sun et al., 1996;Zolezzi & Seminara, 2001] do not surpass MIANDRAS, which means that this model is still at


20/267

Introduction

4

the forefront of meander migration modelling, although equivalent models have becomeavailable.

Finally, models of different complexity can be obtained by applying different degrees ofsimplification to the basic equations of MIANDRAS, which allowed using the numerical code

developed in the framework of this study to analyse the behaviour of entire classes of meandermigration models [Crosato, 2007a and 2007b]. This proved to be helpful for the definition of thefactors governing certain aspects of meandering river behaviour.

1 2 Background of the study

At the start of the project (1987), many key aspects of meandering rivers were in the process of being discovered. An example is the discovery of the overshoot phenomenon by the Delftschool in 1983 [De Vriend & Struiksma, 1984; Struiksma et al., 1985]. Modelling the interaction

between flow and morphology in curved channels was found to give rise to a local overshoot ofthe lateral bed slope at the entrance of river bends and to a steady river bed oscillation indownstream direction. De Vriend & Struiksma were particularly concerned with the overshoot of

point bar elevation for river navigation and called their discovery overshoot phenomenon . Theother side of the coin is that the phenomenon causes extra pool depth at the other side of the river,which may destabilise the river bank. Therefore, the phenomenon was called overdeepening bythe Minnesota school [Johannesson & Parker, 1988]. Resonance , a situation in which bars and

bends in sinuous channels have the tendency to grow indefinitely in time and along the river, wasdiscovered by the Genoa school [Blondeaux & Seminara, 1984 and 1985]. Overshoot,overdeepening and resonance are different aspects of the same phenomenon: the free response ofthe river system to flow disturbances. Resonance occurs when this free response has the form of anon-damped oscillation and has the same wavelength as the developing meanders that act asforcing factors. The years that followed where characterized by ordering [Parker & Johannesson,1989; Mosselman et al., 2006] and by field and laboratory experiment to study the phenomenon.

This work initially aimed at testing Olesens idea [1984] that the overshoot phenomenon, byinfluencing the river bank erosion, can cause straight rivers to meander. The origin of meanderingwas at that time attributed to:

The development of small perturbations of the (straight) channel bed into migratingalternate bars, theory known as bar instability [Hansen, 1967; Callander, 1969;Engelund, 1970 and 1975; Parker, 1976].

The lateral growth of infinitely small river bends, theory known as bend instability [Ikeda, Parker & Sawai, 1981].

The resonance phenomenon [Blondeaux & Seminara, 1985]. The overshoot phenomenon (steady perturbation of flow and river bed caused by

upstream disturbances) [Olesen, 1984]. Large scale turbulence [Yalin, 1977].

A sinuous planform was shown to develop from a perfectly straight channel with an upstreamdisturbance with the mathematical model developed in the framework of this study, MIANDRAS


21/267

Introduction

5

[Crosato, 1989] and, with a similar model, by Johannesson and Parker [1989], which confirmedthat the overshoot/overdeepening phenomenon can cause meandering. This discovery, however,did not exclude other causes. Besides, theories on initiation of meandering may explain why awater course tends to become sinuous, but river meandering is more than that. All theories focuson bank erosion and bank retreat rates and do not define the conditions for the opposite bank to

advance with the same speed. Nevertheless, it is just this phenomenon which makes thedifference between braiding and meandering (Figure 1.1). A meandering river requires that in thelong term the bank retreat rate is counterbalanced by the bank advance rate at the other side. If

bank retreat exceeds bank advance, the river widens and at a certain point, by forming central bars or by cutting through the point bar, assumes a multi-thread planform. If bank advanceexceeds bank retreat, the river narrows and silts up. As a consequence, the bar and bendinstabilities and the overshoot/overdeepening phenomenon create the conditions for the flow to besinuous and not straight, but they are not sufficient to impose a meandering planform to the river.

Figure 1.1. A sinuous water flow isnot sufficient for meandering.

A: straight river planform with bankretreat, but without bank advance.

B: meandering river planform inwhich bank advance counterbalancesbank retreat.

All existing meander migration models, including MIANDRAS, assume retreat and advance ofopposite banks to occur at the same rate. This is a necessary statement to simulate meanderingriver migration, but does not explicitly take into account all the necessary factors and processesfor that to happen. Moreover, considering that bank advance influences opposite bank retreat, the

bank migration coefficients used by most models, including MIANDRAS, are in fact bulk parameters that incorporate also the effects of the opposite bank.

