Meanders

A meander in general is a bend in a sinuous watercourse, also known as an oxbow loop, or simply an oxbow. A meander is formed when the moving water in a river erodes the outer banks and widens its valley. A stream of any volume may assume a meandering course, alternatively eroding sediments 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 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 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.

The term derives from the river 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 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 feature. Strabo said: "... its course is so exceedingly winding that everything winding is called meandering."

The Meander River is located in present-day Turkey, south of Izmir, eastward the ancient Greek town of Miletus, now Turkish Milet. It flows through a graben 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". Meanders are also formed as a result of deposition and erosion.

The technical description of a meandering watercourse is termed meander geometry or meander planform geometry. It is characterized as an irregular waveform. Ideal waveforms, such as a 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 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 River/stream 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. The maximum distance from the down-valley axis to the sinuous axis of a loop is the meander width or 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 varies from a minimum at the apex to infinity at a crossing point (straight line), also called an inflection, because the curvature changes direction in that vicinity. The radius of the loop is considered to be the straight line 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 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 riffles, 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 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.

Meander formation is a somewhat equivocal term referring to the natural factors and processes that result in meanders. The waveform configuration of a stream is constantly changing. Once a sinusoidal channel exists it undergoes a process during which the amplitude and concavity of the loops increase dramatically due to the effect of helicoidal flow in increasing the amount of erosion occurring on the outside of a bend, 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 helical flow is explained as a transfer of momentum from the inside of the bend to the outside. As soon as the flow enters the bend some of its momentum becomes angular, the conservation of which would require an increase of velocity on the inside and a decrease on the outside, exactly the opposite of what happens. Instead centrifugal force superelevates the surface on the outside, moving surface water transversely into it. This water moves down to replace the subsurface water pushed back at the end of the bend. The result is the scouring helical flow, and the greater the curvature, the greater the angular momentum and the stronger the cross-current.

The question of formation is why streams of any size become sinuous in the first place. There are a number theories, not necessarily mutually exclusive.

The stochastic 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 of water to the surface and cohesion of drops produce rivulets at random. Natural surfaces are rough and erodable 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.

In the equilibrium theory, meanders decrease the stream gradient until an equilibrium between the erodability 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 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).

Most meanders occur in the region of a river channel with shallow gradients, a well-developed floodplain, and cohesive floodplain material. Erosion is greater on the outside of the bend where velocity is greatest. Deposition of sediment occurs on the inner edge because the river, moving slowly, cannot carry its sediment load, creating a slip-off slope called a point bar. The faster moving current on the outside bend has more erosive ability 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.

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 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 and streams in the Ozark Plateau are noted for these incised meanders. Such incised meanders form desirable locations for the construction of fortifications.