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A meander is one of a series of regular sinuous curves in the channel of a river or other watercourse. It is produced as a watercourse
erodes
erodes
the
sediment Sediment is a naturally occurring material that is broken down by processes of weathering and erosion, and is subsequently sediment transport, transported by the action of wind, water, or ice or by the force of gravity acting on the particles. ...

sediment
s of an outer, concave bank (
cut bank Image:Point bar and cut bank.jpg, upCut bank erosion and point bar deposition as seen on the Powder River (Montana), Powder River in Montana. A cut bank, also known as a river cliff or river-cut cliff, is the outside bank of a water channel (strea ...
) and deposits sediments on an inner, convex bank which is typically a
point bar A point bar is a depositional feature made of alluvium that accumulates on the inside bend of streams and rivers below the slip-off slope. Point bars are found in abundance in mature or meandering streams. They are crescent-shaped and located on t ...

point bar
. The result of this coupled erosion and sedimentation is the formation of a
sinuous Image:rio-cauto-cuba.JPG, The meandering ''Cauto River, Rio Cauto'' at Guamo Embarcadero, Cuba, is not taking the shortest path downslope. Therefore, its sinuosity index is > 1. Sinuosity, sinuosity index, or sinuosity coefficient of a ...
course as the channel migrates back and forth across the axis of a
floodplain A floodplain or flood plain or bottomlands is an area of land adjacent to a river A river is a natural flowing watercourse, usually freshwater, flowing towards an ocean, sea, lake or another river. In some cases, a river flows int ...
. The zone within which a meandering stream periodically shifts its channel is known as a meander belt. It typically ranges from 15 to 18 times the width of the channel. Over time, meanders migrate downstream, sometimes in such a short time as to create
civil engineering Civil engineering is a professional engineering Regulation and licensure in engineering is established by various jurisdictions of the world to encourage public welfare, safety, well-being and other interests of the general public and to defin ...
challenges for local municipalities attempting to maintain stable roads and bridges.Neuendorf, K.K.E., J.P. Mehl Jr., and J.A. Jackson, J.A., eds. (2005) ''Glossary of Geology'' (5th ed.). Alexandria, Virginia, American Geological Institute. 779 pp. Charlton, R., 2007. ''Fundamentals of fluvial geomorphology.'' Routledge, New York, New York. 234 pp. The degree of meandering of the channel of a river, stream, or other watercourse is measured by its ''
sinuosity The meandering '' Rio Cauto'' at Guamo Embarcadero,  1..html" ;"title="Cuba, is not taking the shortest path downslope. Therefore, its sinuosity index is > 1.">Cuba, is not taking the shortest path downslope. Therefore, its sinuosi ...

sinuosity
''. The sinuosity of a watercourse is the ratio of the length of the channel to the straight line down-valley distance. Streams or rivers with a single channel and sinuosities of 1.5 or more are defined as meandering streams or rivers.Leopold, L.B., Wolman, M.G., Wolman, M.G. and Wolman, M.G., 1957. ''River Channel Patterns: Braided, Meandering, and Straight.'' ''United States Geological Survey Professional Paper'' no. 282B, US Government Printing Office, Washington DC., 47 pp.


Origin of term

The term derives from the Meander River located in present-day Turkey and known to the
Ancient Greeks Ancient Greece ( el, Ἑλλάς, Hellás) was a civilization belonging to a period of History of Greece, Greek history from the Greek Dark Ages of the 12th–9th centuries BC to the end of Classical Antiquity, antiquity ( AD 600). This era was ...
as Μαίανδρος ''Maiandros'' (
Latin Latin (, or , ) is a classical language belonging to the Italic languages, Italic branch of the Indo-European languages. Latin was originally spoken in the area around Rome, known as Latium. Through the power of the Roman Republic, it became ...

Latin
: ''Maeander''), characterised by a very convoluted path along the lower reach. As a result, even in
Classical Greece Classical Greece was a period of around 200 years (the 5th and 4th centuries BC) in Ancient Greece Ancient Greece ( el, Ἑλλάς, Hellás) was a civilization belonging to a period of History of Greece, Greek history from the Greek Dar ...
(and in later Greek thought) the name of the river had become a common noun meaning anything convoluted and winding, such as decorative patterns or speech and ideas, as well as the
geomorphological incised into shale at the foot of the North Caineville Plateau, Utah, within the pass carved by the Fremont River (Utah), Fremont River and known as the Blue Gate. Grove Karl Gilbert, GK Gilbert studied the landscapes of this area in great detail, ...

geomorphological
feature.
Strabo Strabo''Strabo'' (meaning "squinty", as in strabismus Strabismus is a condition in which the eyes do not properly align with each other when looking at an object. The eye that is focused on an object can alternate. The condition may be pre ...

