hooke 2013

9.16 River MeanderingJM Hooke, University of Liverpool, Liverpool, UK

r 2013 Elsevier Inc. All rights reserved.

9.16.1 Introduction 260
9.16.2 Research Phases and Topics 262 9.16.3 Approaches and Methods 264 9.16.3.1 Empirical Approaches 264 9.16.3.1.1 Field measurements and observations 264 9.16.3.1.2 Map and remote sensing evidence 265 9.16.3.1.3 Techniques of meander morphology and change analysis 265 9.16.3.2 Theoretical and Numerical Modeling Approaches 265 9.16.3.2.1 Experimental modeling 267 9.16.4 Empirical Evidence and Analysis 268 9.16.4.1 Morphology 268 9.16.4.2 Morphological Change 269 9.16.4.3 Meander Processes 272 9.16.4.3.1 Flow patterns and sediment movement 272 9.16.4.3.2 Bank erosion 275 9.16.4.3.3 Deposition and bar formation 275 9.16.4.4 Bedrock and Incised Meanders 276 9.16.4.5 Spatial Distribution and Controls on Characteristics 276 9.16.5 Theoretical and Conceptual Explanations 277 9.16.5.1 Fundamental Physical and Numerical Analyses 277 9.16.5.2 Conceptual Analyses 279 9.16.5.3 Experimental, Modeling and Numerical Analysis Results 280 9.16.6 Perspective and Synthesis 281 9.16.6.1 Future Research 282 9.16.7 Conclusions 282 References 283
Hooke,

Wohl, E

CA, vol.

260

Abstract

Various phases of progress and differing approaches to research on river meandering are identified. Since early quantifi-cation of equilibrium relations of meander morphology to discharge and sediment, research has been pursued empirically,

theoretically, and experimentally. The theoretical approaches have sought to provide fundamental explanations of meander

development and produced numerical simulations. Empirical work, using field, map, and air photo evidence, has dem-

onstrated variations in meander morphology, and stability and the evolution of meanders over time to compound formsand cut-offs; it has elucidated process mechanisms and interactions. Flume work has investigated the effects of particular

conditions. Research using these differing approaches is now converging.

9.16.1 Introduction

Meandering rivers are single channels with a sinuous plan-

form comprising a series of loops, frequently depicted as

regular and simple in form and size, but in reality often having

some irregularity, asymmetry, and complexity (Figure 1). They

are differentiated from braided channel patterns, which have

multiple channels or multiple free bars within the course, and

straight channels, which have very low sinuosity, though this

lower limit of meandering is somewhat arbitrary. Thresholds

J.M., 2013. River meandering. In: Shroder, J. (Editor in Chief),

. (Ed.), Treatise on Geomorphology. Academic Press, San Diego,

9, Fluvial Geomorphology, pp. 260–288.

Treatise on Geomo

and conditions for development of different types of pattern

have been much investigated. Meandering courses are found

not only in fluvial rivers and in bedrock channels but also in

tidal flows, on glaciers, in oceanic currents, and in submarine

and Martian environments. This implies intrinsic character-

istics of fluid flows, but debate still surrounds the basic

question of why rivers meander. Discussion in this chapter is

confined to fluvial flows in rivers.

Meandering rivers are ubiquitous on the Earth and are the

most common type of channel pattern. They have long been a

source of fascination and esthetic delight (Figure 1) so curiosity

as to their formation and processes of development has driven

much research. Many meandering channels are mobile, with

the meander forms migrating downstream and the channels

rphology, Volume 9 http://dx.doi.org/10.1016/B978-0-12-374739-6.00241-4

(a)

(b)

(c)

(d) (g)

(f)

(e)

Figure 1 Photographs illustrating the characteristics and variability of meander morphology, Images (a)–(c) US National Fish and WildlifeService; Images (d)–(k) Google Earth; Images (l)–(n) J M Hooke.

River Meandering 261

shifting in position within floodplains, producing significant

contribution to landscape change. This occurs on varying

timescales but, where rates of movement are high, it can cause

practical problems for riparian activities and structures. Thus,

much research has also been driven by the practical need to

understand the processes, rates, and patterns of movement and,

if possible, to develop methods of predicting meander move-

ment. Their sensitivity means they are also important indicators

MAC_ALT_TEXT Figure 1

(h)

(k)

(m)

(l) (n)

(i) (j)

Figure 1 Continued.

262 River Meandering

of environmental change and response and are therefore of

global significance. Meandering rivers are very important for

their ecology and biodiversity, offering a range of types of

habitat, and many of these channels and associated floodplains

are under threat from human activities. Conservation goals have

driven much recent research, and a trend to put back meanders

into artificially straightened river courses has required a depth of

understanding of the forms and dynamics of meandering river

channels. This trend to river restoration, or reinstatement

and recreation of meanders, is recognition of the inherent

occurrence and behavior of river meandering in nature. Com-

mon features of river meanders are depicted in Figure 2.

9.16.2 Research Phases and Topics

Research on river meanders has been undertaken in a range

of disciplines, including geomorphology (in geography and

earth sciences), engineering, mathematics and fluid dynamics,

physics, biology, and ecology. The aims and approaches tend


Concave bank

Channelwidth

Pool

Pool

Flow

Point bar

Rc

Rc

Chute

Riffle

Riffle

Tnalweg

Down valley

Vegetation

Vegetation

Vegetation

Point bar

Rad

ius

of c

urva

ture

Concave bank

Cro

ss v

alle

y

Figure 2 Common features of meanders. Redrawn with permission from Lagasse, P.F., Zevenbergen, L.W., Spitz, W.J., Thorne, C.R., 2004.Methodology for predicting channel migration. NCHRP Web-Only Document 67 (Project 24-16). Report prepared for TRB (TransportationResearch Board of the National Academies of the US) http://onlinepubs.trb.org/onlinepubs/nchrp/nchrp_w67.pdf


to differ but all have made contributions to geomorphological

understanding of these features.

Meandering channels were identified early as key com-

ponents of long-term landscape development, in W.M. Davis’

Cycle of Erosion (King and Schumm, 1980), where he provided

detailed description of how meanders develop from original

incised bedrock forms in ‘youthful’ stages to alluvial forms in

open valleys in ‘old age.’ Occurrence and sequences of cut-offs

were recognized. Practical problems associated with the actively

migrating meanders of the Mississippi River were an impetus for

some of the early scientific work. Friedkin (1945) undertook

experiments into meander dynamics, which are still much cited,

and Fisk (1944) studied the meander morphology in relation to

floodplain materials and geomorphological controls.

The major era of quantitative research on river meander

morphology and processes began in the 1950s, continuing

through the 1960s, with the seminal work of Leopold and

Wolman (1957, 1960), Leopold and Langbein (1966), Leopold

et al. (1964), and Schumm (1960, 1963). This work set the

foundations for modern fluvial geomorphology and the basic

understanding of river meanders. Morphometric and process-

form relations, for example, between meander wavelength

and discharge, were quantified. Meander morphology was

thought to fit a sine-generated curve, and theoretical prop-

ositions were made of why rivers attained this form, associated

with arguments of energy distribution and minimum variance.

Other work in the same period, now largely ignored, was that

of Dury (1954, 1955, 1958, 1960) who pioneered an approach,

now recognized as paleohydrology, in which he tried to

explain the formation of valley and misfit meanders and the

longer-term landscape development in relation to former

discharges.

Until the 1970s the assumption was mostly that meander

development took place over long timescales and that me-

anders tended to equilibrium forms. The occurrence of cut-

offs was recognized from the work on the Mississippi and

from the widespread occurrence of relict channels or oxbow

lakes in floodplains (Figure 1). With a shift to research on

shorter-term processes in geomorphology from the late 1960s,

attention began to turn to dynamics of river meander changes,

based on empirical field and historical evidence. Research by

Brice (1973, 1974, 1977), Hickin (1974, 1978), Hickin and

Nanson (1975), Nanson (1980a), Lewin (1972, 1976, 1978),

Knighton (1972, 1973), Hooke (1977, 1979), and Thorne and

Lewin (1979) in the 1970s showed that meander changes were

detectable on timescales of a few years. This research dem-

onstrated the greater complexity of morphology and the

continuous evolution of meanders, in contrast to previous

equilibrium analyses. Asymmetric and compound bends were

identified as part of evolutionary sequences of meander de-

velopment. Processes of erosion and deposition were meas-

ured and analyzed, including seminal research in individual

meander bends (Jackson, 1975; Bridge and Jarvis, 1976;

Dietrich et al., 1979) and research on the sedimentology of

bars (Bluck, 1971; Allen, 1970). By the 1980s much geo-

morphological evidence of meander behavior had been pro-

duced, as demonstrated in the important collection of papers

published in 1984 (Elliott, 1984), though there was still some

tendency to assume that high channel instability was associ-

ated with human interference in catchments.

The amount of field-based and geomorphological empirical

work declined through the 1990s but has recently seen resur-

gence, aided especially by technological developments that

enable detailed and rapid morphological and flow measure-

ments. However, during the 1980s, theoretical and modeling

work on river meanders increased enormously, much of it

emanating from engineering and fluid dynamics spheres. Much

debate was engendered, culminating in a major workshop that

produced the seminal volume on river meandering in 1989

(Ikeda and Parker, 1989). Further developments in numerical

simulation and modeling took place, but by 1995 Mosselman

(Mosselman, 1995) stated that there was still no easily available

software for modeling meander changes and, in a large review

in 2004, Lagasse et al. (2004) found that there was no standard



method of meander movement prediction that they could

apply. The last decade or more has seen a proliferation of

analytical and numerical modeling of increasing sophistication.

Theoretical analyses, reviewed by Seminara (2006), clarify that

meandering is related to fundamental instability mechanisms

associated with the interaction of the flow and erodible

boundary. Hardware experimental modeling has also regained

favor, with much engineering experimentation concentrated on

flow patterns and bed topography in models with rigid walls.

Early experiments undertaken by Friedkin (1945), Hooke

(1975), Parker (1976), Schumm and Kahn (1972), and others

demonstrated meander development and influence of factors,

but most attempts at producing mobile meanders encountered

practical difficulties in preventing braiding. Significant recent

developments have used vegetation to produce self-formed

meanders (Tal and Paola, 2007; Braudrick et al., 2009). An

important impetus to research in the last two decades has been

to develop techniques and tools with which to design new

meandering channels in river restoration schemes (Rinaldi and

Johnson, 1997; Kondolf, 2006).

A key question is why rivers meander. This has proved

difficult to answer and some researchers would dispute whe-

ther it has been achieved. A major review and summary of

arguments to date were provided by Rhoads and Welford

(1991). The major arguments that have been used over time

can be summarized as:

• Coriolis force

• Energy arguments (excess, minimization)

• Bank erosion and sediment effect

• Helical and secondary flows

• Inherent property of turbulent flow

• Interaction between flow and mobile channel

Bar theory

Bend theory.

Seminara (2006) has summarized the answer as ‘‘any small

random perturbation of channel alignment eventually grows,

leading to a meandering pattern, as shown by bend instability

theory.’’ From the ‘bend theory’ it can be summarized that a

straight channel is intrinsically unstable, provided the banks

are erodible. Federici and Seminara (2003) state that ‘‘bar

instability is recognized as the fundamental mechanism

underlying the formation of large-scale forms of rivers,’’ but

this may not be considered adequate to explain nonalluvial

meanders. Other researchers consider the explanation lies in

fundamental characteristics of fluid flow.

