Meander

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A hypothetical stream bed following a tilted valley.

The maximum gradient is along the down-valley

axis represented by a hypothetical straight channel.

Meanders develop, which lengthen the course of the

stream, decreasing the gradient.

Meanders of the Rio Cauto at Guamo

Embarcadero, Cuba.

MeanderFrom Wikipedia, the free encyclopedia

A meander, in general, is a bend in a sinuous watercourseor river. A meander forms when moving water in a streamerodes the outer banks and widens its valley, and the innerpart of the river has less energy and deposits silt. A streamof any volume may assume a meandering course,alternately eroding sediments from the outside of a bendand depositing them on the inside. The result is a snakingpattern as the stream meanders back and forth across itsdown-valley axis. When a meander gets cut off from themain stream, an oxbow lake forms. Over time meandersmigrate downstream, sometimes in such a short time as tocreate civil engineering problems for local municipalitiesattempting to maintain stable roads and bridges.

There is not yet full consistency or standardization ofscientific terminology used to describe watercourses. Avariety of symbols and schemes exist. Parameters based on mathematicalformulae or numerical data vary as well, depending on the database usedby the theorist. Unless otherwise defined in a specific scheme"meandering" and "sinuosity" here are synonymous and mean anyrepetitious pattern of bends, or waveforms. In some schemes,"meandering" applies only to rivers with exaggerated circular loops orsecondary meanders; that is, meanders on meanders.

Sinuosity is one of the channel types that a stream may assume over all orpart of its course. All streams are sinuous at some time in their geologichistory over some part of their length.

Contents

1 Origin of term

2 Meander geometry

3 Formation

3.1 Stochastic theory

3.2 Equilibrium theory

3.3 Geomorphic and morphotectonic theory

4 Associated landforms

4.1 Slip-off slope

4.2 River-cut cliff

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Uvac canyon meander, Serbia

4.3 Erosion mechanics

4.4 Deposits

4.4.1 Incised meanders

4.4.2 Oxbow lakes

4.4.3 Abandoned meander (rincon)

4.4.4 Scroll-bars

5 Derived quantities

6 See also

7 References and notes

8 Bibliography

9 External links

Origin of term

The term derives from a river located in present-day Turkey and known to the Ancient Greeks as Μαίανδρος

Maiandros (Latin: Maeander),[1] characterised by a very convoluted path along the lower reach. As such, even inClassical Greece (and in later Greek thought) the name of the river had become a common noun meaning anythingconvoluted and winding, such as decorative patterns or speech and ideas, as well as the geomorphological

feature.[2] Strabo said: "... its course is so exceedingly winding that everything winding is called meandering."[3]

The Meander River is located south of Izmir, east of the ancient Greek town of Miletus, now, Milet, Turkey. Itflows through a graben in the Menderes Massif, but has a flood plain much wider than the meander zone in its lowerreach. In the Turkish name, the Büyük Menderes River, Menderes is from "Meander".

Meander geometry

The technical description of a meanderingwatercourse is termed meander geometry or

meander planform geometry.[4] It is characterizedas an irregular waveform. Ideal waveforms, such asa sine wave, are one line thick, but in the case of astream the width must be taken into consideration.The bankfull width is the distance across the bed atan average cross-section at the full-stream level,typically estimated by the line of lowest vegetation.

As a waveform the meandering stream follows thedown-valley axis, a straight line fitted to the curve such that the sum of all the amplitudes measured from it is zero.This axis represents the overall direction of the stream.

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Concave bank and convex bank,

Great Ouse Relief Channel, England.

Meander of the River Cuckmere in

Southern England

At any cross-section the flow is following the sinuous axis, the centerline of the bed. Two consecutive crossingpoints of sinuous and down-valley axes define a meander loop. The meander is two consecutive loops pointing inopposite transverse directions. The distance of one meander along the down-valley axis is the meander length orwavelength. The maximum distance from the down-valley axis to the sinuous axis of a loop is the meander width oramplitude. The course at that point is the apex.

In contrast to sine waves, the loops of a meandering stream are more nearly circular. The curvature varies from amaximum at the apex to zero at a crossing point (straight line), also called an inflection, because the curvaturechanges direction in that vicinity. The radius of the loop is the straight line perpendicular to the down-valley axisintersecting the sinuous axis at the apex. As the loop is not ideal, additional information is needed to characterize it.The orientation angle is the angle between sinuous axis and down-valley axis at any point on the sinuous axis.