Strabo
said: ‘…its course is so exceedingly winding that everything winding is called meandering.’ The Meander River is south of Izmir, east of the ancient Greek town of
Miletus Miletus (; gr, Μῑ́λητος, Mīlētos; Hittite language, Hittite transcription ''Millawanda'' or ''Milawata'' (Exonym and endonym, exonyms); la, Miletus; tr, Milet) was an Ancient Greece, ancient Greek city on the western coast of Ana ...
, now Milet, Turkey. It flows through series of three
graben In geology Geology (from the γῆ, ''gē'' ("earth") and -λoγία, ''-logia'', ("study of", "discourse")) is a branch of concerned with both the liquid and , the of which it is composed, and the processes by which they change over ti ...

graben
in the Menderes Massif, but has a flood plain much wider than the meander zone in its lower reach. Its modern Turkish name is the
Büyük Menderes River The Büyük Menderes River (historically the Maeander or Meander, from Ancient Greek Ancient Greek includes the forms of the Greek language used in ancient Greece and the classical antiquity, ancient world from around 1500 BC to 300 BC ...
.


Governing physics

Meanders are a result of the interaction of water flowing through a curved channel with the underlying river bed. This produces ''helicoidal flow'', in which water moves from the outer to the inner bank along the river bed, then flows back to the outer bank near the surface of the river. This in turn increases carrying capacity for sediments on the outer bank and reduces it on the inner bank, so that sediments are eroded from the outer bank and redeposited on the inner bank of the next downstream meander. When a fluid is introduced to an initially straight channel which then bends, the sidewalls induce a pressure gradient that causes the fluid to alter course and follow the bend. From here, two opposing processes occur: (1) irrotational flow and (2)
secondary flow In fluid dynamics In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids—liquids and gases. It has several subdisciplines, including aerodynamics (the study of air and other gases i ...
. For a river to meander, secondary flow must dominate. ''Irrotational flow'': From Bernoulli's equations, high pressure results in low velocity. Therefore, ''in the absence of secondary flow'' we would expect low fluid velocity at the outside bend and high fluid velocity at the inside bend. This classic fluid mechanics result is ''
irrotational vortex In fluid dynamics In and , fluid dynamics is a subdiscipline of that describes the flow of s—s and es. It has several subdisciplines, including ' (the study of air and other gases in motion) and hydrodynamics (the study of liquids in ...

irrotational vortex
flow.'' In the context of meandering rivers, its effects are dominated by those of secondary flow. ''Secondary flow'': A force balance exists between pressure forces pointing to the inside bend of the river and centrifugal forces pointing to the outside bend of the river. In the context of meandering rivers, a
boundary layer In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular su ...
exists within the thin layer of fluid that interacts with the river bed. Inside that layer and following standard boundary-layer theory, the velocity of the fluid is effectively zero. Centrifugal force, which depends on velocity, is also therefore effectively zero. Pressure force, however, remains unaffected by the boundary layer. Therefore, within the boundary layer, pressure force dominates and fluid moves along the bottom of the river from the outside bend to the inside bend. This initiates helicoidal flow: Along the river bed, fluid roughly follows the curve of the channel but is also forced toward the inside bend; away from the river bed, fluid also roughly follows the curve of the channel but is forced, to some extent, from the inside to the outside bend. The higher velocities at the outside bend lead to higher shear stresses and therefore result in erosion. Similarly, lower velocities at the inside bend cause lower sheer stresses and deposition occurs. Thus meander bends erode at the outside bend, causing the river to becoming increasingly sinuous (until cutoff events occur). Deposition at the inside bend occurs such that for most natural meandering rivers, the river width remains nearly constant, even as the river evolves. In a speech before the
Prussian Academy of Sciences The Royal Prussian Academy of Sciences (german: Königlich-Preußische Akademie der Wissenschaften) was an academy An academy ( Attic Greek: Ἀκαδήμεια; Koine Greek Koine Greek (, , Greek approximately ;. , , , lit. "Common Greek"), ...
in 1926,
Albert Einstein Albert Einstein ( ; ; 14 March 1879 – 18 April 1955) was a German-born theoretical physicist, widely acknowledged to be one of the greatest physicists of all time. Einstein is known for developing the theory of relativity The theo ...

Albert Einstein
suggested that because the
Coriolis force In physics, the Coriolis force is an fictitious force, inertial or fictitious force that acts on objects that are in motion within a rotating reference frame, frame of reference that rotates with respect to an inertial frame. In a reference fra ...
of the earth can cause a small imbalance in velocity distribution, such that velocity on one bank is higher than on the other, it could trigger the erosion on one bank and deposition of sediment on the other that produces meanders However, Coriolis forces are likely insignificant compared with other forces acting to produce river meanders.