The current situation in river meandering research is one in

which a large number of theoretical and numerical simulation

models have been proposed, with varying theoretical bases

and assumptions, but many are lacking field validation or

testing with real river meander planforms. Several key differ-

ences in approach and assumptions are evident between fluid

dynamicists who make various assumptions such as equal

width, and geomorphologists who recognize the spatial and

temporal variability of meanders and the influence of factors

such as gradient, bank resistance, and discharge. Although

theoretical and empirical analyses were not entirely divorced

in the past, increasing convergence of approach and com-

parison of results are occurring (Hooke et al., 2011).

9.16.3 Approaches and Methods

A major division can be made into theoretical/modeling ap-

proaches and empirical approaches to river meandering. The

modeling approaches comprise numerical/analytical models

and the experimental (hardware) models. Empirical ap-

proaches entail field measurements and use of historical and

remote sensing data. Some empirical research has produced

inductive or kinematic models and some of these observed

relations have been used in other numerical simulations.

9.16.3.1 Empirical Approaches

9.16.3.1.1 Field measurements and observationsMuch of the field research on river meanders has been focused

on component processes within river bends and along chan-

nels, concentrating on flow processes, bank erosion, and, to a

lesser extent, deposition and bar formation. In the mid-1970s,

several important field studies were undertaken in which

processes within a bend were measured, including flow pat-

terns, sediment movement, erosion, and sedimentation (e.g.,

Jackson, 1975; Bridge and Jarvis, 1976; Dietrich et al., 1979;

Thorne and Lewin, 1979). These still remain as some of the

prime forms of evidence for whole meander bends. From this

period until recently, field measurements of combined pro-

cesses have been largely neglected, though notable exceptions

include the work of Frothingham and Rhoads (2003) in a

compound bend. Technological developments and the need

to validate the large modeling effort are now stimulating in-

creased field efforts.

Flow patterns and characteristics were measured with cur-

rent meters and flow tracers, but these have now been replaced

by a range of acoustic Doppler instruments, enabling 3D

flow direction and intensity to be measured rapidly (e.g., Fro-

thingham and Rhoads, 2003; Dinehart and Burau, 2005). Bank

erosion has been measured directly by various techniques in-

cluding erosion pins, resurvey, exposure measurement instru-

ments, photogrammetry, and terrestrial scanning (Lawler,

1993). Analysis of associated conditions has entailed moni-

toring of pore water pressures, stability, bank composition, and

strength (e.g., Simon et al., 2000; Parker et al., 2008). De-

position has involved particle size measurements and its spa-

tial and temporal variation, and detailed mapping of

sedimentary structures in bars. Changes in bed morphology

have been measured by standard topographic surveying tech-

niques, or in deeper rivers, by bathymetry from boats. Tech-

nological developments are transforming the ability to collect

detailed topography and monitor morphological changes and

processes, particularly the advent of terrestrial scanning

and differential GPS (e.g., Brasington et al., 2000; Heritage and

Hetherington, 2007) and of side scan sonar for large rivers.

Measurement and monitoring of spatial sequences of me-

anders over longer periods of time (more than 2–3 years) have

used more extensive field methods or mainly remote sensing

sources. Meander movement and changes in morphology

are monitored by resurvey of bank lines, field mapping, ground

photography, and cross-sectional surveys. Some field measure-

ments of meander movement entail use of sedimentary and

morphological evidence, for example meander scrolls,


vegetation succession (Hickin and Nanson, 1975; Lawler, 1993;

Malik, 2006) on timescales varying from a few years to the

Quaternary (Alonso and Garzon, 1994). Very little dating of full

meander sequences has yet taken place, but deposits in oxbow

lakes, palaeochannels, and floodplains have been dated, mostly

by 14C. Developments in OSL offer much potential for dating

channel movement and formation of features (Rittenour et al.,

2005; Rodnight et al., 2005; Rowland et al., 2005).

9.16.3.1.2 Map and remote sensing evidenceRiver meandering is primarily a planform characteristic, and

relatively long timescales are often needed to detect change in

meander position and morphology, so major sources of evi-

dence and bases of analysis are maps, aerial photographs, and

other remote sensing imagery. Historical maps have been used

to extend back in time (Figure 3). Amongst the documenta-

tions of river meander changes, one of the most remarkable

was that of Dort (1978) in a compilation of historical courses

of the Kansas River and its major tributaries from 1857, re-

cently republished with additional explanation by the

American Geographical Society (Dort, 2009). Similar histor-

ical compilations include those of the Po River, Italy, from the

twelfth century onwards by Braga and Gervasoni (1989).

Quantitative use of historical maps was pioneered by Hooke

(1977) (Hooke and Kain, 1982; Trimble, 2008), and errors

associated with use of historical map have been analyzed by

Hooke and Redmond (1989), Downward (1995) and Gurnell

et al. (2003). Methods of use of maps and imagery within a

GIS environment have been developed (Gurnell et al., 1994;

Leys and Werritty, 1999; Hughes et al., 2006). Aerial photo-

graphs have the advantage of also showing a range of associ-

ated features such as bars, meander scrolls, and vegetation

cover as well as bank lines (e.g., Brice, 1974; Hickin and

Nanson, 1975; Gurnell, 1997) (Figure 1) and digital photo-

grammetry is now widely applied (Lane, 2000; Chandler et al.,

2002). Increased resolution and availability of satellite im-

agery means their increasing application to river meandering

(e.g., Seker et al., 2005). LIDAR imagery of high resolution is

now becoming widely available and is proving invaluable,

though problems may be encountered in removing vegetation

cover and detecting details of bank topography. Analysis of

past maps and imagery are now regarded as essential in any

engineering or management study as a basis for assessing

channel stability/mobility.

9.16.3.1.3 Techniques of meander morphology andchange analysis

Techniques of characterizing and analyzing river meander

courses identified by Hooke (1984) were: bend parameters,

curve fitting, spectral analysis, graphical analysis, and model-

ing. Major technological developments have taken place since

then, but many of the principles still pertain. Several par-

ameters are needed to characterize the form adequately, to

encompass scale or size, shape or sinuosity, and irregularity

(Ferguson, 1975).

The standard method of characterizing meander morph-

ology is the assumption of a regular wave form and the

measurement of standard parameters as shown in Figure 4.

Many variants on the detail of measurements exist, for example

whether for bank lines or centerlines, from single meanders, or

meander trains. Wavelength is the standard measure of scaling

the size of meanders. (Dimensionless wavenumber (pw/L) is

used in fluid dynamics literature.) Meander amplitude is a

measure of cross-valley breadth. Sinuosity is a measure of the

degree of ‘wiggliness,’ measured for individual bends or, more

often, for a series of meanders. Radius of curvature (r) is a

measure of size by fitting circles to individual meander bends

and r/width is used as a measure of shape or curvature. These

parameters are usually measured directly on plots of meander

courses but are subjective and can be difficult to apply on the

more irregular forms that often occur in nature.

Efforts at automating meander planform analysis have

been made, most using digitized centerlines of courses

(Figure 5). Hooke (1977), Hooke and Kain (1982), Trimble

(2008) and O’Neill and Abrahams (1986) used curvature to

identify points of inflection and subdivide bends objectively.

Howard and Hemberger (1991) developed measures of

sinuosity, wavelength, curvature moments, asymmetry, and

pattern irregularity and showed that natural meander

morphology is different from model simulations. Andrle

(1996) assessed problems of measurement of sinuosity, due to

scale and wavelength, because of subjectivity of bend defin-

ition, and tested an angle measure technique. Similarly,

Lancaster and Bras (2002) suggested the use of different scales

of sinuosity measurement. Coulthard and Van De Wiel (2006)

have developed a method of radius of curvature definition

within raster modeling, as opposed to the usual use of vector

data. An alternative approach, early on, for characterizing

meandering was that of spectral analysis (Speight, 1965), but

this was found to be rather insensitive. Digitization of courses

allows curvature sequences and characteristics to be assessed,

though values are influenced by digitizing interval. Develop-

ments in wavelet analysis may offer much potential. A major

development recently by Guneralp and Rhoads (2008, 2009)

is in characterizing curvature more continuously by fitting

cubic splines to digitized courses.

Various classifications of typologies of change in meander

morphology have been produced (Table 1; Hooke, 1997).

Components of change include shortening, extension, trans-

lation, rotation, enlargement, cut-off, and complex change,

and have been identified on various rivers, for example, the

Ganga (Swamee et al., 2003) and the Luanga (Gilvear et al.,

2000). Bank lines are usually superimposed to detect channel

changes and digitization in GIS enables quantitative analysis.

Approaches to prediction of meander changes have mostly

involved meander modeling, but an empirical approach was

used in a large project undertaken by the US Transportation

Research Board (Lagasse et al., 2004) in which they compiled

historical aerial photograph evidence for three dates from 141

meander sites containing 1503 meander bends on 89 rivers in

the US. Various methods were investigated; the method of

linear extrapolation of trends from simple circle fitting was

adopted, but this is not ideal for nonlinear and compound

development.

9.16.3.2 Theoretical and Numerical Modeling Approaches

An enormous explosion of effort devoted to modeling river

meanders has occurred in the last few years, some of it aimed at

Republican river - parts of sheets 3 and 4, vicinity of Morganville

Color key1

(b)

(c)

(d)(a)

23456789

101112

Saline river - parts of sheets 1 and 2, between Salina and Culver

Solomon river - parts of sheets 1 and 2, vicinity of Bennington

Smoky hill river - parts of sheets 3 and 4, between Solomon and Salina

0 0.25 0.5 1 mile

190718711840

2001

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184018701910194719681984

Historical courses

19841970

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Air photos 1984

100 m

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O.S. map 1968

53

55

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Scale 1:55.000

0 0.25 0.5 1 mile

Scale 1:55.000

0 0.25 0.5 1 mile

Scale 1:55.000

0 0.25 0.5 1 mile

Scale 1:55.000

NW SE

NW SE

NW SE

Figure 3 Examples of meander changes from compilations of historical evidence. (a) Historical compilations of the courses of Republican, Saline, Solomon and Smoky Hill Rivers in Kansas, USA.Reproduced with permission from Dort, W., 2009. Historical Channel Changes of the Kansas River and Its Major Tributaries. American Geographical Society, New York, 80 pp. (b)–(d) Historicalcompilations of the River Dane and Bollin, NW England (Hooke and Harvey, 1983; Hooke, 1987).

266R

iverM

eandering


Cross over

Mea

nder

wid

th M

B

Meander width ML

Location ofpoint bar

Surfacewidth W

Am

plitu

de A

Bend

radius

Axis of bend

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Waveamplitude

Meanderwavelength Concave

bank

Convexbank

(a)

(b)

Thalweg

Conca

ve bank

Conve

x bank

Rm

Figure 4 Standardized parameters of meander morphology. (a) Single meander. Redrawn with permission from Knighton, D., 1998. FluvialForms and Processes a New Perspective. Oxford University Press, Oxford. (b) Meander train. Redrawn from Huggett, R., 2003. Fundamentals ofGeomorphology. Routledge, London, 386 pp.


solving practical problems and providing a means of prediction

and design, others aimed at elucidating the bases of river me-

andering by testing fundamental theory. Models of increasing

sophistication and complexity have been developed, progressing

from simple 1D equations through to 2D representations and

then 3D modeling using computational fluid dynamics (CFD).