A loop at the apex has an outer or convex bank and an inner or concavebank. The meander belt is defined by an average meander widthmeasured from outer bank to outer bank instead of from centerline tocenterline. If there is a flood plain, it extends beyond the meander belt.The meander is then said to be free—it can be found anywhere in theflood plain. If there is no flood plain, the meanders are fixed.

Various mathematical formulae relate the variables of the meandergeometry. As it turns out some numerical parameters can be established,which appear in the formulae. The waveform depends ultimately on thecharacteristics of the flow but the parameters are independent of it andapparently are caused by geologic factors. In general the meander lengthis 10-14 times, with an average 11 times, the fullbank channel width and

3 to 5 times, with an average of 4.7 times, the radius of curvature at the apex. This radius is 2-3 times the channelwidth.

A meander has a depth pattern as well. The cross-overs are marked byriffles, or shallow beds, while at the apices are pools. In a pool directionof flow is downward, scouring the bed material. The major volume,however, flows more slowly on the inside of the bend where, due todecreased velocity, it deposits sediment.

The line of maximum depth, or channel, is the thalweg or thalweg line. Itis typically designated the borderline when rivers are used as politicalborders. The thalweg hugs the outer banks and returns to center over theriffles. The meander arc length is the distance along the thalweg over onemeander. The river length is the length along the centerline.

Formation

Watch a Time Lapse of a Meandering River (http://socalgis.org/2014/03/12/time-lapse-of-a-river-changing-course/)

Meander formation is a result of natural factors and processes. The waveform configuration of a stream is

constantly changing. Fluid flows around a bend in a vortex.[5] Once a channel begins to follow a sinusoidal path, theamplitude and concavity of the loops increase dramatically due to the effect of helical flow sweeping dense eroded

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Life history of a meander

material towards the inside of the bend, and leaving the outside of the bend unprotected and therefore vulnerable to

accelerated erosion, forming a positive feedback loop. In the words of Elizabeth A. Wood:[6]

"... this process of making meanders seems to be a self-intensifying process ... in which greatercurvature results in more erosion of the bank, which results in greater curvature ...."

The cross-current along the floor of the channel is part of the secondary flow and sweeps dense eroded material

towards the inside of the bend.[7] The cross-current then rises to the surface near the inside and flows towards theoutside, forming the helical flow. The greater the curvature of the bend, and the faster the flow, the stronger is the

cross-current and the sweeping.[8]

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Spectacular meander scars, oxbow

lakes and abandoned meanders in the

broad flood plain of the Rio Negro,

Argentina. 2010 astronaut photo from

ISS.

Due to the conservation of angular momentum the speed on the inside of

the bend is faster than on the outside.[9]

Since the flow velocity is diminished, so is the centrifugal pressure.However, the pressure of the super-elevated column prevails, developingan unbalanced gradient that moves water back across the bottom fromthe outside to the inside. The flow is supplied by a counter-flow across

the surface from the inside to the outside.[10] This entire situation is verysimilar to the Tea leaf paradox. This secondary flow carries sedimentfrom the outside of the bend to the inside making the river more

meandering.[11]

As to why streams of any size become sinuous in the first place, there area number of theories, not necessarily mutually exclusive.

Stochastic theory

The stochastic theory can take many forms but one of the most general statements is that of Scheidegger:[12]

"The meander train is assumed to be the result of the stochastic fluctuations of the direction of flowdue to the random presence of direction-changing obstacles in the river path."

Given a flat, smooth, tilted artificial surface, rainfall runs off it in sheets, but even in that case adhesion of water tothe surface and cohesion of drops produce rivulets at random. Natural surfaces are rough and erodible to differentdegrees. The result of all the physical factors acting at random is channels that are not straight, which thenprogressively become sinuous. Even channels that appear straight have a sinuous thalweg that leads eventually to asinuous channel.