Meander geometry

The technical description of a meandering watercourse is termed meander
geometry Geometry (from the grc, γεωμετρία; ' "earth", ' "measurement") is, with , one of the oldest branches of . It is concerned with properties of space that are related with distance, shape, size, and relative position of figures. A mat ...

geometry
or meander planform geometry. It is characterized as an irregular
waveform In electronics The field of electronics is a branch of physics and electrical engineering that deals with the emission, behaviour and effects of electrons The electron is a subatomic particle In physical sciences, subatomic part ...
. Ideal waveforms, such as a
sine wave A sine wave or sinusoid is any of certain mathematical curves that describe a smooth periodic oscillation Oscillation is the repetitive variation, typically in time Time is the indefinite continued sequence, progress of existence and ev ...

sine wave
, are one line thick, but in the case of a stream the width must be taken into consideration. The bankfull width is the distance across the bed at an average cross-section at the full-stream level, typically estimated by the line of lowest vegetation. As a waveform the meandering stream follows the down-valley axis, a straight line
fitted FITTED is an alternative rock band featuring Mike Watt (The Minutemen (band), The Minutemen, Firehose (band), fIREHOSE), Graham Lewis (Wire (band), Wire), Matthew Simms (Wire), and Bob Lee (drummer), Bob Lee (The Black Gang). Graham Lewis' Wire was ...

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. At any cross-section the flow is following the sinuous axis, the centerline of the bed. Two consecutive crossing points of sinuous and down-valley axes define a meander loop. The meander is two consecutive loops pointing in opposite transverse directions. The distance of one meander along the down-valley axis is the meander length or
wavelength In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular su ...

wavelength
. The maximum distance from the down-valley axis to the sinuous axis of a loop is the meander width or
amplitude The amplitude of a period Period may refer to: Common uses * Era, a length or span of time * Full stop (or period), a punctuation mark Arts, entertainment, and media * Period (music), a concept in musical composition * Period, a descriptor for ...

amplitude
. 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 In mathematics Mathematics (from Greek: ) includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces in which they are contained (geometry), and quantities an ...

curvature
varies from a maximum at the apex to zero at a crossing point (straight line), also called an inflection, because the curvature changes direction in that vicinity. The
radius In classical geometry Geometry (from the grc, γεωμετρία; ' "earth", ' "measurement") is, with , one of the oldest branches of . It is concerned with properties of space that are related with distance, shape, size, and relative ...

radius
of the loop is the straight line
perpendicular In elementary geometry Geometry (from the grc, γεωμετρία; ' "earth", ' "measurement") is, with , one of the oldest branches of . It is concerned with properties of space that are related with distance, shape, size, and relativ ...

perpendicular
to the down-valley axis intersecting 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
concave Concave means curving in or hollowed inward, as opposed to convex. Concave may refer to: * Concave function In mathematics, a concave function is the additive inverse, negative of a convex function. A concave function is also synonymously called ...
bank and an inner or
convex Convex means curving outwards like a sphere, and is the opposite of concave. Convex or convexity may refer to: Science and technology * Convex lens A lens is a transmissive optics, optical device which focuses or disperses a light beam by me ...
bank. The meander belt is defined by an average meander width measured from outer bank to outer bank instead of from centerline to centerline. If there is a
flood plain A floodplain or flood plain or bottomlands is an area of land adjacent to a river which stretches from the banks of its channel to the base of the enclosing valley walls, and which experiences flooding during periods of high discharge.Goudi ...
, it extends beyond the meander belt. The meander is then said to be free—it can be found anywhere in the flood plain. If there is no flood plain, the meanders are fixed. Various mathematical formulae relate the variables of the meander geometry. As it turns out some numerical parameters can be established, which appear in the formulae. The waveform depends ultimately on the characteristics of the flow but the parameters are independent of it and apparently are caused by geologic factors. In general the meander length is 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 In differential geometry Differential geometry is a Mathematics, mathematical discipline that uses the techniques of differential calculus, integral calculus, linear algebra and multilinear algebra to study problems in geometry. The Differentia ...
at the apex. This radius is 2–3 times the channel width. A meander has a depth pattern as well. The cross-overs are marked by
riffle A riffle is a shallow in a flowing channel, and it has specific topographic, sedimentary, and hydraulic indicators. These are almost always assessed at a very low discharge compared to the flow that fills the channel (approximately 10–20%), ...

riffle
s, or shallow beds, while at the apices are pools. In a pool direction of flow is downward, scouring the bed material. The major volume, however, flows more slowly on the inside of the bend where, due to decreased velocity, it deposits sediment. The line of maximum depth, or channel, is the
thalweg In geography and fluvial geomorphology, a thalweg or talweg () is the line of lowest elevation within a valley or watercourse. Under international law, a thalweg is the middle of the primary navigable channel of a waterway that defines the boundar ...

thalweg
or thalweg line. It is typically designated the borderline when rivers are used as political borders. The thalweg hugs the outer banks and returns to center over the riffles. The meander arc length is the distance along the thalweg over one meander. The river length is the length along the centerline.


