![Zoltan Kluger](https://upload.wikimedia.org/wikipedia/commons/d/d2/Zoltan_Kluger._The_Jordan%2C_near_the_Dead_Sea.jpg)
A meander is one of a series of regular sinuous curves in the
channel
Channel, channels, channeling, etc., may refer to:
Geography
* Channel (geography), in physical geography, a landform consisting of the outline (banks) of the path of a narrow body of water.
Australia
* Channel Country, region of outback Austral ...
of 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 ...
or other
watercourse
A stream is a continuous body of surface water flowing within the bed and banks of a channel. Depending on its location or certain characteristics, a stream may be referred to by a variety of local or regional names. Long large streams are ...
. It is produced as a watercourse
erodes the
sediment
Sediment is a naturally occurring material that is broken down by processes of weathering and erosion, and is subsequently transported by the action of wind, water, or ice or by the force of gravity acting on the particles. For example, sand an ...
s of an outer, concave bank (
cut bank
A cut bank, also known as a river cliff or river-cut cliff, is the outside bank of a curve or meander in a water channel (stream), which is continually undergoing erosion.Essentials of Geology, 3rd Ed, Stephen Marshak Cut banks are found in abu ...
) 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 ...
. The result of this coupled erosion and sedimentation is the formation of a
sinuous
Sinuosity, sinuosity index, or sinuosity coefficient of a continuously differentiable curve having at least one inflection point is the ratio of the curvilinear length (along the curve) and the Euclidean distance (straight line) between the ...
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 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 ...
.
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 discipline that deals with the design, construction, and maintenance of the physical and naturally built environment, including public works such as roads, bridges, canals, dams, airports, sewage ...
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
Sinuosity, sinuosity index, or sinuosity coefficient of a continuously differentiable curve having at least one inflection point is the ratio of the curvilinear length (along the curve) and the Euclidean distance (straight line) between the e ...
''. 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 winding river
Menderes located in
Asia-Minor
Anatolia, tr, Anadolu Yarımadası), and the Anatolian plateau, also known as Asia Minor, is a large peninsula in Western Asia and the westernmost protrusion of the Asian continent. It constitutes the major part of modern-day Turkey. The reg ...
and known to the
Ancient Greeks
Ancient Greece ( el, Ἑλλάς, Hellás) was a northeastern Mediterranean civilization, existing from the Greek Dark Ages of the 12th–9th centuries BC to the end of classical antiquity ( AD 600), that comprised a loose collection of cultu ...
as Μαίανδρος ''Maiandros'' (
Latin
Latin (, or , ) is a classical language belonging to the Italic branch of the Indo-European languages. Latin was originally a dialect spoken in the lower Tiber area (then known as Latium) around present-day Rome, but through the power of the ...
: ''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,The "Classical Age" is "the modern designation of the period from about 500 B.C. to the death of Alexander the Great in 323 B.C." ( Thomas R. Marti ...
(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
Geomorphology (from Ancient Greek: , ', "earth"; , ', "form"; and , ', "study") is the scientific study of the origin and evolution of topographic and bathymetric features created by physical, chemical or biological processes operating at or n ...
feature.
Strabo
Strabo''Strabo'' (meaning "squinty", as in strabismus) was a term employed by the Romans for anyone whose eyes were distorted or deformed. The father of Pompey was called "Pompeius Strabo". A native of Sicily so clear-sighted that he could see ...
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, Mī́lētos; Hittite transcription ''Millawanda'' or ''Milawata'' (exonyms); la, Mīlētus; tr, Milet) was an ancient Greek city on the western coast of Anatolia, near the mouth of the Maeander River in a ...
, now Milet, Turkey. It flows through series of three
graben
In geology, a graben () is a depressed block of the crust of a planet or moon, bordered by parallel normal faults.
Etymology
''Graben'' is a loan word from German, meaning 'ditch' or 'trench'. The word was first used in the geologic contex ...
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: Μαίανδρος, ''Maíandros''; tr, Büyük Menderes Irmağı), is a river in southwestern Turkey. It rises in west central Turkey near Dinar before flo ...
.