Mostly, the simpler models simulate meander behavior in a

meander train (sequence of meander loops) but, because of

computational demands, the more complicated models tend

only to produce simulations for single bends or limited reaches.

The theoretical modeling approaches are based on fundamental

physics (dynamical or analytical modeling) and formulations of

flow interactions with the boundary. Much of the modeling

builds hierarchically on previous work (Camporeale et al.,

2007). Much of it is linear and reductionist in approach, but

developments in nonlinear modeling are now taking place. A

major underlying theory is that bank erosion and bend move-

ment are related to excess near-bank velocity. Many of the

models have been based on the original theory by Ikeda et al.

(1981), later modified by Johannesson and Parker (1989)

and others. Some other models are built on empirically

derived relations (kinematic modeling), much of it based on

movement–curvature relations. Some models simulate develop-

ment of meanders from straight; others start with a meandering

form, usually a sine-generated curve, and simulate changes.

Models of individual processes, such as bank erosion, are now

being incorporated into meander movement simulations. Some

integrated models of flow pattern, sediment transport, bed

topography, and grain size sorting in bends have been developed

and compared with field evidence (e.g., Bridge, 1992).

9.16.3.2.1 Experimental modelingEarly efforts at hardware, experimental simulation of natural

behavior of meander movement and change in flumes en-

countered problems of creating enough resistance in the banks

to produce a persistent single, meandering channel. Many

produced low-sinuosity, self-formed channels with submerged

bars (e.g., Friedkin, 1945; Wolman and Brush, 1961; Ackers and

Charlton, 1970) (Figure 6(b)) but tended toward a braided

planform as the channel migrates (Parker, 1998). Attempts

were made by these and others (e.g., Smith, 1998) to solve the

problem by using clay mixtures with sand. A more recent

phase of experimentation is producing mobile meanders more

successfully (Peakall et al., 2007; Tal and Paola, 2007;

Braudrick et al., 2009). Braudick et al.’s experiments created

self-maintaining meandering channels with cut-offs by using

vegetation in the form of alfalfa sprouts to provide the appro-

priate resistance (based on an idea from Tal and Paola)

(Figure 6(a)). In the flume experiments of Peakall et al. sedi-

mentary structures of bars were reproduced. Most other


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Figure 5 Digitization and curvature analysis. (a) Digitization points,direction and angle difference of links. (b) Curvature and wavelengthcalculation for a sine-generated course. (c) Direction and curvature foran irregular course, several bends in length. Redrawn with permissionfrom Knighton, D., 1998. Fluvial Forms and Processes a NewPerspective. Oxford University Press, Oxford.


laboratory experiments have focused on flow patterns and/or

bed topography in meandering channels and most have used

fixed bank channels, and some fixed beds. Some experiments

use complex, high sinuosity channels or sharp-angle bends

(e.g., Whiting and Dietrich, 1993a, b; Blanckaert and de Vriend,

2004, 2005; Abad and Garcia, 2008; Blanckaert, 2009; Termini,

2009; Zeng et al., 2008) rather than simple low curvature, sine-

generated forms. Most experiments are run with constant dis-

charge and uniform sediment size. Many of the experimental

results are used for testing theoretical or numerical simulation

model results (e.g., Zolezzi et al., 2005; Shams et al., 2008). A

few of the numerical and flume models have been tested

against field data; for example, Ferguson et al. (2003) tested a

CFD model of flow in a high angle bend against field data.

9.16.4 Empirical Evidence and Analysis

9.16.4.1 Morphology

The outer banks of meander bends are generally steep and

eroding, with a pool present in the bed at the apex, and sloping

bed topography from the point bar on the opposite inner bank

(Figures 1 and 2). Riffles or shallowings are present in the in-

flection regions of the bend, in the straight limbs between api-

ces, and the cross sections and banks are more symmetrical

there. Meanders are usually depicted in reference books as

regular, symmetric sine-generated curves, as in Figure 4, a form

introduced by Langbein and Leopold (1966), who argued that it

represented the minimum variance form and most uniform

distribution of change along the curve. However, many actual

meanders were recognized by them (and earlier) as being

commonly asymmetric and skewed, then more planforms were

examined by Brice (1973) and Lewin (1972, 1978) amongst

others, so that by 1983 Carson and Lapointe (1983) said that

use of sine-generated curves should be ‘abandoned as the

standard description of the equilibrium type of freely me-

andering rivers’ because most meanders were asymmetric. Yet

this form is still widely used as the basis for much modeling. A

particular shape of skewed and fattened, tortuous meander,

commonly occurring, has been named a ‘Kinoshita’ curve after

its originator; convoluted meanders are also called goosenecks.

In a neglected study of the Jordan River, Schattner (1962)

named a range of bend forms and analyzed their spatial distri-

bution. Carey (1969) identified smoothly curving caving bends

and abrupt angle bends but considered them to differ from true

meanders. Occurrence of sharp angled bends has been recog-

nized by many researchers (e.g., Alvarado-Ancieta and Ettmer,

2008), and highly convoluted loops and cut-offs have been re-

ported from a range of environments, including humid tropical

(e.g., Ebisemiju, 1993; Gilvear et al., 2000; Gautier et al., 2007).

Low sinuosity channels that are more angular and react to

local controls without developing true meanders are termed

wandering rivers or pseudo-meandering (Bartholdy and Billi,

2002). Confined and incomplete meandering are terms used to

refer to meandering that is constrained by valley width,

as is particularly common in many formerly glaciated environ-

ments (Lewin and Brindle, 1977; Nicoll and Hickin, 2010).

Subdivisions of meander types have been suggested, mostly

based on sinuosity classes (Schumm, 1963; Brice, 1982;

Church, 1992) (Figure 7). Meanders have been subject to

fractal analysis and found to have asymmetrical (self-affine)

fractal scaling (Nikora, 1991; Montgomery, 1996; Stolum,

1996). Montgomery (1996) showed that fractal dimension

and sinuosity are highly correlated.


Table 1 Classifications or typologies of change

Author Model/classification

Kondrat’yev (1968) Graphical mode of change from simple bend through to cut-off.Daniel (1971) Fitted a sine-generated curve to meanders. Identified five types of movement involving expansion, rotation

and translation.Keller (1972) Processes of change and relationship to bedforms in a five-stage model.Brice (1974) Classification of morphology defined by circle combinations and analysis of sequences of change.Hickin (1974) Pattern of meander change developed from analysis of erosion pathlines.Hickin and Nanson (1975) Predictive model for determining rates of channel bend migration.Kellerhals et al. (1976) Identified six types of lateral activity:

• downstream progression,

• progression and cut-offs,

• mainly cut-offs,

• entrenched loop development,

• irregular lateral activity, and

• avulsion.

Hooke (1977) Used Daniel’s (1971) primary elements of movement in double and triple combinations to compose a suiteof 70 models of movement. Primary elements:

• extension,

• translation,

• rotation,

• enlargement,

• lateral movement, and

• complex change.

Hooke and Harvey (1983) Seven categories of change defined:

• simple migration,

• confined migration,

• growth (extension),

• lobing and compound growth,

• retraction and cut-off,

• complex changes (islands, abandonment, etc.), and

• stable bends, no change.

Brice (1984) Classified changes in meander form according to mode of bank erosion.


Meanders are also frequently depicted as of uniform width,

and this is an assumption of many models; but Brice (1982)

showed that the most active meanders are wider at apices than

crossings, and Lagasse et al. (2004) in their large data com-

pilation confirmed that variation in width around a meander

is an indication of activity. Carson (1986) also recognized that

overwidened sections are common and Luchi et al. (2010)

recently quantified the systematic variation in width around

active meander bends.

In the era of quantification of morphology and process-

form relations, many equations formulating the interrelations

of meander parameters (defined in Figure 4) or the relations

of meander forms to controls, mainly discharge, were pro-

duced (Leopold et al., 1964). Wavelength (ML) is a measure of

scale of meanders and is found generally to be 10–14 times

channel width. It correlates with discharge, though the ap-

propriate measure of discharge was much debated (Carlston,

1965), and with drainage area as a surrogate of discharge.

Pools and riffles are conventionally regarded as spaced at 5–7

channel widths, in phase with the wave form. Radius of

curvature is also closely related to channel width, averaging

2–3 widths and 0.2 of the wavelength. Amplitude is much less

closely related to width or discharge. Leopold and Wolman

(1960) produced power form equations of the morphological

relations and they have since been widely tested (Bridge,

2003). Type of channel pattern and degree of meander in-

tensity is closely related to sediment load and to channel re-

sistance (Schumm, 1960, 1963), with alluvial channels being

more sinuous in material with higher percentage silt-clay.

9.16.4.2 Morphological Change

It has long been recognized that meanders migrate down-

stream, as was well known from rivers such as the Mississippi.

It was also known that many meanders exhibit skewing and

asymmetry, but it was assumed that this was due to inho-

mogeneities in the floodplain material, producing differential

erosion rates in different parts of the meander train.

A major development in analysis of meanders was the

recognition of a common sequence of evolution of meander

form over time, stemming largely from the work of Brice (1973,

1974, 1984) in which he proposed the sequence of types in

Figure 8(a) and from the work of Hickin and Nanson (1975)

(Figure 8(b)) on the Beatton river in Canada, using the evi-

dence of meander scrolls mapped from aerial photographs.

Some other sequences were produced, for example, Keller’s

(1972) (Figure 8(c)) model, but elongation of meander limbs is

less widely applicable. Hickin (1978) generalized his obser-

vations into the very important conceptual model (Figure 9(a)),

which became the basis for much other empirical analysis and

(a)

(b) (c)

Figure 6 (a) Photograph of flume experiment using alfalfa sprouts to simulate vegetation cover. Reproduced with permission from Braudrick, C.A.,Dietrich, W.E., Leverich, G.T., Sklar, L.S., 2009. Experimental evidence for the conditions necessary to sustain meandering in coarse-bedded rivers.Proceedings of the National Academy of Sciences of the United States of America 106(40), 16936–16941. (b) Flume experiment showing developmentof bars in a straight channel. Reproduced from Seminara, G., 2006. Meanders. Journal of Fluid Mechanics 554, 271–297, with permission fromCambridge University Press. (c) Bar development in a straightened channel for comparison. From Jaeggi, M. 1984. Formation and effects of alternatebars. Journal of Engineering, American Society of Civil Engineers 110, 142–156.


kinematic modeling. This shows a nonlinear increase in mi-

gration rate with curvature (decreasing r/w) to a maximum at a

critical curvature, identified as r/2w 2–3, and decrease in mi-

gration rates again beyond this critical curvature value. Hooke

(1997) compiled data from other rivers, showing similar

envelope curves to meander behaviors, though with some

tighter curves and higher rates at low r/w than the original

(Figure 9(b)), later also identified by Hudson and Kesel (2000)

on the Mississippi. Brice (1974), Hooke and Harvey (1983) and

others recognized the importance of compound forms, and

Hooke and Redmond (1992) and Hooke (1995b) produced the

qualitative model in Figure 8(d) of sequence through to neck

cut-off, which involves change in the position and number of

pools and riffles (Hooke and Harvey, 1983).