Formation

Once a channel begins to follow a sinusoidal path, the amplitude and concavity of the loops increase dramatically. This is due to the effect of helical flow which sweeps dense eroded material towards the inside of the bend, and leaves the outside of the bend unprotected and vulnerable to accelerated erosion. This establishes a
positive feedback loop Positive feedback (exacerbating feedback, self-reinforcing feedback) is a process that occurs in a feedback loop which exacerbates the effects of a small disturbance. That is, the effects of a perturbation on a system include an increase in th ...

positive feedback loop
. In the words of Elizabeth A. Wood:
‘…this process of making meanders seems to be a self-intensifying process…in which greater curvature 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 In fluid dynamics In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids—liquids and gases. It has several subdisciplines, including aerodynamics (the study of air and other gases i ...
and sweeps dense eroded material towards the inside of the bend. The cross-current then rises to the surface near the inside and flows towards the outside, 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. Due to the conservation of
angular momentum In , angular momentum (rarely, moment of momentum or rotational momentum) is the rotational equivalent of . It is an important quantity in physics because it is a —the total angular momentum of a closed system remains constant. In three , the ...

angular momentum
the speed on the inside of the bend is faster than on the outside. Since the flow velocity is diminished, so is the centrifugal pressure. The pressure of the super-elevated column prevails, developing an unbalanced gradient that moves water back across the bottom from the outside to the inside. The flow is supplied by a counter-flow across the surface from the inside to the outside. This entire situation is very similar to the
Tea leaf paradox File:Tea leaf Paradox Illustration.svg, The blue line is the secondary flow that pushes the tea leaves to the middle of the bottom. The tea leaf paradox is a phenomenon where tea leaf, tea leaves in a teacup, cup of tea migrate to the center and ...
. This secondary flow carries sediment from the outside of the bend to the inside making the river more meandering. As to why streams of any size become sinuous in the first place, there are a number of theories, not necessarily mutually exclusive.


Stochastic theory

The
stochastic Stochastic () refers to the property of being well described by a random In common parlance, randomness is the apparent or actual lack of pattern or predictability in events. A random sequence of events, symbols or steps often has no :wi ...
theory can take many forms but one of the most general statements is that of Scheidegger: ‘The meander train is assumed to be the result of the stochastic fluctuations of the direction of flow due 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 Adhesion is the tendency of dissimilar particles In the Outline of physical science, physical sciences, a particle (or corpuscule in older texts) is a small wikt:local, localized physical body, object to which can be ascribed several physic ...

adhesion
of water to the surface and cohesion of drops produce rivulets at random. Natural surfaces are rough and erodible to different degrees. The result of all the physical factors acting at random is channels that are not straight, which then progressively become sinuous. Even channels that appear straight have a sinuous
thalweg In geography and fluvial geomorphology, a thalweg or talweg () is the line of lowest elevation within a valley or watercourse. Under international law, a thalweg is the middle of the primary navigable channel of a waterway that defines the boundar ...

thalweg
that leads eventually to a sinuous channel.


Equilibrium theory

In the equilibrium theory, meanders decrease the stream
gradient In vector calculus Vector calculus, or vector analysis, is concerned with differentiation Differentiation may refer to: Business * Differentiation (economics), the process of making a product different from other similar products * Prod ...
until an equilibrium between the
erodibilityErodability (or erodibility) is the inherent yielding or nonresistance of soils and rocks to erosion In earth science, erosion is the action of surface processes (such as Surface runoff, water flow or wind) that removes soil, Rock (geology), rock ...
of the terrain and the transport capacity of the stream is reached. A mass of water descending must give up
potential energy In physics, potential energy is the energy In , energy is the that must be to a or to perform on the body, or to it. Energy is a ; the law of states that energy can be in form, but not created or destroyed. The unit of measure ...
, which, given the same velocity at the end of the drop as at the beginning, is removed by interaction with the material of the stream bed. The shortest distance; that is, a straight channel, results in the highest energy per unit of length, disrupting the banks more, creating more sediment and aggrading the stream. The presence of meanders allows the stream to adjust the length to an equilibrium energy per unit length in which the stream carries away all the 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, or tectonic (plate) structure of the rock. The features included under these categories are not random and guide streams into non-random paths. They are predictable obstacles that instigate meander formation by deflecting the stream. For example, the stream might be guided into a fault line (morphotectonic).


