Meander

Meander

Overview

A meander in general is a bend in a sinuous
Sinuosity
Sinuosity or sinuosity index is a measure of deviation of a path between two points from the shortest possible path...

 watercourse. A meander is formed when the moving water in a stream erodes the outer banks and widens its valley. A stream
Stream
A stream is a body of water with a current, confined within a bed and stream banks. Depending on its locale or certain characteristics, a stream may be referred to as a branch, brook, beck, burn, creek, "crick", gill , kill, lick, rill, river, syke, bayou, rivulet, streamage, wash, run or...

 of any volume may assume a meandering course, alternately eroding
Erosion
Erosion is when materials are removed from the surface and changed into something else. It only works by hydraulic actions and transport of solids in the natural environment, and leads to the deposition of these materials elsewhere...

 sediment
Sediment
Sediment is naturally occurring material that is broken down by processes of weathering and erosion, and is subsequently transported by the action of fluids such as wind, water, or ice, and/or by the force of gravity acting on the particle itself....

s from the outside of a bend and depositing them on the inside. The result is a snaking pattern as the stream meanders back and forth across its down-valley axis.
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Encyclopedia

A meander in general is a bend in a sinuous
Sinuosity
Sinuosity or sinuosity index is a measure of deviation of a path between two points from the shortest possible path...

 watercourse. A meander is formed when the moving water in a stream erodes the outer banks and widens its valley. A stream
Stream
A stream is a body of water with a current, confined within a bed and stream banks. Depending on its locale or certain characteristics, a stream may be referred to as a branch, brook, beck, burn, creek, "crick", gill , kill, lick, rill, river, syke, bayou, rivulet, streamage, wash, run or...

 of any volume may assume a meandering course, alternately eroding
Erosion
Erosion is when materials are removed from the surface and changed into something else. It only works by hydraulic actions and transport of solids in the natural environment, and leads to the deposition of these materials elsewhere...

 sediment
Sediment
Sediment is naturally occurring material that is broken down by processes of weathering and erosion, and is subsequently transported by the action of fluids such as wind, water, or ice, and/or by the force of gravity acting on the particle itself....

s from the outside of a bend and depositing them on the inside. The result is a snaking pattern as the stream meanders back and forth across its down-valley axis. When a meander gets cut off from the main stream, an oxbow lake
Oxbow lake
An oxbow lake is a U-shaped body of water formed when a wide meander from the main stem of a river is cut off to create a lake. This landform is called an oxbow lake for the distinctive curved shape, named after part of a yoke for oxen. In Australia, an oxbow lake is called a billabong, derived...

 is formed. Over time meanders migrate downstream, sometimes in such a short time as to create civil engineering problems for local municipalities attempting to maintain stable roads and bridges.

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

Sinuosity is one of the channel types
Channel types
A wide variety of river and stream channel types exist in limnology. All these can be divided into two groups by using the water-flow gradient as either low gradient channels for streams or rivers with less than two percent flow gradient, or high gradient channels for those with greater than a 2%...

 that a stream may assume over all or part of its course. All streams are sinuous at some time in their geologic history over some part of their length.

Origin of term


The term derives from a river located in present-day Turkey and known to the ancient Greeks as (Μαίανδρος) Maiandros or Maeander, characterised by a very convoluted path along the lower reach. As such, even in Classical Greece
Classical Greece
Classical Greece was a 200 year period in Greek culture lasting from the 5th through 4th centuries BC. This classical period had a powerful influence on the Roman Empire and greatly influenced the foundation of Western civilizations. Much of modern Western politics, artistic thought, such as...

 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
Geomorphology is the scientific study of landforms and the processes that shape them...

 feature. Strabo
Strabo
Strabo, also written Strabon was a Greek historian, geographer and philosopher.-Life:Strabo was born to an affluent family from Amaseia in Pontus , a city which he said was situated the approximate equivalent of 75 km from the Black Sea...

 said: "... its course is so exceedingly winding that everything winding is called meandering."

The Meander River is located south of Izmir, east of the ancient Greek town of Miletus
Miletus
Miletus was an ancient Greek city on the western coast of Anatolia , near the mouth of the Maeander River in ancient Caria...