Debate continues on the mechanism and conditions, and

reasons for the compound development. Hooke and Harvey

(1983) showed that the compound development was associ-

ated with development of an additional riffle in the apex re-

gion as the pathlength increased beyond some critical value. It

was assumed that this leads to breakdown of secondary flow

patterns (Thompson, 1986). Lofthouse and Robert (2008)

identified a lengthening of pools with increased angular

deflection up to a critical length at which formation of

a new riffle took place. One of the few studies to examine

flow relations in a compound bend is that of Frothingham

and Rhoads (2003) (see below: flow patterns). From empirical

analysis, Guneralp and Rhoads (2009) demonstrate that

the spatial structure of the planform curvature effect on

migration rates depends on the complexity of the planform

geometry. Evidence on variation in rate of erosion and

migration through the meander evolution sequence is

somewhat contradictory, with Hickin and Nanson suggesting

the nonlinear increase to a curvature limit, supported by evi-

dence from Hooke and Harvey (1983) but Furbish (1988,

1991) suggesting monotonic increase. Hooke and Yorke

(2010) now show acceleration of rate through the growth

phase and a slowing during the compound phase. Some of

the confusion is due to the lack of distinction between

bank erosion rates and extent of downvalley or cross-valley

movement.

Meander movement and change in morphology can pro-

duce cut-offs, with oxbow lakes in the abandoned channel.

Former channels at various stages of infill are very common

features of meandering river floodplains. The timing, process,

and distribution and effects of cut-offs have received much

attention, with a resurgence of interest in recent years, much of

this driven by ecological and conservation interests. Lewis and

Lewin (1983) identified five types of cut-off – chute, neck,


Single phase, equiwidth channel, deep

Single phase, equiwidth channel

Single phase, wider at bends, chutes rare

Single phase, wider at bends, chutes common

Single phase, irregular width variation

Two-phase underfit, low water sinuosity

Two-phase bimodal bankfull sinuosity

(a)

(b)

(c)

(d)

(e)

(f)

(g)

Figure 7 Modified Brice classification of meander forms. Redrawnfrom Lagasse, P.F., Zevenbergen, L.W., Spitz, W.J., Thorne, C.R.,2004. Methodology for predicting channel migration. NCHRP Web-OnlyDocument 67 (Project 24–16). Report prepared for TRB(Transportation Research Board of the National Academies of the US)http://onlinepubs.trb.org/onlinepubs/nchrp/nchrp_w67.pdf


mobile bar, mulitloop chute, and mulitloop neck; of these,

two main types are usually distinguished, chute and neck

cut-off.

Neck cut-offs (Figure 1) can be the endpoint of the me-

ander evolution illustrated above (Figures 8 and 9). It was

assumed that these mostly take place in, and can be caused by,

high flow events. Some case studies have now shown that

actual cut-off may occur in moderate flow events if the bend

neck has narrowed sufficiently (Hooke, 1995a; Gautier et al.,

2007). Very few studies have followed the adjustments im-

mediately after cut-off, but both Hooke (1995a) and Fuller

et al. (2003) have shown variable and high amounts of sedi-

mentation, channel erosion, and morphological change

within the main channel in the period immediately suc-

ceeding cut-off. Plugs are formed in the upstream entrance to

the old channel very quickly and more slowly downstream,

but the actual dynamics and subsequent infill of the aban-

doned channel are related to angle and lake connectivity to

main channel and its dynamics (Citterio and Piegay, 2009).

Piegay et al. (2000) measured sedimentation rates in 39

oxbow lakes in SE France, producing a mean rate

0–2.57 cm yr�1. This was linked to water depth and decrease

from entrance as a function of overbank frequency, which also

varies with channel geometry, Gautier et al. (2007) found on

the Beni that the functioning of abandoned branches is

strongly associated with the mobility of the main channel

rather than with flood intensity. The length of oxbow lakes is

closely related to the sinuosity of the channel (Constantine

and Dunne, 2008). Cut-offs are important in preservation of

flood history and environmental changes and some have been

dated as part of understanding floodplain chronologies (see

Chapter 9.32).

Controls and mechanisms of chute cut-offs are still

somewhat debated and not fully understood, though height of

floodplain, sediment supply, and discharge regime may be

factors. One mechanism is by formation of headcuts on the

downstream side of the bend and progression upstream (Gay

et al., 1998). Much longer-length channel avulsions can occur

on meandering rivers where the river breaks out of its course

to form a new channel down a length of valley. Explanation

and prediction of avulsion is still proving challenging (Sling-

erland and Smith, 1998; Aslan et al., 2005; Phillips, 2009) (see

Chapter 9.32). Both Peakall et al. (2007) and Braudrick et al.

(2009) have reproduced chute cut-offs in their hardware

models.

Overall, meandering systems are found to exhibit a wide

range of behaviors (e.g., Hooke, 2007; Seker et al., 2005;

Goswami et al., 1999), varying from meanders which are

evolving very slowly such as channels in bedrock or resistant

material, channels with highly vegetated banks or very low

slopes (e.g., Biedenharn et al., 1984; Rhoads and Miller, 1991;

Swanson, 1984) to those which are highly complex and dy-

namic. Timescales of the full sequence of meander evolution

have not been established for many rivers and more research is

needed. Dort (2009) suggested from the meander scroll and

cartographic evidence that meander development from initi-

ation to cut-off on the Kansas River takes at most a few dec-

ades. Harmar and Clifford (2006) have suggested that

meander trains on the Lower Mississippi River are continually

formed and modified over a period of approximately 120

years. Hooke (2004) found that on the River Bollin bends had

evolved from low curvature to cut-off in 120–150 years. The

periods for complete floodplain reworking ranged from 600 to

7000 years on streams in Devon, if current rates are simply

extrapolated (Hooke, 1980). Rates and timescales of flood-

plain reworking have been found to vary even in the same

region. For example, Mertes et al. (1996) calculated an alluvial

plain recycling time ranging from 1000 to 4000 years on the

Solimoes–Amazon River, but Gautier et al. (2007) found that

it is about 10 times higher on the tributary Beni River. Beechie

et al. (2006) calculated a turnover recurrence interval of 60

years on meandering forested mountain river systems of the

Pacific Northwest, USA.


1 2 3 4 5Stages Initiation

Migration

GrowthCutoff

Pool

RiffleErosion

Asymmetric shoal forstages 1�2, point barfor stages 3, 4�5

Pool

Riffle

Double-heading

Erosion

Primary flow

Depositional bar

Simple symmetrical

Simple asymmetrical

Compound asymmetrical

Compound symmetrical

1 1A D

B

C

(a) (b)

(c) (d)

E

F

2

1

1

Meander scrolls

2

2

2

1 2

1

Erosin path lines

2

Figure 8 Models of sequences of meander development. (a) Sequence through from simple symmetric bends to asymmetric and compound.Reproduced from Brice, J.C., 1974. Evolution of meander loops. Bulletin of Geological Society of America 85, 581–586, with permission from GSA. (b)Elongation, skewing and compound development, based on meander scroll bar evidence on Canadian rivers. Reproduced from Figure 7 in Hickin, E.J.,1974. Development of meanders in natural river-channels. American Journal of Science 274(4), 414–442. (c) Sequence of limb elongation withadditional pool and riffles in the limbs. Reproduced from Keller, E.A., 1972. Development of alluvial stream channels: a five-stage model. GeologicalSociety of America Bulletin 83, 1531–1540, with permission from GSA. (d) Sequence of migration, growth and compound development through to cut-off, involving development of additional riffle in apex. Reproduced from Hooke, J.M., 1995b. Processes of channel planform change on meanderingchannels in the UK. In: Gurnell, A., Petts, G.E. (Eds.), Changing River Channels. Wiley, Chichester, pp. 87–116.


9.16.4.3 Meander Processes

9.16.4.3.1 Flow patterns and sediment movement

Flow patterns in meander bends were characterized from early

on as a periodically reversing helical motion helicoidal flow,

with Leliavsky (1955) explaining that any small flow deviations

will cause a centrifugal force from one side of a bend to

the other, which will promote development of transverse flow.

Recognition of more complex patterns of secondary flows,

particularly the existence of an outer bank cell came from

the field measurements of Bathurst, Hey, and Thorne in the

mid-1970s (e.g., Bathurst et al., 1977; Thorne and Hey, 1979).

The essential characteristics of flow patterns in meander bends

are summarized by Markham and Thorne (1992) in

Figure 10(a).

Major features of flow from detailed field measurements are

exemplified from the work of Dietrich in a bend on Muddy

Creek, Wyoming (Figures 10(b) and 10(c)) (Dietrich, 1987).


7.06.05.04.03.0rm (w)

2.01.000

0.5

Mig

ratio

n ra

te (

m y

ear−1

)

1.0

Ter

min

atio

n st

age

Initi

atio

n st

age

Grw

oth

perio

d

0 2 4 6 8 10 12 140.0

0.1

Ero

sion

rat

e w

idth

s (m

w−1

)

0.2

Beatton river (Hickin and Nanson)

Canadian rivers (Hickin and Nanson)Red Rivers (Biedenham et al.)R. Bollin

R. Dane (Hooke)

0 1 2

D

D

C

C

B

B

A

A

3 4 5Bend curvature (r/w)

6 7 8 9 10 11

Bollin envelope curve

StabilizingMigrating

Neck cutoff

Chute cutoff

12 130.0

0.1

Rat

e of

mov

emen

t (w

idth

yea

r−1)

0.2

0.3

(c)

(b)

(a)

Figure 9 Relationship of rate of movement or erosion to curvature. (a) Conceptual generalization of meander development and accelerating rateof movement with increase in bend curvature (decrease of r/w). Reproduced from Hickin, E.J., 1978. Hydraulic factors controlling channelmigration. In: Davidson-Arnott, R., Nickling, W. (Eds.), Research in Fluvial Geomorphology, Proceedings Fifth Guelph Symposium onGeomorphology, pp. 59–66. (b) Envelope curves of data of dimensionless movement rates in relation to bend curvature for several rivers.Reproduced from Hooke, J.M., 1997. Styles of channel change. In: Thorne, C., Hey, R., Newson, M. (Eds.), Applied Fluvial Geomorphology forRiver Engineering and Management. Wiley, Chichester, pp. 237–268. (c) Hypothetical trajectories for different meander behavior over time.Reproduced from Hooke, J.M., 2003. River meander behaviour and instability; a framework for analysis. Transactions of Institute of BritishGeographers 28, 238–253.