Associated landforms


Cut bank

A ''
cut bank Image:Point bar and cut bank.jpg, upCut bank erosion and point bar deposition as seen on the Powder River (Montana), Powder River in Montana. A cut bank, also known as a river cliff or river-cut cliff, is the outside bank of a water channel (strea ...
'' is an often vertical bank or cliff that forms where the outside, concave bank of a meander cuts into the floodplain or valley wall of a river or stream. A cutbank is also known either as a ''river-cut cliff'', ''river cliff'', or a ''bluff'' and spelled as ''cutbank''. Erosion that forms a cut bank occurs at the outside bank of a meander because helicoidal flow of water keeps the bank washed clean of loose sand, silt, and sediment and subjects it to constant erosion. As a result, the meander erodes and migrates in the direction of the outside bend, forming the cut bank. Reineck, H.E. and Singh, I.B., 2012. ''Depositional sedimentary environments: with reference to terrigenous clastics.'' Springer Science & Business Media, New York, New York. 551 pp. As the cut bank is undermined by erosion, it commonly collapses as slumps into the river channel. The slumped sediment, having been broken up by slumping, is readily eroded and carried toward the middle of the channel. The sediment eroded from a cut bank tends to be deposited on the point bar of the next downstream meander, and not on the point bar opposite it. This can be seen in areas where trees grow on the banks of rivers; on the inside of meanders, trees, such as willows, are often far from the bank, whilst on the outside of the bend, the tree roots are often exposed and undercut, eventually leading the trees to fall into the river.Fisk, H.N., 1948. ''Fine-grained Alluvial Deposits and Their Effects on Mississippi River Activity.'' War Department, Corps of Engineers, Mississippi River Commission, Vicksburg, Mississippi. 2 Vols., 82 pp.


Meander cutoff

A ''
meander cutoff A meander cutoff, the natural form of a cutting or cut in a river occurs when a pronounced meander Meanders of the '' Rio Cauto'' at Guamo Embarcadero, Cuba A meander is one of a series of regular sinuous curves, bends, loops, turns, or winding ...
'', also known as either a ''cutoff meander'' or ''abandoned meander'', is a meander that has been abandoned by its stream after the formation of a neck cutoff. A lake that occupies a cutoff meander is known as an ''
oxbow lake An oxbow lake is a U-shaped lake that forms when a wide meander of a river is Meander cutoff, cut off, creating a free-standing body of water. In south Texas, oxbows left by the Rio Grande are called ''resaca (channel), resacas''. In Australia ...

oxbow lake
''. Cutoff meanders that have cut downward into the underlying bedrock are known in general as ''incised cutoff meanders''. As in the case of the Anderson Bottom Rincon, incised meanders that have either steep-sided, often vertical walls, are often, but not always, known as ''rincons'' in the
southwest United States The points of the compass are an evenly spaced set of horizontal directions (or azimuth An azimuth (; from Arabic اَلسُّمُوت ''as-sumūt'', 'the directions', the plural form of the Arabic noun السَّمْت ''as-samt'', meaning 't ...
.Shoemaker, E.M. and Stephens, H.G., 1975. ''First photographs of the Canyon Lands.'' in Fassett, J.E., ed., pp. 111–122, ''Canyonlands Country, A Guidebook of the Four Corners Geological Society Eighth Field Conference — September 22–25, 1975.'' Four Corners Geological Society, Durango, Colorado. pp. 278. ''Rincon'' in English is a nontechnical word in the southwest United States for either a small secluded valley, an alcove or angular recess in a cliff, or a bend in a river.Merriam-Webster, Incorporated, 2017
''Dictionary by Merriam-Webster: America's most-trusted online dictionary''.
last accessed November 22, 2017


Incised meanders

The meanders of a stream or river that has cut its bed down into the
bedrock Bedrock in geology Geology (from the γῆ, ''gē'' ("earth") and -λoγία, ''-logia'', ("study of", "discourse")) is a branch of concerned with both the liquid and , the of which it is composed, and the processes by which they cha ...