Equilibrium theory

In the equilibrium theory, meanders decrease the stream gradient until an equilibrium between the erodibility of the

terrain and the transport capacity of the stream is reached.[13] A mass of water descending must give up potentialenergy, which, given the same velocity at the end of the drop as at the beginning, is removed by interaction with thematerial of the stream bed. The shortest distance; that is, a straight channel, results in the highest energy per unit oflength, disrupting the banks more, creating more sediment and aggrading the stream. The presence of meandersallows the stream to adjust the length to an equilibrium energy per unit length in which the stream carries away allthe sediment that it produces.

Geomorphic and morphotectonic theory

Geomorphic refers to the surface structure of the terrain. Morphotectonic means having to do with the deeper, ortectonic (plate) structure of the rock. The features included under these categories are not random and guidestreams into non-random paths. They are predictable obstacles that instigate meander formation by deflecting thestream. For example, the stream might be guided into a fault line (morphotectonic).

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The depositional slip-off slope is on

the left whilst there is a small river

cliff to the right. River Ashes Hollow,

UK.

Glen Canyon, USA

Associated landforms

Slip-off slope

On the inside of a meander is a gentle slope referred to as the slip-offslope. It is often marked by a point bar in the river.

River-cut cliff

On the outside of a meander the river cuts into the bank, often resulting ina river[-cut] cliff, also known as a cut bank, or a bluff.

Erosion mechanics

Most meanders occur in the region of a river channel with shallowgradients, a well-developed floodplain, and cohesive floodplain material.Deposition of sediment occurs on the inner edge, because the secondary

flow of the river[14] sweeps and rolls sand, rocks and other submerged objects across the bed of the river towardsthe inside radius of the river bend, creating a point bar below the slip-off slope. Erosion is greater on the outside ofthe bend where the soil is not protected by deposits of sand and rocks. The current on the outside bend is moreeffective in eroding the unprotected soil, and the inside bend receives steadily increasing deposits of sand androcks, and the meander tends to grow in the direction of the outside bend, forming a small cliff called a cut bank.This can be seen in areas where willows grow on the banks of rivers; on the inside of meanders, willows are oftenfar from the bank, whilst on the outside of the bend, the roots of the willows are often exposed and undercut,eventually leading the trees to fall into the river. This demonstrates the river's movement. Slumping usually occurs onthe concave sides of the banks resulting in mass movements such as slides.

Deposits

Incised meanders

If the slope of an established meandering stream is suddenly increased,it will resume downward erosion – this happens when the base level ofthe stream is reduced, for example due to tectonic uplift of the region, aglobal fall in sea-level, collapse of a moraine-dammed lakedownstream, or by capture of the stream by a steeper one. As thestream erodes downwards, its established meandering pattern willremain as a deep valley known as an incised meander or entrenchedmeander. Rivers in the Colorado Plateau, the Kentucky RiverPalisades in central Kentucky, and streams in the Ozark Plateau are noted for these incised meanders.

Oxbow lakes

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Goosenecks of the San Juan River, SE

Utah. Note cut-off meander at right

center.

Meanders, scroll-bars and oxbow lakes

in the Songhua River

Oxbow lakes are created when growing meanders intersect each other and cut off a meander loop, leaving itwithout an active cutting stream. This process is usually linked to flooding where the river will tend to the path of

least resistance.[15] The oxbow, being of much lower energy than the more direct path, collects more and moredeposited sediment each season of flooding until it becomes independent from the river. The largest oxbow lakeswill be in areas with wider flood plains where the rivers have moreroom to meander. Over a period of time, these oxbow lakes tend todry out or fill in with sediments.

Abandoned meander (rincon)

Sometimes an incised meander is cut off, similar to an oxbow lake. Theresulting landform is known as an abandoned meander. In thesouthwest United States it is also known as a rincon. One dramaticexample, on Lake Powell, is called "The Rincon."