Governing physics
![Bend2](https://upload.wikimedia.org/wikipedia/commons/9/91/Bend2.png)
Meanders are a result of the interaction of water flowing through a curved channel with the underlying river bed. This produces ''
helicoidal flow
Helicoidal flow is the cork-screw-like flow of water in a meander. It is one example of a secondary flow.
Helicoidal flow is a contributing factor to the formation of slip-off slopes and river cliffs in a meandering section of the river. The he ...
'', 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, flow can be decomposed into primary plus secondary flow, a relatively weaker flow pattern superimposed on the stronger primary flow pattern. The primary flow is often chosen to be an exact solution to simplified or approximated ...
. 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, a vortex ( : vortices or vortexes) is a region in a fluid in which the flow revolves around an axis line, which may be straight or curved. Vortices form in stirred fluids, and may be observed in smoke rings, whirlpools in th ...
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 and fluid mechanics, a boundary layer is the thin layer of fluid in the immediate vicinity of a bounding surface formed by the fluid flowing along the surface. The fluid's interaction with the wall induces a no-slip boundary condi ...
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 established in Berlin, Germany on 11 July 1700, four years after the Prussian Academy of Arts, or "Arts Academy," to which "Berlin ...
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 and most influential physicists of all time. Einstein is best known for developing the theory ...
suggested that because the
Coriolis force
In physics, the Coriolis force is an inertial or fictitious force that acts on objects in motion within a frame of reference that rotates with respect to an inertial frame. In a reference frame with clockwise rotation, the force acts to the ...
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 Carstairs meanders from the air (geograph 5676421)](https://upload.wikimedia.org/wikipedia/commons/4/47/The_Carstairs_meanders_from_the_air_%28geograph_5676421%29.jpg)
The technical description of a meandering watercourse is termed meander
geometry
Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is c ...
or meander
planform
In technical drawing and computer graphics, a multiview projection is a technique of illustration by which a standardized series of orthographic two-dimensional pictures are constructed to represent the form of a three-dimensional object. Up to ...
geometry. It is characterized as an irregular
waveform
In electronics, acoustics, and related fields, the waveform of a signal is the shape of its graph as a function of time, independent of its time and magnitude scales and of any displacement in time.David Crecraft, David Gorham, ''Electronic ...
. Ideal waveforms, such as a
sine wave
A sine wave, sinusoidal wave, or just sinusoid is a curve, mathematical curve defined in terms of the ''sine'' trigonometric function, of which it is the graph of a function, graph. It is a type of continuous wave and also a Smoothness, smooth p ...
, 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
Cross section may refer to:
* Cross section (geometry)
** Cross-sectional views in architecture & engineering 3D
*Cross section (geology)
* Cross section (electronics)
* Radar cross section, measure of detectability
* Cross section (physics)
**Ab ...
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 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, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats.
It is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, tro ...
. 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 periodic variable is a measure of its change in a single period (such as time or spatial period). The amplitude of a non-periodic signal is its magnitude compared with a reference value. There are various definitions of amplit ...
. 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, curvature is any of several strongly related concepts in geometry. Intuitively, the curvature is the amount by which a curve deviates from being a straight line, or a surface deviates from being a plane.
For curves, the canonic ...
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, a radius ( : radii) of a circle or sphere is any of the line segments from its center to its perimeter, and in more modern usage, it is also their length. The name comes from the latin ''radius'', meaning ray but also the ...
of the loop is the straight line
perpendicular
In elementary geometry, two geometric objects are perpendicular if they intersect at a right angle (90 degrees or π/2 radians). The condition of perpendicularity may be represented graphically using the ''perpendicular symbol'', ⟂. It can ...
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.
![Great Ouse Relief Channel](https://upload.wikimedia.org/wikipedia/commons/2/2b/Great_Ouse_Relief_Channel.jpg)
A loop at the apex has an outer or
concave
Concave or concavity may refer to:
Science and technology
* Concave lens
* Concave mirror
Mathematics
* Concave function, the negative of a convex function
* Concave polygon, a polygon which is not convex
* Concave set
* The concavity
In ca ...
bank and an inner or
convex
Convex or convexity may refer to:
Science and technology
* Convex lens, in optics
Mathematics
* Convex set, containing the whole line segment that joins points
** Convex polygon, a polygon which encloses a convex set of points
** Convex polytope ...
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, the radius of curvature, , is the reciprocal of the curvature. For a curve, it equals the radius of the circular arc which best approximates the curve at that point. For surfaces, the radius of curvature is the radius o ...
at the apex. This radius is 2–3 times the channel width.