Superelevated water surfaceOuter bank cell

Outrward shoaling flowacross point bar

Pathe lines of secondary flow

Characteristicsecondaryvelocity profiles

Water surface elevation(E )

High

� b m

ax �b max � b

max

�b max

Low

Bar exposedat low flow

Near bed velocity

Break in bed slope

Near surface velocity

Thalweg

(a)

(b)

(c)

High

High

Usg R

w2−

ΔEn

ΔEn

ΔEs

ΔEs

ΔEsΔEn ≅Δs

−II−N

S =

s

s

+n

+n

s

+n

−n

�b ≅ pghS

Low

Low

Figure 10 (a) Generalized pattern of flow in meander bends. Reproduced from Markham, A.J., Thorne, C.R., 1992. Geomorphology of gravel-bed rivers. In: Billi, P., Hey, R.D., Thorne, C.R., Tacconi, P. (Eds.), Dynamics of Gravel – Bed Rivers. Wiley and Sons, Chichester, pp. 433–456.(b) Channel curvature and bed topography effects on the boundary shear stress field. Reproduced from Figure 8.6 in Dietrich, W., 1987.Mechanics of flow and sediment transport in river bends. In: Richards, K.S. (Ed.), River Channels: Environment and Processes. Blackwell, Oxford,pp. 179–227. (c) Flow field in equilibrium with bed topography in bends with well developed bars. Reproduced from Figure 8.9 in Dietrich, W.,1987. Mechanics of flow and sediment transport in river bends. In: Richards K.S. (Ed.), River Channels: Environment and Processes. Blackwell,Oxford, pp. 179–227.




Water surface is superelevated round bends, the slope increasing

with the tightness of bends. This has an effect on the distribution

of boundary shear stress and the velocity fields. The centrifugal

force produces secondary circulation. Bed topography takes on

the form of bar-pool units (Figure 10(b)) with a break in bed

slope, commonly termed a bar or lobe front, extending across

the channel and around the front of the exposed point bar. The

maximum-velocity thread crosses from near the inner bank at

the bend entrance to the outer bank at the bend exit, crossing at

the zone of maximum curvature. In a simple bend, of the

morphology shown, the maximum shear stress is downstream of

the apex, resulting in bend migration. The zone of spiral motion

with outward flow near the surface and inward flow near the bed

is confined to the deepest 20–30% of the cross-section. This

detailed flow pattern differs from that of Hey and Thorne (1975)

in exhibiting less cross-stream orientation, a shoaling-induced

outward flow over the bar and lack of dual cells in the crossings,

and with a much smaller outer bank cell. Much subsequent

research on flow patterns, particularly in flumes, has aimed to

understand the controls on these variations.

Bagnold (1960) identified that in tight bends flow

separation can take place, developing at the inner bank

downstream of the bend apex at first, then a second zone

developing at the outer bank in very tight bends. Hodskinson

and Ferguson (1998) made field measurements to test a nu-

merical model of flow separation and showed that existence

and extent of concave bank flow separation can be signifi-

cantly influenced by changes in bend planform, point bar

topography and upstream planform. In very tight (abrupt

angle) bends or where the outer bank is constrained outer,

concave-bank deposition and inner, convex-bank erosion can

occur (Andrle, 1994).

Understanding of the mechanisms of development of

compound loops and bend asymmetry have been helped by

the field measurements of flow pattern in a compound me-

ander containing multiple pool-riffle structures made by Fro-

thingham and Rhoads (2003). The downstream velocity field

is characterized by a high-velocity core that shifts slightly

outward as flow moves through individual lobes of the loop.

For some of the measured flows this core becomes submerged

below the water surface downstream of the lobe apexes. Skew-

induced helical motion develops within the pools near lobe

apexes and decays over riffles where channel curvature is less

pronounced. Maximum rates of bank retreat generally occur

near lobe apexes where impingement of the flow on the outer

channel bank is greatest. However, maximum rates and loci of

bank retreat differ for upstream and downstream lobes of the

loop, leading to increasing asymmetry of loop geometry

over time.

The pattern and mechanisms of grain sorting in bends has

been examined in some field research (e.g., Jackson, 1975;

Bridge and Jarvis, 1976; Lapointe and Carson, 1986). Anthony

and Harvey (1991) showed that in a meandering river with

high sediment supply the flow and sediment transport pat-

terns differed with discharge level. Clayton and Pitlick (2007),

building on previous work, found that fine and coarse frac-

tions are differently routed in bends, with fine grains swept

inward over the point bar, and coarse grains routed outward

toward the pool. At bankfull, all sizes were transported but

size increased toward the outer bank.

9.16.4.3.2 Bank erosionSome debate still surrounds the details of the influence of

the flow pattern on bank erosion, but the proposition by

Leliavsky (1966) and later developments by Parker et al.

(1983) and Hasegawa (1989) indicating that erosion in a

meander bend is primarily controlled by the excess near-bank

velocity are widely accepted and have become the basis for

much modeling (e.g., Howard, 1992).

Mechanisms and processes of bank erosion were reviewed

by Lawler et al. (1997). Major lateral movement of channels in

meanders occurs by bank erosion that is mainly associated

with high flows but influenced by the soil moisture status and

the pore water pressures. Composition and height of the bank

affect stability. Many floodplain banks of alluvial meanders

have a composite structure of a coarse, gravel base and finer

material above (Thorne and Tovey, 1981). Julian and Torres

(2006) found, by testing various flow properties, that the

amount of hydraulic erosion of cohesive riverbanks is dictated

by flow peak intensities. Erosion rates are highly influenced by

bank resistance, particularly bank material and vegetation (e.g.,

Schumm, 1963; Hooke, 1979), but vegetation effects have

proved difficult to quantify, though research is continuing.

Within-event evidence indicates that much of the bank

failure takes place by erosion of the lower gravel layer then

toppling (cantilever failure) of the fine layer (e.g. Pizzuto,

1984). In finer or more homogenous material and with high

pore water pressures the failure may be by sliding. Luppi et al.

(2009) found that the occurrence of mechanisms on the

Cecina R, Italy varied between the seven flow events in one

year. Slide failures were closely related to peak flow, and

cantilever failures occurred in late phases of the hydrograph. If

blocks remain at the base of the bank then they may reduce

subsequent erosion (Thorne and Tovey, 1981; Lapointe and

Carson, 1986). In active bends, bank erosion may take place

in several events a year (Hooke 1979, 1980). Larsen et al.

(2006) applied an empirical relation between erosion rate and

stream power to assess the effects of variable discharge on

lateral channel movement. The balance between bank erosion

and deposition varies with discharge, Pizzuto (1994) showing

from a large number of bank erosion measurements on the

Powder River, USA, that high flows were producing erosion

dominance. Pizzuto (2009) derived an empirical model from

field measurements of bank erosion in which he finds that

cohesive bank erosion has a strong stochastic component, but

that hydraulic erosion is responsible for 87% of all erosion.

9.16.4.3.3 Deposition and bar formationSeveral different types of bars are recognized in river channels

(e.g., Church and Jones, 1982) but those most characteristic of

meandering channels are point bars, found on the inner side

of meander bends. These are termed fixed or steady bars. Bars

separated from the floodplain that migrate are termed free.

Formation of free alternate bars in straight channels is often a

precursor to formation of true meanders. The coexistence of

free and fixed bars was recognized from field observations by

Kinoshita and Miwa (1974). Single mid-channel bars are quite

common in active meandering channels and may indicate

transition to braiding, but these bars have been shown to

be significant in the sequence of development of some me-

anders (Hooke, 1986; Hooke and Yorke, 2010). Few studies

Figure 11 Photograph of the incised ‘gooseneck’ meanders of theSan Juan River, Utah, USA.


have quantified the timescale of development of bars,

but Church and Rice (2009) examined long-term evidence

of alternate type bars in the Fraser River and found that in-

dividual bars have a life history of about 100 years, except in

certain protected positions. A newly formed gravel bar quickly

assumes its ultimate thickness and relatively quickly ap-

proaches its equilibrium length. Growth continues mainly by

lateral accretion of unit bars. Hooke (1986, 2007b; Hooke and

Yorke, 2011) identified a life-cycle of 7–9 years average for

mid-channel bars on a small river in NW England.

The field measurements of Jackson (Jackson, 1975) and of

Bridge and Jarvis (1976) of flow and sediment movement in

bends were aimed at fuller understanding of the development

of sedimentary structures on point bars. The classical model is

of a simple fining upward sequence and lateral bar face struc-

tures (Allen, 1970), but they found sequences and structures

were more complex and spatially varied than this. Formation

of point bars and other bars contributes to floodplain con-

struction (see Chapter 9.32). Point bar morphology is greatly

influenced by the w/d ratio (cross-sectional shape) of the

channel with high w/d channels having wide, flat-topped bars

(Dietrich, 1987). In laboratory experiments in sharper bends,

Kawai and Julien (1996) found that point bar morphology

depends on particle size and that point bars were considerably

smaller in coarse sand than fine sand. Differing views over the

major mechanisms of point bar deposition, whether due to

secondary flow circulation producing inward flow at the bed

on bars or whether due to deceleration of longitudinal flow

and distribution of shear stress are still apparent, and both

flume and field experiments are being used to investigate this.

In terms of dynamics, Bennett et al. (1998) measured temporal

variations in point bar morphology on a low w/d ratio channel

over 2 years in two bends and found erosion and coarser bars

in winter, but deposition and finer bar texture in summer. Net

changes at each site were synchronous and equal in magnitude.

In contrast, Hooke (2008) found spatial and temporal vari-

ability in depositional characteristics within a reach.

Counterpoint bars or concave bank benches/bars (Lewin,

1983; Page and Nanson, 1982) can form in meander bends

where separation takes place at the outer bend and/or rapid

migration takes place leaving a large zone of low velocity and

shear stress in which relatively fine material is deposited. Such

bar deposits can be much thicker than point bars (Burge and

Smith, 1999). More continuous bank benches have been

recognized (e.g., Shi et al., 1999) and can occur from dom-

inance of deposition over erosion (Pizzuto, 1994).

9.16.4.4 Bedrock and Incised Meanders

Large bedrock meanders have long been recognized in the

landscape, including by W.M. Davis (King and Schumm, 1980).

Major valley features are termed either entrenched, in which the

valley sides are steep and symmetrical, or ingrown, in which

some lateral cutting has occurred, producing a more open

valley with slip-off spurs. Dury (Dury, 1954, 1955, 1958, 1960)

studied valley meanders, identifying them as fossil features

formed by much greater discharges in a previous hydrological

period, and now occupied by misfit channels with a smaller

scale of present meandering. The long-held assumption on

valley meanders was that the meandering form was inherited by

superimposition or antecedence. Schumm (1977) found from

experiments on formation of incised meanders that they could

not be created from superimposition but they did occur by base

level lowering (analogous to vertical uplift) and he produced

the convoluted meanders typical of the famous San Juan goo-

senecks (Figure 11). Shepherd (1972) showed in flume ex-

periments that the forms were influenced by the sediment load

transported. Local base level and gradient influence the incision

and morphology, as do tectonics (Harvey, 2007). A study of the

distribution and geometry of 600 km of incised meanders in

the central Colorado Plateau (Harden, 1990) found that most

meander cross sections in the area are relatively symmetrical,

but highly ingrown forms are also present and that, in general,

symmetric bends are associated with resistant bedrock units,

whereas ingrown forms develop in massive sandstone and in

highly erodible bedrock. Gradient significantly influences the

distribution of ingrown bends, with asymmetric meanders

concentrated in reaches of low average gradient; and this is a

greater influence than the lithology itself. In contrast, Tooth

et al. (2002) and McCarthy and Tooth (2004) consider that the

nature of the bedrock influences the nature and processes of

incision and bedrock meander formation. Complex sequences

of meanders can occur in mixed bedrock and alluvial reaches,

with subtle variations in sediment load (Tooth et al., 2004;

Marren et al., 2006), and sedimentary features are able to form

and persist over short to medium timescales even while bed-

rock erosion is ongoing. Mechanisms of formation of meanders

in bedrock still remain to be elucidated, but it has been found

that many bedrock meanders have the same features as alluvial

meanders (e.g., Kale, 2005), and can be highly complex (Zhang

et al., 2008) even exhibiting double-heading and compound

forms (Hooke, 2003). Cut-offs are common features of incised

bedrock meanders. (Bedrock channels are discussed more fully

in Chapter 9.28).