Scroll-bars

Scroll-bars are a result of continuous lateral migration of a meander

loop that creates an asymmetrical ridge and swale topography[16] onthe inside of the bends. The topography is generally parallel to the

meander, and is related to migrating bar forms and back bar chutes,[17]

which carve sediment from the outside of the curve and depositsediment in the slower flowing water on the inside of the loop, in aprocess called lateral accretion. Scroll-bar sediments are characterized

by cross-bedding and a pattern of fining upward.[18] Thesecharacteristics are a result of the dynamic river system, where largergrains are transported during high energy flood events and thengradually die down, depositing smaller material with time (Batty 2006).Deposits for meandering rivers are generally homogeneous and laterally

extensive unlike the more heterogeneous braided river deposits.[19]

There are two distinct patterns of scroll-bar depositions; the eddyaccretion scroll bar pattern and the point-bar scroll pattern. Whenlooking down the river valley they can be distinguished because thepoint-bar scroll patterns are convex and the eddy accretion scroll bar

patterns are concave.[20] Scroll bars often look lighter at the tops of theridges and darker in the swales. This is because the tops can be shapedby wind, either adding fine grains or by keeping the area unvegetated, while the darkness in the swales can beattributed to silts and clays washing in during high water periods. This added sediment in addition to water thatcatches in the swales is in turn is a favorable environment for vegetation that will also accumulate in the swales.

Derived quantities

The meander ratio[21] or sinuosity index[22] is a means of quantifying how much a river or stream meanders (howmuch its course deviates from the shortest possible path). It is calculated as the length of the stream divided by thelength of the valley. A perfectly straight river would have a meander ratio of 1 (it would be the same length as its

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valley), while the higher this ratio is above 1, the more the river meanders.

Sinuosity indices are calculated from the map or from an aerial photograph measured over a distance called thereach, which should be at least 20 times the average fullbank channel width. The length of the stream is measuredby channel, or thalweg, length over the reach, while the bottom value of the ratio is the downvalley length or airdistance of the stream between two points on it defining the reach.

The sinuosity index plays a part in mathematical descriptions of streams. The index may require elaboration,because the valley may meander as well—i.e., the downvalley length is not identical to the reach. In that case thevalley index is the meander ratio of the valley while the channel index is the meander ratio of the channel. Thechannel sinuosity index is the channel length divided by the valley length and the standard sinuosity index is the

channel index divided by the valley index. Distinctions may become even more subtle.[23]

Sinuosity Index has a non-mathematical utility as well. Streams can be placed in categories arranged by it; forexample, when the index is between 1 to 1.5 the river is sinuous, but if between 1.5 and 4, then meandering. Theindex is a measure also of stream velocity and sediment load, those quantities being maximized at an index of 1(straight).

See also

Riffle-pool sequence

Helicoidal flow

Baer's law

Meander cutoffs in Avulsion (river)

Meander scar

Crevasse splay

Jet stream exhibits meander also

References and notes

1. ^ "Meander" (http://www.merriam-webster.com/dictionary/meander). Merriam-Webster. Retrieved July 12, 2012.

2. ^ "Meander" (http://www.etymonline.com/index.php?term=meander&allowed_in_frame=0). Online Etymology

Dictionary. Retrieved July 12, 2012.

3. ^ Strabo, Geography, Book 12 Chapter 8 Section 15.

4. ^ The technical definitions of this section rely heavily on Julien, Pierre Y. (2002). River Mechanics. Cambridge

University press. pp. 179–184. ISBN 0-521-52970-0. In addition concepts are utilized from Graf, Walter (1984).

Hydraulics of Sediment Transport. Water Resources Publications. pp. 261–265. ISBN 0-918334-56-X.

5. ^ Lewalle, Jacques (2006). "Flow Separation and Secondary Flow: Section 9.1"

(http://www.ecs.syr.edu/faculty/lewalle/FluidDynamics/fluidsCh9.pdf). Lecture Notes in Incompressible Fluid

Dynamics: Phenomenology, Concepts and Analytical Tools. Syracuse, NY: Syracuse University..

6. ^ Wood, Elizabeth A. (1975). Science from Your Airplane Window: 2nd Revised Edition. New York: Courier

Dover Publications. p. 45. ISBN 0-486-23205-0.

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Bibliography

Hickin, Edward J. (2003). "Meandering Channels". In Middleton, Gerard V. Encyclopedia of Sediments

7. ^ Hickin 2003, p. 432. One of the important consequences of helical flow in meanders is that sediment eroded

from the outside of a meander bend tends to move to the inner bank or point bar of the next downstream bend.

8. ^ Hickin 2003, p. 434.

