A meander, in general, is a bend in a
sinuous watercourse or river. A meander
forms when moving water in a stream
erodes the outer banks and widens its
valley, and the inner part of the river
has less energy and deposits silt. A
stream of any volume may assume a
meandering course, alternately 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 forms. 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.
Origin of term
The term derives from a river located in
present-day Turkey and known to the
Ancient Greeks as Μαίανδρος Maiandros,
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 south of
Izmir, east of the ancient Greek town of
Miletus, now, Milet, Turkey. 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".
Meander geometry
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 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. 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
maximum at the apex to zero at a
crossing point, also called an
inflection, because the curvature
changes direction in that vicinity. The
radius of the loop is 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.
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. 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 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. 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 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 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 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 and morphotectonic theory=
Geomorphic refers to the surface
structure of the terrain. Morphotectonic
means having to do with the deeper, or
tectonic 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.
Associated landforms
= Slip-off slope=
On the inside of a meander is a gentle
slope of sedementation referred to as
the slip-off slope. It is often marked
by a point bar in the river.
= River-cut cliff=
On the outside of a meander the river
cuts into the bank, often resulting in a
river[-cut] cliff, also known as a cut
bank, or a bluff.
= Erosion mechanics=
Most meanders occur in the region of a
river channel with shallow gradients, a
well-developed floodplain, and cohesive
floodplain material. Deposition of
sediment 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 point bar below
the slip-off slope. 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.
= Deposits=
Point bar
Point Bars are simply an accumulation of
deposited alluvium that collects on the
inside bank of a meander curve. This
accumulation occurs due to the stream's
lower velocity in the interior portion
of the curve. In accordance with the
Hjulström curve, sediment will settle
more readily at lower velocities. Point
bars typically are composed of sediment
ranging in size from pebbles to granular
sands. Only in still water do silt
particles settle.
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 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, the
Kentucky River Palisades in central
Kentucky, and streams in the Ozark
Plateau are noted for these incised
meanders.
Oxbow lakes
Oxbow lakes are created when growing
meanders intersect each other and cut
off a meander loop, leaving it without
an active cutting stream. This process
is usually linked to flooding where the
river will tend to the path of least
resistance. The oxbow, being of much
lower energy than the more direct path,
collects more and more deposited
sediment each season of flooding until
it becomes independent from the river.
The largest oxbow lakes will be in areas
with wider flood plains where the rivers
have more room to meander. Over a period
of time, these oxbow lakes tend to dry
out or fill in with sediments.
Abandoned meander
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, 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 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. 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 is
a means of quantifying how much a river
or stream meanders. It is calculated as
the length of the stream divided by the
length of the valley. A perfectly
straight river would have a meander
ratio of 1, while the higher this ratio
is above 1, the more the river meanders.
Sinuosity indices are calculated from
the map or from an aerial photograph
measured over a distance called 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 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.
See also
Riffle-pool sequence
Helicoidal flow
Baer's law
Meander cutoffs in Avulsion
Meander scar
Crevasse splay
Jet stream exhibits meander also
References and notes
Bibliography
Hickin, Edward J.. "Meandering
Channels". In Middleton, Gerard V.
Encyclopedia of Sediments and
Sedimentary Rocks. Kluwer Academic
Encyclopedia of Earth Sciences.
Dordrecht; Boston: Kluwer Academic
Publishers. pp. 430–434. ISBN
1-4020-0872-4. 
Leopold, Luna B.; Langbein, W.B.. "River
Meanders". Scientific American: 60. 
Virtual Luna Leopold
Thonemann, P., The Maeander Valley: A
historical geography from Antiquity to
Byzantium.
External links
Movshovitz-Hadar, Nitsa; Alla Shmuklar.
"River Meandering and a Mathematical
Model of this Phenomenon".
Physicalplus).