![Meander-Cuckmere River-MT](https://upload.wikimedia.org/wikipedia/commons/2/2f/Meander-Cuckmere_River-MT.JPG)
A meander has a depth pattern as well. The cross-overs are marked by
riffle
A riffle is a shallow landform in a flowing channel. Colloquially, it is a shallow place in a river where water flows quickly past rocks. However, in geology a riffle has specific characteristics.
Topographic, sedimentary and hydraulic indica ...
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 bounda ...
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
ARC may refer to:
Business
* Aircraft Radio Corporation, a major avionics manufacturer from the 1920s to the '50s
* Airlines Reporting Corporation, an airline-owned company that provides ticket distribution, reporting, and settlement services
* ...
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
Helicoidal flow is the cork-screw-like flow of water in a meander. It is one example of a secondary flow.
Helicoidal flow is a contributing factor to the formation of slip-off slopes and river cliffs in a meandering section of the river. The he ...
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 the ...
. 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, flow can be decomposed into primary plus secondary flow, a relatively weaker flow pattern superimposed on the stronger primary flow pattern. The primary flow is often chosen to be an exact solution to simplified or approximated ...
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
Helicoidal flow is the cork-screw-like flow of water in a meander. It is one example of a secondary flow.
Helicoidal flow is a contributing factor to the formation of slip-off slopes and river cliffs in a meandering section of the river. The he ...
. 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 physics, angular momentum (rarely, moment of momentum or rotational momentum) is the rotational analog of linear momentum. It is an important physical quantity because it is a conserved quantity—the total angular momentum of a closed syst ...
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
The tea leaf paradox is a phenomenon where tea leaves in a cup of tea migrate to the center and bottom of the cup after being stirred rather than being forced to the edges of the cup, as would be expected in a spiral centrifuge. The correct p ...
. 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 probability distribution. Although stochasticity and randomness are distinct in that the former refers to a modeling approach and the latter refers to phenomena themselv ...
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 or surfaces to cling to one another ( cohesion refers to the tendency of similar or identical particles/surfaces to cling to one another).
The forces that cause adhesion and cohesion can be ...
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 bounda ...
that leads eventually to a sinuous channel.
Equilibrium theory
In the equilibrium theory, meanders decrease the stream gradient
In vector calculus, the gradient of a scalar-valued differentiable function of several variables is the vector field (or vector-valued function) \nabla f whose value at a point p is the "direction and rate of fastest increase". If the gradi ...
until an equilibrium between the erodibility Erodability (or erodibility) is the inherent yielding or nonresistance of soils and rocks to erosion. A high erodability implies that the same amount of work exerted by the erosion processes leads to a larger removal of material. Because the mechani ...
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 held by an object because of its position relative to other objects, stresses within itself, its electric charge, or other factors.
Common types of potential energy include the gravitational potentia ...
, 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
A cut bank, also known as a river cliff or river-cut cliff, is the outside bank of a curve or meander in a water channel (stream), which is continually undergoing erosion.Essentials of Geology, 3rd Ed, Stephen Marshak Cut banks are found in abu ...
'' 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 is a natural form of a cutting or cut in a river occurs when a pronounced meander (hook) in a river is breached by a flow that connects the two closest parts of the hook to form a new channel, a full loop. The steeper drop in grad ...
'', 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 or pool that forms when a wide meander of a river is cut off, creating a free-standing body of water. In South Texas, oxbows left by the Rio Grande are called '' resacas''. In Australia, oxbow lakes are call ...
''. 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 Southwestern United States, also known as the American Southwest or simply the Southwest, is a geographic and cultural region of the United States that generally includes Arizona, New Mexico, and adjacent portions of California, Colorado, Ne ...
.[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
In geology, bedrock is solid Rock (geology), rock that lies under loose material (regolith) within the crust (geology), crust of Earth or another terrestrial planet.