Bank advance is a complex and little studied phenomenon. This thesis indicates possible ways todescribe this process, with the aim of providing the basis for the development of a meandermigration model that distinguishes and simulates both bank advance and retreat. However, due toa lack of measurements and field observations, this work alone cannot solve the issue and, in

particular, it cannot provide an answer to the difficult question of which are the conditions thateventually lead to river meandering or braiding. Therefore, this work also aims to define aresearch agenda on this topic.

B

A


22/267

Introduction

6

1 3 Objectives

The main objective of the thesis is the analysis and modelling of large-scale, medium- to long-term (engineering scale) phenomena of meandering rivers. Medium- to long-term refers to thetemporal scale of a lateral meander shift that can be scaled with the river corridor width; large-

scale refers to several meanders.In particular the objectives of this study are:

1. To identify the characteristics and processes of meandering rivers (Chapter 2).2. To identify the factors controlling river meandering (Chapter 3).3. To describe the state of the art and identify the knowledge gaps (Chapter 4).4. To develop a mathematical model for the analysis of river meandering (Chapter 5).5. To assess the conditions for the occurrence of the overshoot/overdeepening phenomenon

in flume experiments (Chapter 6).6. To analyse the model behaviour analytically and against experimental data (Chapter 7).7. To identify the predictability limits of the developed model and compare it with other

existing models of different complexity (Chapters 7 and 8).8. To implement the model in a numerical code (Chapter 8).9. To test the numerical model against field data (Chapter 9).10. To explain some specific aspects of river meandering observed in the field (Chapter 9).11. To define a research agenda to fill in the knowledge gaps (Chapter 10).

1 4 General approach

River meandering is first studied by means of an extensive literature review, which is used todescribe:

the processes involved at different spatial and temporal scales; the factors controlling the river planform formation; the state of the art; the knowledge gaps in the field.

The thesis further focuses on large spatial and medium-long temporal scale phenomena, such asmeander migration, bend growth and changes of river sinuosity. In order to be able to study these

processes, an appropriate mathematical and numerical model is developed. The model basicallydescribes the location of the channel axis as a function of time, taking into account the effects of

both the overshoot/overdeepening phenomenon and the channel centreline curvature on flow

field, river bed topography and bank advance or retreat. This is obtained by coupling themomentum and continuity equations for curved water flow with a sediment transport formula anda sediment balance equation. Considering that the channel migration is a relatively slow

phenomenon, the bank erosion rate is related to the equilibrium near-bank flow characteristics. Incase of variable discharge, the model takes into account the time scale of the bed development.The model is constructed in such a way that, by applying different degrees of simplification to the

basic equations, three meander migration models of different complexity can be obtained:


23/267

Introduction

7

A no-lag kinematic model, in which the bank retreat is directly linked to the local channelcentreline curvature, without any space lag. Existing kinematic models impose anempirical space lag between the migration rate and the channel curvature in order to takeinto account downstream migration of meanders [e.g. Ferguson, 1984; Howard, 1984;Lancaster & Bras, 2002]. The derived no-lag kinematic model does not include this

feature. An Ikeda-type model (after Ikeda et al. [1981]), in which the space lag between bank

retreat and channel centreline curvature is obtained from the momentum and continuityequations of water, leading to a term accounting for the longitudinal adaptation of thenear-bank flow velocity. For certain aspects, this model can be considered representativealso for the models of Abad & Garcia [2006] and Coulthard & van de Wiel [2006].

MIANDRAS, which includes also the longitudinal adaptation of the water depth througherosion and sedimentation. It is therefore able to reproduce the overshoot/overdeepening

phenomenon, i.e. the formation of a steady harmonic response of the bed topography andthe flow downstream of disturbances. For several aspects, this model can be consideredrepresentative of the models of Johannesson & Parker [1989], Howard [1992], Sun et al.

[1996] and Zolezzi & Seminara [2001].

Experimental tests are carried out to define the conditions for the overshoot/overdeepening phenomenon and the equilibrium bed topography in case of upstream flow disturbances. Themodel behaviour is assessed by means of comparisons between model results and experimentaldata and by performing analytical studies. The mathematical model is finally implemented in anumerical code allowing distinguishing the three meander migration models of differentcomplexity. Several numerical tests are carried out to study the performances of the three modelsin complex situations for which analytical studies cannot be carried out, with the aim of studyingthe effects of simplifications. Some aspects of river meandering as well as the influence ofnumerical schematisations are studied by comparison between these three models. Finally, several

rivers, and in particular the Geul (the Netherlands), the Dhaleswari (Bangladesh) and the Allier(France), are used as case studies to assess the capability of MIANDRAS to reproduce the

behaviour of real rivers. The following aspects of river meandering receive special attention:

initiation and further development of meanders; point bar location with respect to the bend apex at varying conditions; lag distance between flow velocity and bed topography; effects of increasing bend sharpness on local migration rates; average river migration speed in relation to the growth of river meanders; number of bars in a channel cross-section; knowledge gaps.

