Flows, sediments and bedforms

Bedform


A bedform is a morphological feature formed by the interaction between a flow and cohesion less sediment on a bed. Ripples in sand in a flowing stream and sand dunes in deserts are both examples of bedforms, the former resulting from flow in water, the latter by airflow. The patterns of ripples and dunes are products of the action of the flow and the formation of bedforms creates distinctive layering and structures within the sediment that can be preserved in strata. Recognition of sedimentary structures generated by bedforms provides information about the strength of the current, the flow depth and the direction of sediment transport. A fluid flowing over a surface can be divided into a free stream, which is the portion of the flow unaffected by boundary effects, a boundary layer, within which the velocity starts to decrease due to friction with the bed, and a viscous sublayer,a region of reduced turbulence that is typically less than a millimetre thick. The thickness of the viscous sublayer decreases with increasing flow velocity but is independent of the flow depth. The relationship between the thickness of the viscous sublayer and the size of grains on the bed of flow defines an important property of the flow. If all the particles are contained within the viscous sublayer the surface is considered to be hydraulically smooth, and if there are particles that project up through this layer then the flow surface is hydraulically rough. As will be seen in the following sections, processes within the viscous sublayer and the effects of rough and smooth surfaces are fundamental to the formation of different bedforms. The following sections are concerned mainly with the formation of bedforms in flowing water in rivers and seas, but many of the fluid dynamic principles also apply to aeolian (wind-blown) deposits.

Current ripples



Flow within the viscous sublayer is subject to irregularities known as turbulent sweeps, which move grains by rolling or saltation and create local clusters of grains. These clusters are only a few grains high but once they have formed they create steps or defects that influence the flow close to the bed surface. Flow can be visualised in terms of streamlines in the fluid, imaginary lines that indicate the direction of flow. Streamlines lie parallel to a flat bed or the sides of a cylindrical pipe, but where there is an irregularity such as a step in the bed caused by an accumulation of grains, the streamlines converge and there is an increased transport rate. At the top of the step, a streamline separates from the bed surface and a region of boundary layer separation forms between the flow separation point and the flow attachment point downstream. Beneath this streamline lies a region called the separation bubble or separation zone. Expansion of flow over the step results in an increase in pressure and the sediment transport rate is reduced, resulting in deposition on the lee side of the step. 
Current ripples are small bedforms formed by the effects of boundary layer separation on a bed of sand. The small cluster of grains grows to form the crest of a ripple and separation occurs near this point. Sand grains roll or saltate up to the crest on the upstream stoss side of the ripple. Avalanching of grains occurs down the downstream or lee side of the ripple as accumulated grains become unstable at the crest. Grains that avalanche on the lee slope tend to come to rest at an angle close to the maximum critical slope angle for sand at around 308. At the flow attachment point there are increased stresses on the bed, which result in erosion and the formation of a small scour, the trough of the ripple.

Current ripples and cross-lamination


A ripple migrates downstream as sand is added to the crest and accretes on the lee slope. This moves the crest and hence the separation point downstream, which in turn moves the attachment point and trough downstream as well. Scour in the trough and on the base of the stoss side supplies the sand, which moves up the gentle slope of the stoss side of the next ripple and so a whole train of ripple troughs and crests advance downstream. The sand that avalanches on the lee slope during this migration forms a series of layers at the angle of the slope. These thin, inclined layers of sand are called cross-laminae, which build up to form the sedimentary structure referred to as cross-lamination. 
Linguoid ripple
When viewed from above current ripples show a variety of forms. They may have relatively continuous straight to sinuous crests (straight ripples or sinuous ripples) or form a pattern of unconnected arcuate forms called linguoid ripples. The relationship between the two forms appears to be related to both the duration of the flow and its velocity, with straight ripples tending to evolve into linguoid forms through time and at higher velocities. Straight and linguoid ripple crests create different patterns of cross-lamination in three dimensions. A perfectly straight ripple would generate cross-laminae that all dipped in the same direction and lay in the same plane: this is planar cross-lamination. Sinuous and linguoid ripples have lee slope surfaces that are curved, generating laminae that dip at an angle to the flow as well as downstream. As linguoid ripples migrate, curved cross-laminae are formed mainly in the trough-shaped low areas between adjacent ripple forms resulting in a pattern of trough cross-lamination.