, now, Milet, Turkey. It flows through a graben
Graben
In geology, a graben is a depressed block of land bordered by parallel faults. Graben is German for ditch. Graben is used for both the singular and plural....

 in the Menderes Massif, but has a flood plain much wider than the meander zone in its lower reach. In the Turkish name, the Büyük Menderes River, Menderes is from "Meander".

Meander geometry



The technical description of a meandering watercourse is termed meander geometry
Geometry
Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....

 or meander planform
Plans (drawings)
Plans are a set of drawings or two-dimensional diagrams used to describe a place or object, or to communicate building or fabrication instructions. Usually plans are drawn or printed on paper, but they can take the form of a digital file.- Overview :...

 geometry. It is characterized as an irregular waveform
Waveform
Waveform means the shape and form of a signal such as a wave moving in a physical medium or an abstract representation.In many cases the medium in which the wave is being propagated does not permit a direct visual image of the form. In these cases, the term 'waveform' refers to the shape of a graph...

. Ideal waveforms, such as a sine wave
Sine wave
The sine wave or sinusoid is a mathematical function that describes a smooth repetitive oscillation. It occurs often in pure mathematics, as well as physics, signal processing, electrical engineering and many other fields...

, 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 (geometry)
In geometry, a cross-section is the intersection of a figure in 2-dimensional space with a line, or of a body in 3-dimensional space with a plane, etc...

 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
Curve fitting
Curve fitting is the process of constructing a curve, or mathematical function, that has the best fit to a series of data points, possibly subject to constraints. Curve fitting can involve either interpolation, where an exact fit to the data is required, or smoothing, in which a "smooth" function...

 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
Wavelength
In physics, the wavelength of a sinusoidal wave is the spatial period of the wave—the distance over which the wave's shape repeats.It is usually determined by considering the distance between consecutive corresponding points of the same phase, such as crests, troughs, or zero crossings, and is a...

. The maximum distance from the down-valley axis to the sinuous axis of a loop is the meander width or amplitude
Amplitude
Amplitude is the magnitude of change in the oscillating variable with each oscillation within an oscillating system. For example, sound waves in air are oscillations in atmospheric pressure and their amplitudes are proportional to the change in pressure during one oscillation...

. 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
Curvature
In mathematics, curvature refers to any of a number of loosely related concepts in different areas of geometry. Intuitively, curvature is the amount by which a geometric object deviates from being flat, or straight in the case of a line, but this is defined in different ways depending on the context...

 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
Radius
In classical geometry, a radius of a circle or sphere is any line segment from its center to its perimeter. By extension, the radius of a circle or sphere is the length of any such segment, which is half the diameter. If the object does not have an obvious center, the term may refer to its...

 of the loop is considered to be the straight line perpendicular
Perpendicular
In geometry, two lines or planes are considered perpendicular to each other if they form congruent adjacent angles . The term may be used as a noun or adjective...

 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 convex bank and an inner or concave 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 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 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
Riffle
A Riffle is a short, relatively shallow and coarse-bedded length of stream over which the stream flows at higher velocity and higher turbulence than it normally does in comparison to a pool....

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
Thalweg
Thalweg in geography and fluvial geomorphology signifies the deepest continuous inline within a valley or watercourse system.-Hydrology:In hydrological and fluvial landforms, the thalweg is a line drawn to join the lowest points along the entire length of a stream bed or valley in its downward...

 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 (geometry)
In geometry, an arc is a closed segment of a differentiable curve in the two-dimensional plane; for example, a circular arc is a segment of the circumference of a circle...

 length is the distance along the thalweg over one meander. The river length is the length along the centerline.

Formation


Meander formation is a result of natural factors and processes. The waveform configuration of a stream is constantly changing. Fluid flows around a bend in a vortex
Vortex
A vortex is a spinning, often turbulent,flow of fluid. Any spiral motion with closed streamlines is vortex flow. The motion of the fluid swirling rapidly around a center is called a vortex...