The following aspects of meander migration modelling receive special attention:

applicability of the developed model; ability to reproduce the physical behaviour of meandering rivers; calibration coefficients; numerical effects.


24/267

Introduction

8


25/267

General aspects of meandering rivers

9

2 Meandering rivers

2 1 Introduction

This chapter provides an introductory description of meandering alluvial rivers and the main processes that characterize them. Meandering rivers are first presented in the context of all river planform styles. The underlying mechanisms of water flow, sediment transport, bank erosion and bank accretion are introduced in a descriptive, phenomenological manner only. Chapter 3discusses the role of these mechanisms as factors that determine whether a river assumes ameandering planform or not, whereas subsequent chapters deal with the modelling of theunderlying mechanisms.

2 2 Meandering and other planform styles of alluvial riversAlluvial rivers exhibit a large variety of planform styles. There are rivers with several conveyingchannels, separated by ephemeral sediment deposits or almost permanent islands, and riversformed by a single channel. Different planform styles can even be observed along the same watercourse because the morphology of a river continuously evolves along the way from the mountainsto the sea.

In the upper parts rivers generally have an irregular planform, which is mainly controlled by thelocal geology. The river bed consists of coarse sediment, such as gravel, cobbles and boulders.The longitudinal bed level profile is characterized by an alternation of deep and shallow parts,

named pools and riffles or runs . The shallow parts are called riffles if the water surface is rough(white water) and runs if the water surface is smooth.

Where the valley slope becomes milder (approximately less than 4%) rivers generally assume a braided planform. The water flows through several branches, or braids , within the bank lines of asingle (multi-thread) broad channel (Figure 2.1). Ephemeral islands, formed by large sedimentdeposits, separate the braids. The river bed is often formed by coarse-grained sediment, such asgravel and sand. Usually, the banks also consist of coarse-grained sediment, but sometimes have acohesive top layer. Once this is eroded or undermined by the river flow, banks and river bed

behave in a similar way. As a consequence, the topography of a braided river can change rapidly,the channel may widen and one braid may be abandoned and replaced by a new one in the time-

span of a single flood event.


26/267


1 0

Figure 2.1. Braided planform (multi-threadchannel): Tsang Po in China (Image: Scienceand Analysis Laboratory, NASA-JohnsonSpace Center).

Braided rivers are typical of piedmont areas. Further downvalley, rivers tend to have a moreregular planform. They are anabranched (or anastomosed ) (Figure 2.2), if they are split intoseveral channels; meandering, if the water flows through one single channel. In anabranchedrivers each anabranch is a distinct, rather permanent, channel with distinctive bank lines. Theriver bed is mainly constituted by loose sediment, such as sand and gravel, whereas silt prevails atthe inner parts of bends and where the water is calm. Anabranches are generally formed withindeposits of fine material. Vegetation and soil cohesiveness stabilize the river banks and theislands separating the anabranches, so that the planimetric changes are slow if compared to theriver bed changes. The presence of a rich vegetation cover enhances the deposition of finesediment, mainly silt and clay, on the flood plains, contributing to the (slow) rise of the alluvial

plains and to the cohesiveness and fertility of the soil around the river.

Figure 2.2. Anabranched planform: the Amazon River near Iquitos, Peru (courtesy of Erik Mosselman).

Meandering rivers are mostly found in low-land alluvial plains characterized by a dense

vegetation cover and cohesive soils. They have a single, rather permanent, sinuous channelwithout large longitudinal width variations. A beach, formed by a sediment deposit at the innerside of bends is the active part of the point bar 1 (Figure 2.3). A pool is present at the opposite sideof the channel, where the flow velocity is higher. The outer bank progressively retreats due toerosion and the inner bank accretes, due to sedimentation. In the long term the two processes of

bank retreat and accretion have more or less the same speed and for this reason the channel width

1 When not otherwise specified, the term point bar refers to the active part of the point bar.


27/267


1 1

presents short-time oscillations, but negligible long-term variations. As a result of the interaction between bank retreat and advance, river bends progressively increase in amplitude and migrate(Figure 2.3).