9.16.4.5 Spatial Distribution and Controls onCharacteristics

Research on the threshold of meandering with braiding

helps to explain the distribution of meandering, relating it to

stream gradient, discharge, sediment supply, and erodibility



of boundaries (see Chapter 9.17). Spatial variability

of morphology and stability can be high within river

reaches (Figures 1 and 3). Characteristics of meanders in

different zones within and between rivers are related to the

gradient and/or resistance of banks influenced by material

and/or vegetation and land use, and rock type and structure

(e.g., Timar, 2003; Zhang and Fu, 2003; Alvarado-Ancieta and

Ettmer, 2008; Zhang et al., 2008). Generally, it is found that

the most active meanders are in the steepest alluvial reaches

and those with highest stream power but with erodible ma-

terial, often in the middle reaches of a river. Rates of lateral

movement have been analyzed particularly in relation to dis-

charge and stream power and in relation to curvature. They

show a strong, square-root scale relationship to drainage area,

as a surrogate of discharge (Brice, 1984; Hooke, 1980; Lawler,

1993). Stream power is a strong influence (e.g., Lewin, 1983;

Hickin and Nanson, 1984; Richard et al., 2005; Larsen et al.,

2006) and Nicoll and Hickin (2010) recently found that it

explained 450% of variation in migration rate on a selection

of confined meanders in the Canadian prairies. Differing

channel materials influence the channel form and mobility

(e.g., Fisk, 1944; Biedenharn et al., 1984; Rhoads and Miller,

1991; Hudson and Kesel, 2000; Wolfert and Maas, 2007) as

does vegetation. Bank erosion and rates of lateral movement

have been shown to be generally higher on unvegetated or

grassed banks than forested (Beeson and Doyle, 1995; Burc-

khardt and Todd, 1998; Harmel et al., 1999) and vary with the

type of land use (e.g., Micheli et al., 2004). Individual

trees and vegetation can increase roughness and resistance

(Ebisemiju, 1994; Thorne and Furbish, 1995). Much field and

experimental work is now ongoing into vegetation effects.

Tectonics affect channel pattern and form of meanders

(Schumm, 2005) mainly by the influence on slope. For ex-

ample, Gomez and Marron (1991) detected differential

morphology and changes upstream and downstream of uplift

axes. Tectonics can also cause lateral tilting of meander courses

(Nanson, 1980; Aswathy et al., 2008).

Although the autogenic nature of meander evolution and

the lack of inherent stabilization of many meanders is now

widely recognized, it is still acknowledged that the primary

controls on behavior and morphology are discharge, sediment

size and supply, bank resistance, and gradient, and thus if any

of these change then a response in the river channel is likely.

Many studies have aimed to identify and measure the re-

sponses of meandering channels to such allogenic alterations

(e.g., Bradley and Smith, 1984; Erskine et al., 1992; Klein,

1985; Uribelarrea et al., 2003; Tiegs and Pohl, 2005).

The problems caused by channel mobility are such that

very many meandering channels are now controlled by struc-

tures to prevent or reduce bank erosion and channel move-

ment. Much engineering modeling has aimed to predict the

effects of proposed structures and some empirical studies have

examined the effects of modifications. Not only does the

prevention of bank erosion have effects at the site, but also the

reduction in sediment supply downstream has ramifications. A

common solution to the problem of channel mobility and

bank erosion, as well as to flooding, was that of channeliza-

tion. Very many channels worldwide have been straightened.

The detrimental effects of straightening naturally meandering

channels are now widely acknowledged and have led to the

massive movement toward river restoration. Most of these

schemes involve remeandering the channels and that has

meant producing designs for the new channel. Some have

been based on empirical evidence of past morphology, others

on theoretical, experimental, or empirical modeling (Kondolf,

2006). Rinaldi and Johnson (1997) and Kondolf (2006)

provide analyses of the accuracy of empirical relations of me-

ander parameters for use in meander restoration procedures.

9.16.5 Theoretical and Conceptual Explanations

9.16.5.1 Fundamental Physical and Numerical Analyses

The basic theoretical components of meandering and their

interactions are summarized by Camporeale et al. (2007) in

Figure 12, with the two key elements being curvature and an

erodible boundary. Derived linear models are based on the laws

of mass and momentum conservation governing fluid mechanics

within open channel flows with movable boundaries (bed and

banks) and therefore are held to fully account for meander

mechanics (flow properties, bed deformation, channel migra-

tion), although in a rather simplified way. In terms of the fun-

damental theory underlying much of the numerical modeling,

the basic premises for many of the models were developed by

Ikeda et al. (1981), Parker et al. (1983), Struiksma et al. (1985),

Parker and Andrews (1986), Johannesson and Parker (1989),

Odgaard (1989), and Ikeda and Parker (1989), based on earlier

fundamental work by Rozovski (1961), Leliavsky (1955, 1966),

Engelund (1974), and Kalwijk and de Vriend (1980), and others

on flow and bed topography in curved channels. Johanessen and

Parker’s paper corrected problems of Ikeda et al.’s model of not

satisfying sediment continuity; corrections also incorporated by

Blondeaux and Seminara’s (1985) earlier paper. Leliavsky (1966),

Ikeda et al. (1981), and Hasegawa (1989) proposed that there is a

linear relation of channel migration rate to the excess near-bank

longitudinal velocity, a fundamental explanation that is widely

accepted. Nevertheless, the extent of longitudinal flow, secondary

flow, and topographic steering influences on meandering has

been the subject of much modeling and experimentation.

In Seminara’s (2006) view, the major components of fun-

damental theory and modeling of meanders comprise: a

nonlinear planform evolution equation obtained by stipu-

lating that the centerline of erodible channels moves in the

lateral direction with some lateral migration speed; an erosion

rule relating this erosion speed to the near-bank hydro-

dynamics; and a model of flow and bed topography in sinu-

ous channels required to predict near-bank flow. Seminara

(2006) explains the mechanisms as follows:

The lateral pressure gradient associated with a lateral free surface

slope in a bend y[produces].. a secondary flow .. directed outward

close to the free surface and inward close to the bed. y.[which]

downstream, y.transfers momentum toward the outer bend...

Secondary flow transports sediments in the lateral inward direction

building up a rhythmic sequence of forced (point) bars and pools

respectively at the inner and outer bends of a train of meanders.

The establishment of a bar-pool pattern then gives rise to a further

‘topographically induced’ component of the secondary flow, which

drives an additional contribution to sediment transport and further

modifies the bed topography.

Curvature

Vortex-inducedstresses

Secondary currents(driven by curvature)

Transversalflow field

Bedload

Erodible boundary

(bed) (banks)

FrictionFree bars

Resonance

Secondary currents(driven by topography)

Gravity

Bank erosionPhase lag in the longitudinal flow

phase lag in the secondary currents

Momentumredistribution

Inwardbed stresses

Outward shifting ofbulk of the stream

Excess bankstress Downstream migration

and skewness

Shoaling(point bars)

+–

+

+

Topographicsteering

Figure 12 Components and interrelationship of factors influencing meander development. Redrawn from Camporeale, C., Perona, P., Porporato,A., Ridolfi, L., 2007. Hierarchy of models for meandering rivers and related morphodynamic processes. Reviews of Geophysics 45(1), RG1001,with permission from AGU.


Thus once a perturbation is induced this is amplified.

Since the early experiments (Friedkin, 1945), it has been

recognized that free bars form in alternate patterns in straight

channels that transport sediment (Figure 6(c)), and that

channels with erodible boundaries eventually evolve into a

curved channel pattern with fixed (steady) bars in each bend

(point bars). The formation of alternate free bars in straight

channels has been analyzed theoretically in ‘bar theory’;

Tubino et al. (1999) state that

The formation of bars has been conclusively explained in terms of

an inherent instability of erodible bed subject to a turbulent flow in

almost straight channels, which leads to the spontaneous devel-

opment of bottom perturbations (free bars) migrating downstream.

Tubino and Seminara (1990) originally identified that free

bars in straight channels become suppressed and become fixed

bars as channel curvature increases, the threshold value at

which this occurs being a function of meander wavenumber

and sediment characteristics for given flow. Blondeaux and

Seminara (1985) identified a condition of resonance in which

the meander wavenumber and the width ratio of the channel

take values such as to force formation of free bars which

neither grow nor decay either in time or in space. Both theory

and experiments suggest that the formation of free bars is

controlled by a threshold of width/depth ratio of the channel

that depends on the Shields stress and roughness.

Fluvial bars may also be considered to arise as the result of

forcing effects of curvature or possibly width variations or

confluences. This complementary approach (Tubino et al.,

1999) is termed ‘bend theory’ whereby ‘meander development

is controlled by the nonlinear interaction between self-excited

(free) and curvature-driven (forced) bed responses’. The major

bend theory was further developed by Seminara et al. (2001)

and Zolezzi and Seminara (2001) who produced theoretical

formulations to show that crossing the resonance barrier leads

to a reverse in directions of meander and bar perturbation

migration, the subresonant condition having downstream

influence on bar migration and bend form and super-

resonance having upstream influence. The w/d (or aspect ratio

w/2d) is a fundamental control on behavior. Simulations

using this theory have now produced compound bend evo-

lution (e.g., Frascati and Lanzoni, 2009).

Much debate has long surrounded the role of alternate bars

in meander development. Mosselman et al. (2006) explain

overdeepening as essentially being due to the superimposition

of a steady alternate bar pattern on a streamwise uniform bed

topography. Both Sun et al. (1996) and Lancaster and Bras

(2002) argue that the influence of alternate bars on the initial

development of meander loops appears to be negligible. The

argument between free bars becoming fixed (bar theory) and

fixed (steady) bars being induced by the planform (bend

theory) can be termed as a difference between a temporal and

a spatial approach to the formation of steady bars (Crosato

and Mosselman, 2009). These authors have used a modeling

approach suited to fixed (steady) bars, which they argue is

more appropriate for real rivers than is a free migrating bar

method because most rivers have curvature.

A component of meandering and bar formation is grain

sorting in bends. Seminal theoretical work on this was by



Parker and Andrews (1985) in which two-dimensional bed

load transport of graded material was produced by incorpor-

ating effects of gravity on lateral slopes and of secondary flows.

The model indicated that the locus of the coarse sediment

transport shifts from the inner to the outer bank near the bend

apex. An integrated model of flow, sediment transport, bed

topography, and grain sorting was produced by Bridge (1992),

and further developments incorporating bank erosion were

produced by Darby et al. (2002) and Duan and Julien (2005).