. Once a channel begins to follow a sinusoidal path, the amplitude and concavity of the loops increase dramatically due to the effect of helical flow sweeping dense eroded material towards the inside of the bend, and leaving the outside of the bend unprotected and therefore vulnerable to accelerated erosion, forming a positive feedback loop. In the words of Elizabeth A. Wood:
"... 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 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
Angular momentum
In physics, angular momentum, moment of momentum, or rotational momentum is a conserved vector quantity that can be used to describe the overall state of a physical system...

 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. However, 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
Tea leaf paradox
The tea leaf paradox describes 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 from a spiral centrifugal force...

. 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
Stochastic refers to systems whose behaviour is intrinsically non-deterministic. A stochastic process is one whose behavior is non-deterministic, in that a system's subsequent state is determined both by the process's predictable actions and by a random element. However, according to M. Kac and E...

 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
Adhesion is any attraction process between dissimilar molecular species that can potentially bring them in close contact. By contrast, cohesion takes place between similar molecules....

 of water to the surface and cohesion
Cohesion (chemistry)
Cohesion or cohesive attraction or cohesive force is the action or property of like molecules sticking together, being mutually attractive...

 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 to be straight have a sinuous thalweg that leads eventually to a sinuous channel.

Equilibrium theory


In the equilibrium theory, meanders decrease the stream gradient until an equilibrium between the erodibility of the terrain and the transport capacity of the stream is reached. A mass of water descending must give up potential energy, 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/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).

Erosion Mechanics



Most meanders occur in the region of a river channel with shallow gradient
Gradient
In vector calculus, the gradient of a scalar field is a vector field that points in the direction of the greatest rate of increase of the scalar field, and whose magnitude is the greatest rate of change....

s, a well-developed floodplain
Floodplain
A floodplain, or flood plain, is a flat or nearly flat land adjacent a stream or river that stretches from the banks of its channel to the base of the enclosing valley walls and experiences flooding during periods of high discharge...

, and cohesive floodplain material. Deposition of sediment
Sediment
Sediment is naturally occurring material that is broken down by processes of weathering and erosion, and is subsequently transported by the action of fluids such as wind, water, or ice, and/or by the force of gravity acting on the particle itself....

 occurs on the inner edge, because the secondary flow of the river sweeps and rolls sand, rocks and other submerged objects across the bed of the river towards the inside radius of the river bend, creating a slip-off slope called a point bar
Point bar
A point bar is a depositional feature of streams. Point bars are found in abundance in mature or meandering streams. They are crescent-shaped and located on the inside of a stream bend, being very similar to, though often smaller than towheads, or river islands.Point bars are composed of sediment...

. Erosion is greater on the outside of the bend where the soil is not protected by deposits of sand and rocks. The current on the outside bend is more effective in eroding the unprotected soil, and the inside bend receives steadily increasing deposits of sand and rocks, and the meander tends to grow in the direction of the outside bend, forming a small cliff called a cut bank. This can be seen in areas where willows grow on the banks of rivers; on the inside of meanders, willows are often far from the bank, whilst on the outside of the bend, the roots of the willows are often exposed and undercut, eventually leading the trees to fall into the river. This demonstrates the river's movement. Slumping usually occurs on the concave sides of the banks resulting in mass movements such as slides.

Incised meanders




If the slope of an established meandering stream is suddenly increased, it will resume downward erosion – this happens when the base level of the stream is reduced, for example due to tectonic uplift
Tectonic uplift
Tectonic uplift is a geological process most often caused by plate tectonics which increases elevation. The opposite of uplift is subsidence, which results in a decrease in elevation. Uplift may be orogenic or isostatic.-Orogenic uplift:...

 of the region, a global fall in sea-level, collapse of a moraine-dammed lake downstream, or by capture of the stream by a steeper one. As the stream erodes downwards, its established meandering pattern will remain as a deep valley known as an incised meander or entrenched meander. Rivers in the Colorado Plateau
Colorado Plateau
The Colorado Plateau, also called the Colorado Plateau Province, is a physiographic region of the Intermontane Plateaus, roughly centered on the Four Corners region of the southwestern United States. The province covers an area of 337,000 km2 within western Colorado, northwestern New Mexico,...

 and streams in the Ozark Plateau are noted for these incised meanders.