Figure 2.3. Scroll-bars and oxbow lakes on the floodplains and point bars at the inner side of bends (inwhite, covered with snow) in a meandering affluent of the Ob River, Russia (courtesy of Saskia van Vuren).

The old positions of the top of the active parts of the point bars form a system of ridges andswales ( scroll bars ), which can be seen across floodplains (Figures 2.3 and 2.4). The ridges thatmark the scroll bars are formed by the natural levees that are built during floods when the watercomes out of its confined channel and sediment is deposited near the channel edge [Pizzuto,1987]. The swales are related to the sediment deposits that are formed during lower flow stages.Meander translation and growth continue until the flow cuts the bend short ( neck cutoff ). At first,only a fraction of the flow crosses the bend neck, but this fraction progressively increases andeventually the old course is abandoned. At this point, the old channel forms an oxbow lake

(Figure 2.3), which gradually silts up and disappears. The occurrence of cutoffs limits meandergrow, so that the river is seen to migrate in a confined area, which is usually referred to as themeander belt , the river corridor or the river streamway .

point bars

oxbow lake

scroll bars


28/267


1 2

Figure 2.4. River Allier (France).Scroll bars are visible onthe point bar (courtesy of

Erik Mosselman).

Close to the sea the river can split into several channels forming a delta, as the Po in NorthernItaly, or remain concentrated in a single channel forming a funnel-shaped estuary, such as the

Severn in the United Kingdom. Sometimes the river forms a combined delta-estuary, such as theScheldt in the Netherlands. In this zone the river is influenced by the sea, which introduces tides,storm surges and salt intrusion in the system. Natural river banks are often fronted by marshvegetation. The formation of a delta rather than an estuary is governed by many factors, such asthe local geology and the tidal characteristics, and not only by the river characteristics [Roy,1984].

2 3 Planimetric characteristics of meandering rivers

2 3 1 Channel sinuosityThe sinuosity of meandering rivers is defined as the ratio between the length of the rivermeasured along its thalweg (line of maximum depth, Figure 2.5) or along its centreline, and thevalley length between the upstream and downstream sections [Rust, 1978]:

0

T LS L

= (2.1)

where:S = river sinuosity (-)

LT = the distance between start and end point of the considered river reachcomputed along the thalweg or along the channel centreline (m)

L0 = the valley length between the same start and end point (m).

According to Brice [1984] meandering rivers have a sinuosity larger than 1.25; according toLeopold et al. [1964] and Rosgen [1994] the lower limit is 1.5. To visualize the physical meaningof these values it can be useful to consider that a river planimetry made up of a series of oppositesemicircles has sinuosity equal to / 2 =1.57.


29/267


1 3

Figure 2.5. Typical meandering river cross-sections (dotted line = river thalweg).

2 3 2 Size of meanders

According to Leopold et al. [1964] a meander consists of a pair of opposing loops, but in

common practice also a single river bend is often called meander. In this study a meander is asingle river bend.

It is generally accepted that a relationship exists between size of rivers and size of their meanders[Jefferson, 1902; Bates, 1939; Leopold & Wolman, 1960]. Fergusson [1863] stated: All riversoscillate in curves, whose extent is directly proportional to the quantity of water flowing throughthe rivers. Laboratory experiments by Friedkin [1945] indicate that the size of meanders isinfluenced by the hydraulic river regime, the sediment, the valley slope and the boundaryconditions. According to Leopold & Wolman [1960], the meander wavelength is proportional tothe channel width, which is in turn determined by hydraulic river regime, sediment and valleyslope. They found that the proportionality coefficient is equal to approximately 10.9, whereas

Garde & Raju [1977] indicate a value of approximately 6. If the meander wavelength is computedalong the channel centreline the relation becomes:

(10.9 or 6) M L SB= (2.2)

in which S is the channel sinuosity and B the channel width.

A

A

B

B

C

Csection A-A

section B-B

section C-C

point bar

pool

thalweg

R c

More or lessrectangular

More or lesstriangular


30/267


1 4

Many theories have been developed to predict the wavelength of meanders at their initial stage,i.e. for S = 1. Hansen [1967] used a stability model and obtained:

2

0

7 M b

L Fr h i

(2.3a)

where:

L M = incipient meander wavelength (measured along the channel) (m) ib = channel bed slope (-)

Fr = Froude number:0

0r

u F

gh= (-)

0u = reach-averaged flow velocity (m/s)

0h = reach-averaged water depth (m)

g = acceleration due to gravity (m/s 2).