Meander growth and meander migration arise from the

occurrence of a phase lag between bank erosion, produced by

the flow pattern, and channel curvature. It is argued that a lag

between curvature of the channel and flow produces a spatial

memory effect and the characteristic skewness found in many

bends. Seminara (2006) considers that nonlinear analytical

solutions of theoretical equations show that ‘‘patterns emer-

ging from observations of geomorphologists [such as sine-

generated and Kinoshita curves] are not purely empirical

correlations, but rather different approximations of an exact

periodic solution of the planform evolution equation’’ related

to the harmonics of the curvature relations. Thus multilobe

meander loops have been explained by growth of higher order

harmonics (Seminara et al., 2001; Sun et al., 2001). Seminara

et al. (2001) also noted that no equilibrium solution has been

found, though they consider the evidence indicates that the

meander growth rate is found to decrease sharply in the late

stage of meander development, whereas the migration speed

of the meander train is found to decrease monotonically from

incipient formation to cut-off.

There are a number of limiting assumptions of the pre-

vailing linear theory and models, and a current debate is the

extent to which processes and relations are linear or nonlinear.

Theories and models are now being developed which in-

corporate nonlinearities and reduce some of the present lim-

iting assumptions (Pittaluga et al., 2009), though these are

still within a reductionist, mechanistic framework. Mosselman

et al. (2006) reviewed the history of the ‘shifting interpret-

ations’ of the overdeepening theory and demonstrate that

mathematical analyses of physical systems ‘do not produce

straightforward answers or predictions, but inherently require

interpretations based on experimental evidence and a thor-

ough understanding of the underlying physical processes’. The

nature of the curvature influence in bends is still not fully

understood and Guneralp and Rhoads (2009) suggest that ‘the

convolution functions used in theoretical models of meander

migration are hypothetical in nature and none has been

evaluated empirically using data on the spatial structure of the

curvature–migration relation obtained from natural me-

andering rivers’.

9.16.5.2 Conceptual Analyses

At a more conceptual level, underlying much of the inter-

pretation of morphology and morphological changes in flu-

vial geomorphology is the theory of equilibrium and

adjustment. It is assumed that channel form, as measured by

variables such as meander wavelength and channel width, is

adjusted to the discharge and sediment load delivered to it.

This is evidenced by statistically stable relations from

empirical measurements. It is assumed that, as changes in

these basic external controls take place, for example, by

climate change or by land-use change, water control or ab-

straction, the channel form will adjust to a new equilibrium.

Numerous case studies have demonstrated such adjustment

and net change in meander characteristics. Changes in

channel form are therefore explained as adjustment to chan-

ged extrinsic factors. In the equilibrium state it is assumed

that meanders migrate but do not change in morphology,

once the period of development is complete, and that cut-offs

are largely due to variation in rates of movement associated

with differing resistance and constraints within the channel

system, mainly valley width. Firmly embedded in the

traditional theory of extrinsic controls and explanation of

meander morphology and allogenic causes of change are ideas

of major factors influencing river planform. Though discharge

largely controls scale of meanders, caliber and amount of

sediment load, gradient, channel resistance (including vege-

tation), structure and tectonics, valley size, and long-term

landscape development can all affect the details of

morphology.

Leopold and associates, in research in the 1960s, argued

that the quasi-equilibrium meander form that develops is re-

lated to the most probable state, that of minimization of

variance, which is a compromise between minimum total

work and uniform distribution of power expenditure, and that

the sine-generated form minimizes variance (Leopold, 1994).

Such arguments have been dismissed as teleological. Equi-

librium behavior has been reexamined by Eaton et al. (2006)

in a conceptual model of meander initiation, within an

equilibrium and slope-minimizing context. They attempt to

explain why uniform shear stress distributions are nearly al-

ways unstable, once perturbed. They base this on the feedback

process between asymmetry of cross section shear stress dis-

tribution and local transport capacity. The initial perturbation

is related to turbulence on side walls.

The research on meander change in the 1970s and early

1980s showed that many meanders exhibit no stabilization to

an equilibrium form, rather that continuous evolution occurs,

in some cases through to cut-off. At first there was an as-

sumption amongst geomorphologists that this was still an

adjustment to changed controls. Eventually, partly from the

empirical evidence and partly from theoretical modeling, it

has become more accepted that such a sequence is autogenic

and intrinsic. Hickin and Nanson (1975) suggested that the

increase in migration rate is nonlinear to a maximum at a

critical curvature, usually r¼2–3, and decreases at higher

curvature and this has since been substantiated by other evi-

dence (Hooke, 1997; Hudson and Kesel, 2000). The Hickin

and Nanson relation is empirical rather than theoretically

derived, but it has now been argued that it is predicted by

physics-based models (Crosato, 2009). The rising limb can be

explained by the decrease in relative lag distance between

near-bank flow velocity and forcing curvature as r/w increases.

The falling limb results from the decrease in local channel

curvature and near-bank flow velocity excess. Bagnold (1960)

argued that energy losses were at a minimum at r/w 2–3 and

Hooke (1975) had predicted from experiments that the most

stable meander geometry would occur at r/w 2–3 because of

the shear stress distribution.


Development of nonlinear dynamical or chaos theory and

ideas of self-organization have been applied to river me-

andering at a conceptual level (Stolum, 1996, 1998; Phillips,

2007). The idea of self-organized criticality (SOC) originates

from Bak (Bak, 1996; Bak et al., 1987; Bak and Chen, 1991).

Many composite systems naturally evolve to a critical state in

which a minor event starts a chain reaction that can affect any

number of elements in the system. It is a holistic theory, which

does not depend on microscopic mechanisms. Based on this,

Stolum (1996, 1998) developed a simulation model of me-

anders based on fluid mechanics theory and showed that me-

anders will tend toward a critical state of sinuosity and then

oscillate by occurrence of cut-offs. A straight course represents

order and a highly sinuous course chaos. In the model, bends

developed and cut-offs occurred to bring about self-organiza-

tion. Meanders in an unconstrained state developed toward a

critical sinuosity limit of 3.14 (which is p). Beyond this limit,

cut-offs occur to maintain the steady state of the critical sinu-

osity. The system may at times undershoot or overshoot. In the

phase approaching criticality then occasional cut-offs occur, but

in the supercritical state clusters of meanders or avalanches

occur. Stolum (1998) also recognized a power-law distribution

of size of cut-offs, tested by an example of satellite imagery of

some rivers in Brazil. Hooke (2004) produced an example

which she suggests fits this framework, with clustering of cut-

offs explained by the sinuosity state. Montgomery (1996) used

modeling and comparison with natural river reaches to plot

attractors and concluded that the rivers were not clearly chaotic.

It has been argued by others that cut-offs induce long-term

equilibrium and reduce complexity of sinuosity (e.g., Howard

and Knutson, 1984; Camporeale et al., 2005, 2008). Perucca

et al. (2005) and Frascati and Lanzoni (2010) suggest there is

no evidence of chaotic behavior in the long-term in me-

andering rivers. Not all rivers are highly mobile and Hooke

(2003, 2007) has suggested a framework in which high activity

may be reconciled with equilibrium behavior.

Theoretical and experimental models have mostly assumed

a temporally constant and spatially equal channel width.

Those that have allowed for variation have assumed that

movement of the outer bank line (erosion) and inner bank

(deposition) are balanced within short time periods. Alter-

ations in width over time were assumed to be adjustments to

altered discharge or occurrence of flood events. Recent re-

search suggests that the two banks may be operating more

independently (Lauer and Parker, 2008) though Nanson and

Hickin (1983) suggested that the annual lateral migration of

river bends is not a continuous process in space and time;

rather it is a process in which ‘the concave bank rushes ahead

only to stop and wait until the convex bank catches up before

rushing ahead again.’

9.16.5.3 Experimental, Modeling and Numerical AnalysisResults

Much of the flume experimentation is aimed at understanding

the influences of flow structure on magnitude and position of

scour and deposition in meander bends and extent of over-

deepening (outer-bend pools being deeper than the equi-

librium outer bend water depth). Differences persist in the

detailed flow structure produced by various studies, particularly

the intensity, size, and position of secondary flow cells. Many

researchers are examining the influence of curvature on flow

structure and processes (e.g., Blanckaert, 2009; Termini, 2009);

for example, the difference in flow structure in upstream and

downstream skewed Kinoshita bends (Abad and Garcia,

2009), or the conditions giving rise to development of outer

bank secondary cells (Blanckaert and de Vriend, 2004). Many

of the experiments use idealized configurations, including the

sine-generated curve, so questions still remain on the applic-

ability to real meandering channels, and field testing is still

limited.

In more realistic simulations in which self-formed meanders

are allowed to develop, Braudrick et al. (2009) found that

elevated bank strength (provided by alfalfa sprouts) relative to

the cohesionless bed material and the blocking of troughs

(chutes) in the lee of point bars via suspended sediment de-

position were the necessary ingredients to successful me-

andering. Varying flood discharge was not necessary but sand

supply may be essential. Pyrce and Ashmore (2005) confirmed

from flume experiments an inherent connection between the

loci of particle deposition and point bar formation, largely

controlled by the morphology of the channel with deposition

typically focused around the point bar apex, downstream of the

apex (contributing to downstream bar migration), and at the

bar head/riffle surface, but loci of deposition vary with stage of

flow and of development of the bend.

Many numerical models are now simulating the details of

specific component processes. Olsen (2003) and Ruther and

Olsen (2007) demonstrate that 3D CFD can now be used to

model features of meandering including migration and chute

cut-offs. Numerical modeling such as that of Chen and Duan

(2006) is now simulating migration of meandering channel

including downstream translation, lateral extension, expan-

sion, and downstream and upstream rotation. They found that

low-sinuosity, free meanders migrate rapidly downstream. As

the sinuosity increases, downstream translation diminishes,

and meandering loops expand laterally with the head rotating

toward downstream and then upstream (as found in empirical

studies). The simulated results indicated that the gradient of

the longitudinal sediment transport rate is essential in mod-

eling meandering evolution. Bank erosion rates and mech-

anisms are obviously very influential, and basal erosion and

bed load transport are particularly important (Duan and

Julien, 2005). Darby et al. (2002) show that cohesion of bank

material significantly influences equilibrium bed topography,

as does the bed material size in energetic rivers.

Simulation models from quite an early stage (e.g., Howard

and Knutson, 1984; Lancaster and Bras, 2002) implied that

multiloop bends may be sensitive to bank roughness, sup-

porting field experimental evidence that roughness may influ-

ence meander morphology (Thorne and Furbish, 1995).

Though few models are able to produce compound forms and

neck cut-offs, the Zolezzi-Seminara (ZS) model has done so

(Seminara et al., 2001; Camporeale et al., 2007) (Figure 13).