bedrock
are known as either incised, intrenched, entrenched, inclosed or ingrown meanders. Some Earth scientists recognize and use a finer subdivision of incised meanders. ThornburyThornbury, W. D., 1954, ''Principles of Geomorphology,'' John Wiley & Sons, New York, New York. 618 pp. argues that ''incised'' or ''inclosed meanders'' are synonyms that are appropriate to describe any meander incised downward into bedrock and defines ''enclosed'' or ''entrenched meanders'' as a subtype of incised meanders (inclosed meanders) characterized by a symmetrical valley sides. He argues that the symmetrical valley sides are the direct result of rapid down-cutting of a watercourse into bedrock.Fairbridge, R.W. 1968, ''Incised meander.'' In Fairbridge, R.W., ed., pp 548–550, ''The Encyclopedia of Geomorphology.'' Encyclopedia of Earth Sciences Series, Vol. 3. McGraw-Hill Company, Inc., New York, New York, 1295 pp. In addition, as proposed by Rich,Rich, J.L., 1914. ''Certain types of stream valleys and their meaning.'' ''The Journal of Geology'', 22(5), pp. 469–497. Thornbury argues that incised valleys with a pronounced asymmetry of cross section, which he called ''ingrown meanders'', are the result of the lateral migration and incision of a meander during a period of slower channel
downcutting 300px, Several stages of downcutting by the San Juan River (Colorado River), San Juan River in Utah can be identified in this 1927 photo. Remnants of former floodplains stand as fluvial terrace, terraces above the river's modern level. Downcutti ...
. Regardless, the formation of both entrenched meanders and ingrown meanders is thought to require that
base level In geology Geology (from the Ancient Greek γῆ, ''gē'' ("earth") and -λoγία, ''-logia'', ("study of", "discourse")) is an Earth science concerned with the solid Earth, the rock (geology), rocks of which it is composed, and the processe ...
falls as a result of either relative change in mean
sea level Mean sea level (MSL) (often shortened to sea level) is an average In colloquial, ordinary language, an average is a single number taken as representative of a list of numbers, usually the sum of the numbers divided by how many numbers are in th ...

sea level
, isostatic or
tectonic Tectonics (; ) are the processes that control the structure and properties of the Earth's crust and its evolution through time. These include the processes of mountain building A mountain is an elevated portion of the Earth's crust, gen ...
uplift, the breach of an ice or
landslide Landslides, also known as landslips, are several forms of mass wasting Mass wasting, also known as mass movement, is a general term for the movement of rock Rock most often refers to: * Rock (geology) A rock is any naturally occurri ...

landslide
dam, or regional tilting. Classic examples of incised meanders are associated with rivers in the
Colorado Plateau The Colorado Plateau, also known as the Colorado Plateau Province, is a physiographic and desert region of the Intermontane Plateaus, roughly centered on the Four Corners region of the southwestern United States The southwestern United State ...
, the in central
Kentucky Kentucky ( , ), officially the Commonwealth of Kentucky, is a state State may refer to: Arts, entertainment, and media Literature * ''State Magazine'', a monthly magazine published by the U.S. Department of State * The State (newspaper), ...
, and streams in the
Ozark Plateau The Ozarks, also known as the Ozark Mountains or Ozark Plateau, is a physiographic region in the U.S. states of Missouri, Arkansas, Oklahoma and the extreme southeastern corner of Kansas. The Ozarks cover a significant portion of northern Arka ...
.Barbour, J.R., 2008. ''The origin and significance of sinuosity along incising bedrock rivers.'' Doctoral dissertation, Columbia University, New York, New York, 172 pp. As noted above, it was initially either argued or presumed that an incised meander is characteristic of an antecedent stream or river that had incised its channel into underlying
strata In geology and related fields, a stratum (plural: strata) is a layer of sedimentary rock or soil, or igneous rock that was formed at the Earth's surface, with internally consistent characteristics that distinguish it from other layers. The "str ...
. An antecedent stream or river is one that maintains its original course and pattern during incision despite the changes in underlying rock topography and rock types. However, later geologistsHack, J.T., and Young, R.S., 1959. ''Intrenched meanders of the North Fork of the Shenandoah River, Virginia.'' ''United States Geological Survey Professional Paper'' 354-A, 10 pp. argue that the shape of an incised meander is not always, if ever, "inherited," e.g., strictly from an antecedent meandering stream where it meander pattern could freely develop on a level floodplain. Instead, they argue that as fluvial incision of bedrock proceeds, the stream course is significantly modified by variations in rock type and
fractures Fracture is the separation of an object or material into two or more pieces under the action of stress. The fracture of a solid usually occurs due to the development of certain displacement discontinuity surfaces within the solid. If a displa ...
, faults, and other geological structures into either ''lithologically conditioned meanders'' or ''structurally controlled meanders''.