Anderson [1967] analysed transverse oscillations of the flow and obtained the following formula(later improved by Parker [1976]):

0

72 M L

Fr Bh

= (2.3b)

Based on the idea that the wave length of incipient meanders coincides with the wave length ofsteady alternate bars rather than with the one of migrating bars [Olesen, 1984], Struiksma &Klaassen [1988] suggested using Crosatos [1987] model for the wave number of steady alternate

bars as a predictor for the wave number of incipient meanders (Section 7.4.2). The wavelengthsof the steady alternate bars that develop downstream of flow disturbances are two to three timeslarger than the wavelengths of migrating bars (Sections 6.3 and 6.4) and agree better withobservations [Olesen, 1984].

2 3 3 Size of the meander belt

Camporeale et al. [2005] define the meander belt (or the river corridor) as the proportion offloodplain having 90% probability of containing the river channel during its long-term evolution.Based on the analysis of 44 rivers they found that the width of the meander belt is approximately40 to 50 times the flow adaptation length, W :

(40 50) W W = (2.4)

where:W = meander belt, or river corridor, width (m)


31/267


1 5

0

2W f

hC

= = flow adaptation length [de Vriend & Struiksma, 1984]

2/ f C g C = = friction factor (-)

C = Chzy coefficient (m 1/2/s).

2 3 4 Bend sharpness

The bend sharpness is represented by the ratio of bankfull channel width, B, to radius of curvatureof the channel centreline Rc:

c

B R

= (2.5)

Where is the curvature ratio (-).

Mildly curved bends are characterized by Rc >> B, so that the value of has order of magnitude(0.1)O or smaller. In sharp bends, the radius of curvature can be as small as 1.5 to 3 times the

channel width, so that the value of can have order of magnitude (1)O .

2 3 5 River width

Meandering rivers are characterised by a relatively uniform river width, which can be considered

constant in the long-term.The cross-sectional shape of a river depends on the bed level changes and on the oppositemechanisms of bank erosion and accretion [Parker, 1978; Mosselman, 1992; Allmendiger et al.,2005]. Bank accretion has the effect of decreasing the channel width, whereas bank erosion hasthe opposite effect. Therefore, the equilibrium river width is reached only if bank erosion andopposite bank accretion counterbalance each-other. In this case the river width does not presentany long-term trends (narrowing or widening), although it may still present short-termoscillations. Due to bank retreat and advance the river shifts laterally (Section 2.8).Some meandering rivers are wider inside river bends and narrower in the straight reaches betweenopposite bends. This can be caused by the fact that bank erosion and opposite bank accretion donot occur at the same time, but they alternate (Figure 2.6). In particular, bank erosion occurs

during or just after flood events (Section 2.8.2), whereas bank accretion occurs at high flowstages (deposition) and low flow stages (consolidation and vegetation cover) and is often muchslower (Section 2.8.3).


32/267


33/267


1 7

Free bars originating from the instability phenomenon tend to migrate; those originating fromupstream disturbances, such as a change of channel geometry, do not migrate. Free bars aretherefore distinguished in free migrating bars and free steady bars . The two types of bars,migrating and steady, can co-exist.Large channel curvatures transform free migrating bars into point bars [Tubino & Seminara,

1990]. Migrating bars are therefore only found in mildly-curved or straight river reaches, whichmeans that well-developed meanders mainly present point bars and free steady (alternate) bars (Figure 2.7). Free bar celerity tends to decrease with the increase of the channel width [Seminara& Tubino, 1989b].

Figure 2.7. Steady alternate bars, neck cutoffs and oxbow lakes in the Alatna River, at the Gates of the Arctic National Park, Alaska (www.terragalleria.com).

Due to the presence of point bars, the shape of the cross-sections in meandering rivers variesalong the axis in a typical way:

In the straight reaches between opposite loops, the channel cross-section is more or lessrectangular (Figure 2.5, section B-B).

Inside bends, the channel presents a pool near the outer bank and a large sedimentdeposit, constituting the active part of the point bar, at the inner bend. This gives a moreor less triangular shape to the cross-section (Figure 2.5, sections A-A and C-C).

Due to this configuration of the river bed the thalweg , or line of maximum depth, goes from one bank to the other, crossing the channel in the straight reaches between two loops (Figure 2.5) atthe inflection points, i.e. where the channel curvature changes sign. A beach at the inner side of

bends is the visible part of the point bar, when the water discharge is low (Figure 2.3).