Simulation models produce sequences of meanders but their

morphology may not fit with real meanders (Howard and

Hemberger, 1991), and Frascati and Lanzoni (2009) found that

‘even in the presence of the strong filtering action exerted by

cut-off processes, a close, although not yet complete, similarity

(a)

(b)

y

50

0

−50

−100

100

y

50

0

−50

−100

100

Flow direction

Flow direction

0 100 200 300 400x

500 600 700 800

Figure 13 Example of output from numerical simulation model. Numerical simulations beyond cut-off: (a) subresonant case, b¼9, t�¼0.3,ds¼0.005, E¼10� 8, dune covered bed. (b) superresonant case, b¼13, t�¼0.3, ds¼0.005, E¼10� 8, dune-covered bed. Note the formationof compound loops. Also note that sinuosity decreases as development proceeds. In the subresonant case: red 2.67; green 3.08; black thin1.80;black thick 1.69. In the superresonant case: red 2.98; green 2.22; black thin 2.32; black thick 2.45. (Calculations kindly provided by S.Lanzoni, 2005.) Reproduced from Seminara, G., 2006. Meanders. Journal of Fluid Mechanics 554, 271–297, with permission from CambridgeUniversity Press.


with natural meandering planforms can be achieved only by

adopting a flow field model which yincludes superresonant

conditions.’ Both studies showed that a large number of mor-

phological parameters are needed to characterize meander

morphology adequately, as Ferguson (1975) recognized.

Surprisingly, few comparisons of models have been made

to date, except the review by Camporeale et al. (2007), which

mainly considers the Ikeda et al. (1981), the Johanesson and

Parker (1989) and the Zolezzi and Seminara (2001) (ZS)

models, which build on each other. Flume experiments of

Zolezzi et al. (2005) confirm the theoretical positions that w/d

ratio of channels influence meander behavior and propa-

gation of overdeepening. Recent analysis of data from 100

gravel-bed rivers also appear to support the ideas of controls

on subresonant and superresonant behavior and propagation

of change in downstream and upstream directions by the

bankfull aspect ratio (0.5 w/d) and the Shields stress (Zolezzi

et al., 2009). Dense vegetation and reduced gravel supply were

found to promote the subresonant regime. Frascati and Lan-

zoni (2009) compare synthetic long-term morphology pro-

duced from ZS derived modeling with observed patterns of

rivers and also find two distinct behaviors.

The other main group of numerical models is based on

kinematic or empirical relations, that is, not derived from

fundamental physical principles. These are mainly based on

migration or erosion rate relations to curvature, many of them

derived from Hickin and Nanson (1975). The original em-

pirical relationship showed a nonlinear increase in migration

rate with increased curvature to some critical value (r/w 2–3)

beyond which the rate declined again. Guneralp and Rhoads

(2008) consider that the weakness of current theoretical

models aimed at predicting planform migration is that they

relate the rate of meander migration at a particular location to

the channel curvature at and upstream of that location. Using

a newly developed method of curvature analysis, Guneralp

and Rhoads (2009) demonstrated that the migration–curvature

relation is much more complex and needs more sophisticated

characterization of the curvature. The results also indicate

that the spatial memory of the curvature–migration relation

(i.e., the decay length of the spatial response) of simple bends

is longer than that of compound loops or multilobes. This

finding is in accord with the idea that simple bends migrate

downstream more than they migrate laterally, whereas com-

pound loops migrate laterally more than they migrate down-

stream (Hooke and Harvey, 1983; Hooke and Yorke, 2010;

Seminara et al., 2001). The changing structure of the upstream

curvature effect on migration rates with increasing planform

complexity that Guneralp finds suggests that the relationship

between planform curvature and migration rates is highly

nonlinear and spatially variable.

9.16.6 Perspective and Synthesis

The following is a summary of some of the most important

conclusions on key aspects of river meanders. Some of these

have been known for a long time, but modern research has

substantiated the conclusions and provided greater detail on

mechanisms and controls.

Meanders vary in morphology, with a general scaling factor

but shape varying with bank and bed materials and resistance,

gradient, stage of bend evolution, tectonics, and other con-

trols. Active meanders (rapidly changing) vary in width

through the bends; equal width meanders are a sign of sta-

bility. Discharge and sediment load are major controls and if

either is altered or varies then adjustment of meanders

morphology occurs, for example, in response to climate

change or human factors.

Commonly occurring sequences of meander development

and evolution have been identified, with bends tending to

develop from low curvature form through to high curvature

then compound forms and eventually being cut-off. Such



sequences are autogenic and inherent and can be observed in

timescales of decades on the most active meanders. Low

sinuosity meanders tend to migrate in a downstream direction,

whereas tighter bends grow cross valley. Rates accelerate, that is,

are nonlinear in relation to curvature, through to compound

stage but then may slow again.

Cut-offs may occur in various positions on meander loops

and may represent completion of the evolution sequence

(neck cut-offs) or may interrupt loop development (chute cut-

offs). The overall role of cut-offs and the extent to which

meander behavior is chaotic is debated, but evidence of cha-

otic behavior is limited and cut-offs appear to maintain an

equilibrium of sinuosity in the long-term. However, per-

spective on this may depend on the rates of activity and the

timescale of analysis.

Flow configuration in meanders is generally helicoidal, but

the extent and complexity of development of secondary flow

cells and vortices is still much debated and does vary with

meander morphology, particularly curvature, transverse slope,

and width/depth ratio. Flow pattern influences meander

change because bank erosion is related mainly to the near-

bank velocity. The secondary flow patterns bring sediment to

the inner bank where it forms point bars, but sediment of

different sizes show different trajectories, with coarser material

being carried outward and finer material inward.

Bank erosion occurs primarily by hydraulic erosion related

to peak flows. The mechanisms vary with bank composition,

height, state of moisture, or pore water pressures. Many banks

are composite and fail by cantilever failure. Rate of erosion is

related to near-bank velocity, which is influenced by bend w/d,

asymmetry, gradient, curvature, transverse slope, and to bank

resistance.

Alternate, freely migrating bars develop in straight channels

as a result of perturbation of flow and interaction with the

erodible boundary. Theory predicts that bars become fixed as

sinuosity develops and free (migrating) bars appear to be rare

in meandering channels. Theory suggests limits of sinuosity at

which they become fixed. Other bars are forced by curvature or

width, the most important being point bars, induced by

curvature. Fixed mid-channel bars can be common in me-

andering channels and influence bend development. They

may be width–induced. Erosion and deposition may not be

equal at all times and thus width varies over time.

Debates on explanation by bar or bend theory can be re-

solved into the former being a temporal explanation and the

latter a spatial explanation. Thus in bar theory meanders

gradually develop, but in bend theory curves are already pre-

sent. Theory of resonance indicates that changes may be

propagated in a downstream or upstream direction, de-

pending primarily on w/d ratio, and sediment size in bends.

The debate on why rivers meander is regarded as largely

resolved from a theoretical point of view as a perturbation and

propagation of instability in flow against an erodible bound-

ary in which there is a resonance at certain harmonics.

9.16.6.1 Future Research

Current debates still surround some issues and are the subject

of ongoing research or provide the agenda for future research.

These can be summarized as debates between: equilibrium or

evolution of morphology; extent and distribution of simple or

compound forms; the extent of linear or nonlinear relations;

the degree of allogenic compared with autogenic influences;

the influence of primary versus secondary flows in bend pro-

cesses; and the designs and principles that should be used for

river management and restoration.

The behavior of bends in different environments, materials

and conditions and whether their morphology does stabilize

in some circumstances, with simple downstream migration, or

whether bends have an evolutionary trend and sequence of

development requires further investigation. It may be the case

that both stabilization and evolution are applicable but evi-

dent on different timescales so this needs to be researched

more fully. Not enough evidence is available of the dynamics

of change at various timescales and of the variation between

different environments and types of river. More dating of

sediments and of channel movement is needed to produce

trajectories and timescales of meander development and life

cycles, reworking of floodplains, and life cycles of bars.

Mechanisms of development of meander features need to be

studied in the field over decadal timescales that allow influ-

ence of variations in flow and conditions and of feedback

effects to be analyzed.

More investigation is needed of the mechanisms of devel-

opment of compound forms and the interrelationships of

change in bed topography, locus of erosion and flow patterns,

particularly from field measurements. More discussion and

model development needs to incorporate nonlinear relations

and test their effects. Evidence for and understanding of

autogenic behavior in meandering needs to be further re-

searched, and the extent to which morphology and changes in

form are inherent and predicted by theory and also the extent

to which they are influenced by local factors needs to be more

fully quantified. More field, empirical quantification of re-

sistance, including that of vegetation, and its effects on mi-

gration rates and meander morphology is needed and further

research into the spatial scale of influence on forces, particu-

larly of curvature and width variations.

Numerical and experimental models need to incorporate

feedback effects and adjustment of altered morphology. Major

developments in theoretical modeling have taken place, but

assumptions still need to be reduced, for example, fixed banks,

equal width, and steady flows. Some models are still far from

reality though they help to solve theoretical problems. Most

modeling is linear and reductionist, but nonlinear and holistic

approaches need to be more fully explored. The success of

some kinematic models may indicate that there is an emergent

behavior that is not apparent in reductionist approaches.

Development of realistic predictive models, incorporating the

spatial variability of controls such as gradient and resistance,

interaction of adjacent bends, autogenic sequences and feed-

backs, and complexity is a major goal. All modeling requires

much more empirical and field validation.

9.16.7 Conclusions

Major developments have taken place in understanding river

meandering and the variation in characteristics and activities


that occur. Equilibrium and statistical relations of meander

morphology to major controls such as discharge are still

found to be applied at a general level. However, the com-

plexity of some meander morphology and the widespread

occurrence of sequences of continuous evolution of some

meanders have now been recognized. The variation in mo-

bility and morphology is seen to be related to major factors

such as stream power, gradient, and resistance of boundary

materials, and understanding of localized effects and feedback

mechanisms is increasing.

It is now largely accepted that fundamental bend theory

based on propagation of instabilities in channels explains the

development of meanders, though variations are still apparent

in the details of numerical modeling. The extent of nonlinearity

of behavior is still under discussion. Mathematical theory, pro-

cesses and control of meandering have all been investigated

through experiments in flumes and model channels and by

numerical simulation but much more testing of models with

detailed geomorphological field evidence is still needed. Pre-

dictive models of specific meander behavior and movement are

still proving elusive, but understanding of dynamics of meander

mobility has progressed. Spatial variability of controls such as

gradient and resistance need to be incorporated. Future research

should bring together these approaches and provide further

insight; meander research is entering an exciting phase in which

this integration is being realized.

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Biographical Sketch

Janet Hooke is Professor of Physical Geography in the School of Environmental Sciences at the University of

Liverpool, UK. She obtained her BSc from Bristol University and her PhD from Exeter University. She is a fluvial

geomorphologist specializing in research on river meanders and river channel changes, particularly the spatial and

temporal dynamics of morphological changes on event to historical timescales, the impact of hydrological

variations and the analysis of sediment processes and fluxes. In addition to publishing more than 80 research

papers, books, and book chapters, she has advised on environmental management of rivers and catchments,

especially in relation to erosion and flooding. She has managed more than 30 research projects, including

Coordinator of an EU project on combating land degradation. She works in both semiarid and humid fluvial

systems. In 2009, she was awarded the Busk Medal by the Royal Geographical Society of UK for her field research

into river systems and their conservation and for demonstrating the contribution of physical geography to

environmental management, conservation, and policy. She is a past Chair of the British Society for


Geomorphology.

hooke 2013

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