Oxbow lakes



Oxbow lake
Oxbow lake
An oxbow lake is a U-shaped body of water formed when a wide meander from the main stem of a river is cut off to create a lake. This landform is called an oxbow lake for the distinctive curved shape, named after part of a yoke for oxen. In Australia, an oxbow lake is called a billabong, derived...

s are created when growing meanders intersect each other and cut off a meander loop, leaving it without an active cutting stream. Over a period of time, these oxbow lakes tend to dry out or fill in with sediments.

Abandoned meander (rincon)



Sometimes an incised meander is cut off, similar to an oxbow lake. The resulting landform is known as an abandoned meander. In the southwest United States it is also known as a rincon. One dramatic example, on Lake Powell
Lake Powell
Lake Powell is a huge reservoir on the Colorado River, straddling the border between Utah and Arizona . It is the second largest man-made reservoir in the United States behind Lake Mead, storing of water when full...

, is called "The Rincon."

Scroll-bars



Scroll-bars are a result of continuous lateral migration of a meander loop that creates an asymmetrical ridge and swale topography 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 out 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.

Derived quantities


The meander ratio or sinuosity index
Sinuosity
Sinuosity or sinuosity index is a measure of deviation of a path between two points from the shortest possible path...

 is a means of quantifying how much a river
River
A river is a natural watercourse, usually freshwater, flowing towards an ocean, a lake, a sea, or another river. In a few cases, a river simply flows into the ground or dries up completely before reaching another body of water. Small rivers may also be called by several other names, including...

 or stream
Stream
A stream is a body of water with a current, confined within a bed and stream banks. Depending on its locale or certain characteristics, a stream may be referred to as a branch, brook, beck, burn, creek, "crick", gill , kill, lick, rill, river, syke, bayou, rivulet, streamage, wash, run or...

 meanders (how much its course deviates from the shortest possible path). It is calculated as the length
Length
In geometric measurements, length most commonly refers to the longest dimension of an object.In certain contexts, the term "length" is reserved for a certain dimension of an object along which the length is measured. For example it is possible to cut a length of a wire which is shorter than wire...

 of the stream divided by the length of the valley
Valley
In geology, a valley or dale is a depression with predominant extent in one direction. A very deep river valley may be called a canyon or gorge.The terms U-shaped and V-shaped are descriptive terms of geography to characterize the form of valleys...

. 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
Ratio
In mathematics, a ratio is a relationship between two numbers of the same kind , usually expressed as "a to b" or a:b, sometimes expressed arithmetically as a dimensionless quotient of the two which explicitly indicates how many times the first number contains the second In mathematics, a ratio is...

 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 need to be elaborated 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 to 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

  • Riffle-pool sequence
    Riffle-Pool Sequence
    In a flowing stream, a riffle-pool 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 gravel or coarser sediments. Riffles are formed in shallow areas by coarser materials such...

  • Helicoidal flow
    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...

  • Baer's law
    Baer's law
    In geology, Baer's law, named after Karl Ernst von Baer, says that, because of the rotation of the earth, in the Northern Hemisphere, erosion occurs mostly on the right banks of rivers and in the Southern Hemisphere on the left banks...

  • Meander cutoffs in Avulsion (river)
  • Meander scar
    Meander scar
    A meander scar, occasionally meander scarp, is a geological feature formed by the remnants of a meandering water channel. They are characterized by "a crescentic cut in a bluff or valley wall, produced by...a meandering stream." They are often formed during the creation of oxbow lakes.The term...

  • Crevasse splay
    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. This breach can cause large deposits that spread in a pattern similar to that of an alluvial fan deposit. Once the levee has been breached the...

  • Jet stream
    Jet stream
    Jet streams are fast flowing, narrow air currents found in the atmospheres of some planets, including Earth. The main jet streams are located near the tropopause, the transition between the troposphere and the stratosphere . The major jet streams on Earth are westerly winds...

    exhibits meander also