34/267


1 8

Bend entrances, being a change of the channel curvature a disturbance altering the flow, mayinduce the formation of free steady bars. This results in a bed oscillation superimposed upon the

point bar, causing local increases and decreases of the transverse bed slope along river bends. Forthis reason the phenomenon is known as overshoot phenomenon (after Struiksma et al. [1985])or overdeepening phenomenon (after Parker & Johannesson [1989]) (Section 7.2). In very wide

rivers these free steady bars may develop also upstream of disturbances [Zolezzi & Seminara,2001].

2 5 Discharges

The hydrological regime of meandering rivers depends on the location and size of their basin, butin general, as most meandering rivers are low-land rivers, it is rather regular, with typical floodseasons and high flows of one or more days.

Although the river shape results from the cumulative effect of the discharge hydrograph on theriver morphology, the existence of a formative discharge would be very convenient for riverengineering studies. This would be the value of the discharge causing the same rivermorphological development as the entire discharge hydrograph.

In the course of history the formative discharge has received many different definitions. Highdischarges with a return period of more than one year represent the formative condition for theriver morphology for Wolman & Miller [1960], Ferguson [1987], Peart [1995] and Schouten et al.[2000]. Antropovskiy [1972] adopts the mean annual flood and Bray [1982] the median annualflood discharge, whereas Vogel et al. [2003] suggest that the formative discharge may have return

periods of several years to decades. Biedenharn & Thorne [1994] consider the formativedischarge as the one that transports most sediment: lower discharges have lower transportcapacity; higher discharges have lower frequencies of occurrence. Finally, according to Leopold& Wolman [1957], Ackers & Charlton [1970a], Fredse [1978], Hey & Thorne [1986] and vanden Berg [1995] the formative condition is the flow at bankfull discharge , which occurs when thewater fills the entire channel cross-section without significant inundation of the adjacent flood

plains. The concept of bankfull discharge is convenient for meandering rivers, but not for riverswith a multiple-thread channel, for which it is difficult to define what bankfull is.The main reason why a single formative discharge cannot exist is that in most cases differentdischarge levels contribute to the channel formation in different ways [Nanson & Hickin, 1983;Ferguson, 1987; Church, 1992]. Moreover, Prins & de Vries [1971] have proven theoretically thatthis concept cannot be accurate, because different morphological variables depend in differentnon-linear ways on discharge, so that each morphological variable would need a differentformative discharge. Yet, as a first approximation, a single condition might be identified as therepresentative of the river flow strength and that condition might well be, for meandering rivers,the bankfull discharge. The major implication of doing so is the abandonment of the idea ofmodelling bank accretion, since this process strongly depends on water level variations (seeSubsection 2.8.3).One way to determine the value of the bankfull discharge is by means of direct measurements ofthe flow. However, since bankfull flow is not a frequent condition, this method may be not

practical. A better method is based on the use of stage-discharge curves for a location near the


35/267


1 9

reach of interest. When only discharge time series are available, the bankfull condition can berepresented by the discharge having recurrence of 1.5-2.0 years [Williams, 1978; Parker, et al.2007]. However, in the absence of hydrological data the bankfull discharge could be derived byeither applying the laws for uniform flow conditions, knowing the channel geometry andimposing a reasonable value to the friction coefficient [e.g. Chzy, 1776 (pp. 247-251 of Mouret

1921); Manning, 1889], or using regression relations, based on the observation of a large numberof rivers [Parker el al., 2007].

2 6 Sediment

Through abrasion and selective transport, sediment tends to become finer from the mountains tothe sea [Parker & Andrews, 1985; Parker, 1991; Seal et al., 1998; Ferguson et al., 1998; Gaspariniet al., 1999]. The upper reaches are characterized by gravel and cobbles, the middle reaches bysands. Fine and cohesive sediment, silt and clay, is especially found in the lower river reaches, onthe floodplains and in the delta areas. Therefore, most meandering (low-land) rivers have sandy tosilty river beds, while gravel is characteristic for braided (piedmont) rivers. Although theexamples of natural meandering rivers with a gravel bed seem to noumerous, in many of thesecases the river is either at the transition between meandering and braiding or is governed byerosional processes (i.e. incised river).Due to selective transport, in the same cross-section coarser sediment is found where the flowvelocity is higher; finer sediment is present in the sheltered areas and in general where the flowvelocity is lower. Generally, river bends present finer sediment (sand) near the depositional bank,on the point bar, and coarser sediment in the pool. However, the capacity of the stream totransport sediment is reduced rapidly as velocities diminish during falling river stages. Lowvelocities are capable of transporting only fine materials in suspension, such as silt and clay.During falling river stages, these fine sediments settle over the coarser deposits that had formedduring the previous higher river stages. These deposits are thinner in the locally high places andthicker in the lower places. As a consequence, during low flow stages fine sediment may bedeposited in the pool, where it forms a layer above that of coarse sediment.The sediment forming the banks of meandering rivers is generally fine and has a high content oforganic material (due to the presence of vegetation). The settling of fine sediment on the point

bars favours vegetation growth (during low-flow stages), which in turn favours the settling of finesediment on the point bar. This feed-back phenomenon is one of the processes responsible for theaccretion of the inner bank of river bends, which is of essential importance to river meandering.