9. ^ Hickin 2003, p. 432. "In the absence of secondary flow, bend flow seeks to conserve angular momentum so that

it tends to conform to that of a free vortex with high velocity at the smaller radius of the inner bank and lower

velocity at the outer bank where radial acceleration is lower."

10. ^ Hickin 2003, p. 432. "Near the bed, where velocity and thus the centrifugal effects are lowest, the balance of

forces is dominated by the inward hydraulic gradient of the super-elevated water surface and secondary flow

moves toward the inner bank."

11. ^ Callander, R.A. "River Meandering," Annual Review of Fluid Mechanics, 1978. 10:129-58

12. ^ Scheidegger, Adrien E. (2004). Morphotectonics. Berlin, New York: Springer. p. 113. ISBN 3-540-20017-7.

13. ^ Riley, Ann L. (1998). Restoring Streams in Cities: A Guide for Planners, Policymakers and Citizens. Washington

DC: Island Press. p. 137. ISBN 1-55963-042-6.

14. ^ Chant, Robert J. (2002). "Secondary circulation in a region of flow curvature: Relationship with tidal forcing and

river discharge" (http://www.agu.org/pubs/crossref/2002/2001JC001082.shtml). Journal of Geophysical Research

107.

15. ^ Brower, Lincoln P "The Flooding river a study in riverine ecology," 1972.

16. ^ Woolfe and Purdon; Purdon, Richard (1996). "Deposits of a rapidly eroding meandering river: terrace cut and fill

in the Taupo Volcanic Zone". New Zealand Journal of Geology and Geophysics 39 (2): 243–249.

doi:10.1080/00288306.1996.9514708 (http://dx.doi.org/10.1080%2F00288306.1996.9514708).

17. ^ K. Whipple (September 2004). "Alluvial channels and their landforms". Surface Processes and Landscape

Evolution.

18. ^ Sam Boggs, Jr. (2003). Principles of Sedimentology and Stratigraphy (4 ed.). NJ: Pearson Prentice Hall.

ISBN 0-13-099696-3.

19. ^ G. Wasser (2005). "A Comparison Of Meandering River Deposits From The Middle Belly River And Horsefly

With Recent Milk River Valley Deposits; Central And Southern Alberta". Calgary, Alberta: Canadian Natural

Resource Limited.

20. ^ Norman D. Smith and John Rogers (1999). Fluvial Sedimentology (6 ed.). blackwell publishing. ISBN 0-632-

05354-2.

21. ^ Shaw, Lewis C. (1984). Pennsylvania Gazetteer of Streams Part II. Bulletin No. 16. Commonwealth of

Pennsylvania, Department of Environmental Resources. p. 8. OCLC 17150333

(https://www.worldcat.org/oclc/17150333).

22. ^ Gordon, Nancy D.; Thomas A. McMahon; Christopher J. Gippel; Rory J. Nathan (2005). Stream Hydrology: an

Introduction for Ecologists: Second Edition. John Wiley and Sons. pp. 183–184. ISBN 0-470-84357-8.

23. ^ Singh, R.Y. (2005). "Interface drainage analysis of a water divide". In Jansky, Libor; Haigh, Martin J.; Prasad,

Hushila. Sustainable Management of Headwater Resources: Research from Africa and India. Tokyo, New York:

United Nations University Press. pp. 87–106. ISBN 92-808-1108-8.

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Look up rincón inWiktionary, the freedictionary.

Wikimedia Commons hasmedia related to Meanders.

and Sedimentary Rocks. Kluwer Academic Encyclopedia of Earth Sciences. Dordrecht; Boston: Kluwer

Academic Publishers. pp. 430–434. ISBN 1-4020-0872-4.

Leopold, Luna B.; Langbein, W.B. (June 1966). "River Meanders". Scientific American: 60.

Thonemann, P., The Maeander Valley: A historical geography from Antiquity to Byzantium

(Cambridge, 2011) (Greek Culture in the Roman World Series).

External links

Movshovitz-Hadar, Nitsa; Alla Shmuklar (2006-01-01). "River

Meandering and a Mathematical Model of this Phenomenon"

(http://physicaplus.org.il/zope/home/en/1124811264/1141060775rivers_en). Physicalplus (Israel Physical

Society (IPS)) (7). Retrieved 2008-02-23.

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