Oxbow lakes

The ''
oxbow lake An oxbow lake is a U-shaped lake that forms when a wide meander of a river is Meander cutoff, cut off, creating a free-standing body of water. In south Texas, oxbows left by the Rio Grande are called ''resaca (channel), resacas''. In Australia ...

oxbow lake
'', which is the most common type of fluvial lake, is a crescent-shaped lake that derives its name from its distinctive curved shape.Hutchinson, G.E. 1957. ''A treatise on limnology, v. 1. Geography, Physics and Chemistry.'' Wiley. 1015p. Oxbow lakes are also known as ''cutoff lakes''. Such lakes form regularly in undisturbed floodplains as a result of the normal process of fluvial meandering. Either a river or stream forms a sinuous channel as the outer side of its bends are eroded away and sediments accumulate on the inner side, which forms a meandering horseshoe-shaped bend. Eventually as the result of its meandering, the fluvial channel cuts through the narrow neck of the meander and forms a cutoff meander. The final break-through of the neck, which is called a ''neck cutoff'', often occurs during a major flood because that is when the watercourse is out of its banks and can flow directly across the neck and erode it with the full force of the flood.Fisk, H.N., 1944. ''Geological investigation of the alluvial valley of the lower Mississippi River.'' War Department, Corps of Engineers, Mississippi River Commission, Vicksburg, Mississippi. 78 pp.Toonen, W.H., Kleinhans, M.G. and Cohen, K.M., 2012. "Sedimentary architecture of abandoned channel fills." ''
Earth Surface Processes and Landforms ''Earth Surface Processes and Landforms'' is a peer-reviewed Peer review is the evaluation of work by one or more people with similar competencies as the producers of the work ( peers). It functions as a form of self-regulation by qualified me ...
'', 37(4), pp. 459–472.
After a cutoff meander is formed, river water flows into its end from the river builds small delta-like feature into either end of it during floods. These delta-like features block either end of the cutoff meander to form a stagnant oxbow lake that is separated from the flow of the fluvial channel and independent of the river. During floods, the flood waters deposit fine-grained sediment into the oxbow lake. As a result, oxbow lakes tend to become filled in with fine-grained, organic-rich sediments over time.


Point bar

A ''
point bar A point bar is a depositional feature made of alluvium that accumulates on the inside bend of streams and rivers below the slip-off slope. Point bars are found in abundance in mature or meandering streams. They are crescent-shaped and located on t ...

point bar
'', which is also known as a ''meander bar'', is a fluvial bar that is formed by the slow, often episodic, addition of individual accretions of noncohesive sediment on the inside bank of a meander by the accompanying migration of the channel toward its outer bank. This process is called lateral accretion. Lateral accretion occurs mostly during high water or floods when the point bar is submerged. Typically, the sediment consists of either sand, gravel, or a combination of both. The sediment comprising some point bars might grade downstream into silty sediments. Because of the decreasing velocity and strength of current from the thalweg of the channel to the upper surface of point bar when the sediment is deposited the vertical sequence of sediments comprising a point bar becomes finer upward within an individual point bar. For example, it is typical for point bars to fine upward from gravel at the base to fine sands at the top. The source of the sediment is typically upstream cut banks from which sand, rocks and debris has been eroded, swept, and rolled across the bed of the river and downstream to the inside bank of a river bend. On the inside bend, this sediment and debris is eventually deposited on the slip-off slope of a point bar.


Scroll-bars

Scroll-bars are a result of continuous lateral migration of a meander loop that creates an asymmetrical ridge and swale topography on the inside of the bends. The topography is generally parallel to the meander, and is related to migrating bar forms and back bar chutes, which carve sediment from the outside of the curve and deposit sediment in the slower flowing water on the inside of the loop, in a process called lateral accretion. Scroll-bar sediments are characterized by cross-bedding and a pattern of fining upward. These characteristics are a result of the dynamic river system, where larger grains are transported during high energy flood events and then gradually 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. There are two distinct patterns of scroll-bar depositions; the eddy accretion scroll bar pattern and the point-bar scroll pattern. When looking down the river valley they can be distinguished because the point-bar scroll patterns are convex and the eddy accretion scroll bar patterns are concave. Scroll bars often look lighter at the tops of the ridges and darker in the swales. This is because the tops can be shaped by wind, either adding fine grains or by keeping the area unvegetated, while the darkness in the swales can be attributed to silts and clays washing in during high water periods. This added sediment in addition to water that catches in the swales is in turn is a favorable environment for vegetation that will also accumulate in the swales.