2 7 Bend flow

The water flow in meandering rivers is governed by the succession of opposite bends. It is three-dimensional. Secondary 1 currents are produced by the interaction between the centrifugal force,caused by the curvature of the channel, the vertical gradient of the main flow velocity and the

1 Commonly, primary flow is the water flow that is obtained using a two-dimensional (depth-averaged) model (withor without imposing a vertical flow distribution) and has longitudinal and transverse components. Secondary flowincludes all deviations from this flow and has longitudinal and transverse components.


36/267


2 0

transverse inclination of the water surface layer (leading to transverse pressure gradients)[Rozovskii, 1957; Kalkwijk & de Vriend, 1980; de Vriend, 1981].A simplified way to schematize the flow inside a river bend is based on the hypothesis of aninfinitely long river bend with constant radius of curvature and width (hypothetical case in whichthe river forms a spiral around a vertical axis). In this idealized axisymmetric situation the flow is

said to be fully-developed when it does not change along the river and with time. In this case thehighest velocities are found near the outer side of the bend, the lowest near the inner side [Olesen,1987]. The centrifugal force, caused by the curvature of the flow, drives the flowing watertowards the outer side of the bend, where, for this reason, the water level is higher. This causestransverse pressure gradients, which tend to push the water back, towards the inner side of the

bend. The centrifugal force is higher for the faster water flow near the water surface than for theslower flow near the bed and therefore the combination of pressure head and centrifugal force

produces a transverse current. In the middle of the channel this current is directed outwards in theupper parts of the water and inwards in the deeper parts, near the banks it is vertical, directeddownwards near the outer bank and upwards near the inner bank, resulting in a circulation. Thistransverse circulation, combined with the longitudinal flow, gives rise to the helical flow that is

typical of river bends (Figure 2.8). In case of a mobile bed, sediment is transported towards theinner side of the bend until equilibrium between drag force and gravitational force is found. Thisgives a triangular shape to the cross-section (Figure 2.5), with the shallowest part at the inner side(point bar), and the deepest part at the opposite side (pool). In fully-developed bend flow this(dynamic) equilibrium condition is reached everywhere. Fully-developed bend flow cannotdevelop in real rivers, because the channel geometry is not uniform along the water course. Theentrance of a bend, as every other geometrical change, forces the flow to adapt to the changedchannel geometry. Flow and sediment transport have different adaptations processes, which can

produce steady bars superimposed on the point bars and pools (overshoot/overdeepening phenomenon, see Section 2.4).Due to the longitudinal variation of velocity and bed topography, a thorough description of the

flow in river bends should distinguish between the upstream, central and downstream parts of bends, as well as between mild and sharp curves. For this, refer to Kalkwijk & de Vriend [1980]and Blanckaert & de Vriend [2003 and 2004]. Below the description is limited to general aspectsonly.At the entrance of a river bend, the flow velocity is higher near the inner side than near the outerside, because near the inner side the water level gradient is steeper. Along the bend the centrifugalforce gradually moves the highest velocities towards the outer side of the bend so that thetransverse distribution of flow velocities reverses, with the highest velocity near the outer bendand the lowest velocity near the inner bend. The combination of secondary and main flows formsthe helical flow, as depicted in Figure 2.8. In meandering rivers, downstream of the point havingmaximum curvature the helical flow first grows and then decays. It is gradually replaced by the

new and opposite helical circulation of the bend more downstream.


37/267


2 1

Figure 2.8. Helical flow in a mildly-curved river bend and small width-to-depth ratio. Additionalcirculations might form in strongly-curved bends and large width-to-depth ratios.

Measurements of flow velocity in meandering rivers are reported by Thorne & Hey [1979],Thorne et al. [1995] and Richardson & Thorne [1998]; flume experiments of flow in curvedchannels by Blanckaert & de Vriend [2003, 2004]. The interplay of water flow, sediment transportand bed topography in river bends is described by Dietrich & Smith [1984].