Definition
Bedrock is the solid rock that underlies looser surface mater ...
are known as either incised, intrenched, entrenched, inclosed or ingrown meanders. Some Earth scientists recognize and use a finer subdivision of incised meanders. Thornbury[Thornbury, 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
Downcutting, also called erosional downcutting, downward erosion or vertical erosion is a geological process by hydraulic action that deepens the channel of a stream or valley by removing material from the stream's bed or the valley's floor. The ...
. Regardless, the formation of both entrenched meanders and ingrown meanders is thought to require that base level
In geology and geomorphology a base level is the lower limit for an erosion process. The modern term was introduced by John Wesley Powell in 1875. The term was subsequently appropriated by William Morris Davis who used it in his cycle of erosion ...
falls as a result of either relative change in mean sea level
Mean sea level (MSL, often shortened to sea level) is an average surface level of one or more among Earth's coastal bodies of water from which heights such as elevation may be measured. The global MSL is a type of vertical datuma standardised g ...
, 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, the growth and behavior of the strong, old cores of continents k ...
uplift, the breach of an ice or landslide
Landslides, also known as landslips, are several forms of mass wasting that may include a wide range of ground movements, such as rockfalls, deep-seated grade (slope), slope failures, mudflows, and debris flows. Landslides occur in a variety of ...
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. This province covers an area of ...
, the Kentucky River Palisades The Kentucky River Palisades are a series of steep, scenic Canyon, gorges and limestone outcroppings that stretch for approximately 100 mi (160 km), along the Kentucky River in central Kentucky in the United States.
Geology
The Kentuc ...
in central Kentucky
Kentucky ( , ), officially the Commonwealth of Kentucky, is a state in the Southeastern region of the United States and one of the states of the Upper South. It borders Illinois, Indiana, and Ohio to the north; West Virginia and Virginia to ...
, and streams in the Ozark Plateau
The Ozarks, also known as the Ozark Mountains, Ozark Highlands 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 portio ...
.[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 ( : strata) is a layer of rock or sediment characterized by certain lithologic properties or attributes that distinguish it from adjacent layers from which it is separated by visible surfaces known as ei ...
. 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 geologists[Hack, 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 or pool that forms when a wide meander of a river is cut off, creating a free-standing body of water. In South Texas, oxbows left by the Rio Grande are called '' resacas''. In Australia, oxbow lakes are call ...
'', 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 scientific journal published by John Wiley & Sons on behalf of the British Society for Geomorphology. It covers geomorphology and more in general all aspects of Earth sciences dealing wi ...
'', 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 ...
'', 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 sinuosity index 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 ...
or stream
A stream is a continuous body of water, body of surface water Current (stream), flowing within the stream bed, bed and bank (geography), banks of a channel (geography), channel. Depending on its location or certain characteristics, a stream ...
meanders (how much its course deviates from the shortest possible path). It is calculated as the length
Length is a measure of distance. In the International System of Quantities, length is a quantity with dimension distance. In most systems of measurement a base unit for length is chosen, from which all other units are derived. In the Interna ...
of the stream divided by the length of the valley
A valley is an elongated low area often running between Hill, hills or Mountain, 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 ...
. 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 shows 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 the ...
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
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 changes, leaving the former branch with a dead end. As a result ...
*Crevasse splay
A crevasse splay is a sedimentary fluvial deposit which forms when a stream breaks its natural or artificial levees and deposits sediment on a floodplain. A breach that forms a crevasse splay deposits sediments in similar pattern to an alluvial f ...
*Helicoidal flow
Helicoidal flow is the cork-screw-like flow of water in a meander. It is one example of a secondary flow.
Helicoidal flow is a contributing factor to the formation of slip-off slopes and river cliffs in a meandering section of the river. The he ...
*Jet stream
Jet streams are fast flowing, narrow, meandering thermal wind, air currents in the Atmosphere of Earth, atmospheres of some planets, including Earth. On Earth, the main jet streams are located near the altitude of the tropopause and are west ...
* Meander cutoffs in Avulsion (river)
*Meander scar
A meander scar, occasionally meander scarp,Christopher G. Morris, Academic Press dictionary of science and technology, Gulf Professional Publishing, 1992, , page 1333 is a geological feature formed by the remnants of a meandering water channel. The ...
*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 g ...
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
Rivers
Water streams
Erosion