Slip-off slope

Depending upon whether a meander is part of an entrenched river or part of a freely meandering river within a floodplain, the term ''slip-off slope'' can refer to two different fluvial landforms that comprise the inner, convex, bank of a meander loop. In case of a freely meandering river on a floodplain, a slip-off slope is the inside, gently sloping bank of a meander on which sediments episodically accumulate to form a point bar as a river meanders. This type of slip-off slope is located opposite the cutbank.Scheffers, A.M., May, S.M. and Kelletat, D.H., 2015. ''Forms by Flowing Water (Fluvial Features).'' In ''Landforms of the World with Google Earth.'' (pp. 183–244). Springer, Amsterdam, Netherlands. 391 pp. This term can also be applied to the inside, sloping bank of a meandering tidal channel.Keck, R., Maurer, D. and Watling, L., 1973. ''Tidal stream development and its effect on the distribution of the American oyster.'' ''Hydrobiologia'', 42(4), pp. 369–379. In case of an entrenched river, a slip-off slope is a gently sloping bedrock surface that rises from the inside, concave bank of an asymmetrically entrenched river. This type of slip-off slope is often covered by a thin, discontinuous layer of alluvium. It is produced by the gradual outward migration of the meander as a river cuts downward into bedrock.Davis, W.M., 1913. ''Meandering valleys and underfit rivers.'' ''Annals of the Association of American Geographers'', 3(1), pp. 3–28.Crickmay, C.H., 1960. ''Lateral activity in a river of northwestern Canada.'' ''The Journal of Geology'', 68(4), pp. 377–391. A terrace on the slip-off slope of a meander spur, known as ''slip-off slope terrace'', can formed by a brief halt during the irregular incision by an actively meandering river.Herrmann, H. and Bucksch, H., 2014. ''Dictionary Geotechnical Engineering/Wörterbuch GeoTechnik: English-German/Englisch-Deutsch.'' Springer, Berlin, Germany. 1549 pp.


Derived quantities

The meander ratio or is a means of quantifying how much a
river A river is a natural flowing watercourse, usually freshwater, flowing towards an ocean, sea, lake or another river. In some cases, a river flows into the ground and becomes dry at the end of its course without reaching another body of wate ...

river
or
stream A stream is a body of water (Lysefjord) in Norway Norway, officially the Kingdom of Norway,Names in the official and recognised languages: Bokmål Bokmål (, ; literally "book tongue") is an official written standard for the No ...

stream
meanders (how much its course deviates from the shortest possible path). It is calculated as the
length Length is a measure of distance Distance is a numerical measurement ' Measurement is the number, numerical quantification (science), quantification of the variable and attribute (research), attributes of an object or event, which can be us ...

length
of the stream divided by the length of the
valley A valley is an elongated low area often running between hills or mountains, which will typically contain a river or stream running from one end to the other. Most valleys are formed by erosion of the land surface by rivers or streams over ...

valley
. A perfectly straight river would have a meander ratio of 1 (it would be the same length as its valley), while the higher this
ratio In mathematics, a ratio indicates how many times one number contains another. For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six (that is, 8∶6, which is equivalent to ...

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 the reach, which should be at least 20 times the average fullbank channel width. The length of the stream is measured by channel, or thalweg, length over the reach, while the bottom value of the ratio is the downvalley length or air distance 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 the valley index is the meander ratio of the valley while the channel index is the meander ratio of the channel. The channel 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. Sinuosity Index has a non-mathematical utility as well. Streams can be placed in categories arranged by it; for example, when the index is between 1 and 1.5 the river is sinuous, but if between 1.5 and 4, then meandering. The index is a measure also of stream velocity and sediment load, those quantities being maximized at an index of 1 (straight).


See also

* Baer's law *
Billabong A billabong ( ) is an Australian term for an oxbow lake, an isolated pond left behind after a river changes course. Billabongs are usually formed when the path of a creek or river A river is a natural flowing watercourse, usually freshwat ...

Billabong
* Crevasse splay * Helicoidal flow *
Jet stream Jet streams are fast flowing, narrow, meander A meander is one of a series of regular sinuous curves in the channel of a river or other watercourse. It is produced as a watercourse the s of an outer, concave bank () and deposits sedimen ...
* Meander cutoffs in Avulsion (river) * Meander scar *
Riffle-pool sequence In a flowing stream, a riffle-pool sequence (also known as a pool-riffle sequence) develops as a stream's hydrological flow structure alternates from areas of relatively shallow to deeper water. This sequence is present only in streams carrying gr ...


References and notes


Bibliography

* *
Virtual Luna Leopold
* Thonemann, P., ''The Maeander Valley: A historical geography from Antiquity to Byzantium'' (Cambridge, 2011) (Greek Culture in the Roman World Series).


External links

* {{Authority control Limnology Fluvial landforms
Geomorphology Geomorphology (from the Greek words ''Ge'' = earth, ''morfe'' = form and ''logos'' = study) is the science of surface features and landforms including the forces and processes that create them. Geomorphology has strong ties to geologic structure, ...
Rivers Water streams Erosion