2 8 Channel migration

2 8 1 General descriptionOn the long term, the apparently stationary meanders exhibit planimetric evolution (Figure 2.9),consisting of a combination of translation and extension [Brice, 1984], a phenomenon known aschannel migration or meander migration . The progressive development of the river

planimetry is caused by the two processes of bank erosion and accretion , leading to bank retreat and advance respectively. Sediment is eroded from the outer banks of river bends, causing local

bank retreat, and deposited more downstream, near the inner bank [Friedkin, 1945], where itcontributes to the accretion of the point bar and to bank advance. An important condition forrivers to maintain a meandering planform is that in the long term bank retreat is counterbalanced

by bank advance at the opposite side of the channel. When this does not occur, either the river progressively widens and eventually becomes anabranched or braided or the river progressivelysilts up and disappears.Evidence for meander migration is provided by time sequential bank line diagrams, based onhistorical data [Hooke & Redmond, 1989], and by the presence of scroll bars within the meander

belt, marking the old channel positions (Figure 2.3).

helicalflow

point bar

outer bend

inner bend

longitudinalvelocitycomponent


38/267


39/267


2 3

maximum local migration rates are found to occur at approximately R/B = 2.5 for rivers inWestern Canada [Hickin & Nanson, 1984]. Similar relations were found also for the rivers Allier(France) and Border Meuse (the Netherlands) by De Kramer et al. [2000] (Section 9.2). Themaximum reach-averaged migration rates are found to occur at a sinuosity between 1.6 and 1.9for the Mississippi River [Shen & Larsen, 1988] (Section 9.3).

2 8 2 Bank erosion

Bank erosion is responsible, together with bank accretion, for the migration and growth of rivermeanders. It is caused by two distinct mechanisms [Thorne, 1978]: fluvial erosion andgeomechanical instability. Fluvial erosion regards the entraining of single sediment particles(surface erosion) or of sediment agglomerates (bulk erosion) by the water flow. If the materialforming the bank is cohesive, erosion occurs where the shear stress exerted by the flow exceeds acritical value [Partheniades, 1965; Ariathurai & Arulanandan, 1978; Arulanandan et al., 1980;Winterwerp & van Kesteren, 2004]. For non cohesive sediment, particle entrainment occurs whenthe Shields parameter exceeds a critical value [Shields, 1936]. Geomechanical instability leads to

bank mass failure and usually concerns steep cohesive banks (Figure 2.10). Mass failure occursespecially where the bank is steep, high or undermined by erosion at the toe [Thorne, 1978 and1988; Mosselman, 1992; Darby & Thorne, 1996b; Dapporto et al., 2003]. The material generated

by mass failure ends up on the river bed in front of the bank, where it forms a sediment bufferthat sometimes reinforces the bank. The removal of this material by the flow is called basalclean-out [Wood et al, 2001]. Bank erosion slows down if basal clean-out proceeds slowly, sincethe mass failure products temporary decrease toe erosion.

Figure 2.10. Eroding cohesive bank, Secchia river in North Italy (courtesy Erik Mosselman).

Rapidly eroding banks result in wide shallow cross-sections, whereas slowly eroding banks resultin deep narrow cross-sections [Friedkin, 1945]. According to Friedkin the rate of bank erosionaffects also the longitudinal slope of the river: with resistant banks the slope flattens, whereas


40/267


2 4

with easily eroding banks the slope steepens. This is in agreement with Jansen et al. [1979], whoshow that a wider river requires a steeper slope to transport the same amount of sediment.The rate of bank erosion is influenced by a number of different factors [Thorne, 1978], such as:

Near-bank flow strength [Ikeda et al., 1981]

Near-bank channel bed degradation [Thorne et al., 1981; Andrews, 1982], whichincreases the bank geomechanical instability Opposite bank accretion, which pushes the main flow towards the eroding bank [Dietrich

& Smith, 1984; Mosselman et al., 2000] Physical characteristics of the eroding bank: geometry (slope and height) [Thorne, 1978;

Dapporto et al. 2003], soil composition [Wolfert & Maas, 2007], soil cohesion[Partheniades, 1962; Krone, 1962;] and bulk density of the bank material [Simon &Hupp, 1992]

Presence and type of riparian vegetation [Macking, 1956; Wynn et al., 2004] Ground water flow [Darby & Thorne, 1996b; van Balen, personal communication] Pore water pressure [Dapporto et al., 2003; Rinaldi & Casagli, 1999

Documents

Rios Meandricos