Creating and preserving cross-lamination

Starved ripples
Current ripples migrate by the removal of sand from the stoss (upstream) side of the ripple and deposition on the lee side (downstream). If there is a fixed amount of sand available the ripple will migrate over the surface as a simple ripple form, with erosion in the troughs matching addition to the crests. These starved ripple forms are preserved if blanketed by mud. If the current is adding more sand particles than it is carrying away, the amount of sand deposited on the lee slope will be greater than that removed from the stoss side. There will be a net addition of sand to the ripple and it will grow as it migrates, but most importantly, the depth of scour in the trough is reduced leaving cross-laminae created by earlier migrating ripples preserved. In this way a layer of cross-laminated sand is generated. 
When the rate of addition of sand is high there will be no net removal of sand from the stoss side and each ripple will migrate up the stoss side of the ripple form in front. These are climbing ripples. When the addition of sediment from the current exceeds the forward movement of the ripple, deposition will occur on the stoss side as well as on the lee side. Climbing ripples are therefore indicators of rapid sedimentation as their formation depends upon the addition of sand to the flow at a rate equal to or greater than the rate of downstream migration of the ripples.

Constraints on current ripple formation

The formation of current ripples requires moderate flow velocities over a hydrodynamically smooth bed. They only form in sands in which the dominant grain size is less than 0.6 mm (coarse sand grade) because bed roughness created by coarser sand creates turbulent mixing, which inhibits the small scale flow separation required for ripple formation. Because ripple formation is controlled by processes within the viscous sublayer their formation is independent of water depth and current ripples may form in waters ranging from a few centimetres to kilometres deep. This is in contrast to most other subaqueous bedforms (subaqueous dunes, wave ripples), which are water-depth dependent. Current ripples can be up to 40 mm high and the wavelengths (crest to crest or trough to trough distances) range up to 500 mm. The ratio of the wavelength to the height is typically between 10 and 40. There is some evidence of a relationship between the ripple wavelength and the grain size, approximately 1000 to 1. It is important to note the upper limit to the dimensions of current ripples and to emphasise that ripples do not ‘grow’ into larger bedforms.

Dunes

Sand dunes
Beds of sand in rivers, estuaries, beaches and marine environments also have bedforms that are distinctly larger than ripples. These large bedforms are called dunes: the term ‘mega-ripples’ is also sometimes used, although this term fails to emphasise the fundamental hydrodynamic distinctions between ripple and dune bedforms. Evidence that these larger bedforms are not simply large ripples comes from measurement of the heights and wavelengths of all bedforms. The data fall into clusters which do not overlap, indicating that they form by distinct processes which are not part of a continuum. The formation of dunes can be related to large-scale turbulence within the whole flow; once again flow separation is important, occurring at the dune crest, and scouring occurs at the reattachment point in the trough. The water depth controls the scale of the turbulent eddies in the flow and this in turn controls the height and wavelength of the dunes: there is a considerable amount of scatter in the data, but generally dunes are tens of centimetres high in water depths of a few metres, but are typically metres high in the water depths measured in tens of metres.

Dunes and cross-bedding

Trough cross bedding.
Tabular cross bedding
The morphology of a subaqueous dune is similar to a ripple: there is a stoss side leading up to a crest and sand avalanches down the lee slope towards a trough. Migration of a subaqueous dune results in the construction of a succession of sloping layers formed by the avalanching on the lee slope and these are referred to as cross-beds. Flow separation creates a zone in front of the lee slope in which a roller vortex with reverse flow can form. At low flow velocities these roller vortices are weakly developed and they do not rework the sand on the lee slope. The cross-beds formed simply lie at the angle of rest of the sand and as they build out into the trough the basal contact is angular. Bedforms that develop at these velocities usually have low sinuosity crests, so the three-dimensional form of the structure is similar to planar cross-lamination. This is planar cross-bedding and the surface at the bottom of the cross-beds is flat and close to horizontal because of the absence of scouring in the trough. Cross-beds bound by horizontal surfaces are sometimes referred to as tabular cross-bedding. Cross-beds may form a sharp angle at the base of the avalanche slope or may be asymptotic (tangential) to the horizontal. At high flow velocities the roller vortex is well developed creating a counter-current at the base of the slip face that may be strong enough to generate ripples (counter-flow ripples), which migrate a short distance up the toe of the lee slope. 
A further effect of the stronger flow is the creation of a marked scour pit at the reattachment point. The avalanche lee slope advances into this scoured trough so the bases of the cross-beds are marked by an undulating erosion surface. The crest of a subaqueous dune formed under these conditions will be highly sinuous or will have broken up into a series of linguoid dune forms. Trough cross-bedding formed by the migration of sinuous subaqueous dunes typically has asymptotic bottom contacts and an undulating lower boundary.

Constraints on the formation of dunes

Dunes range in size from having wavelengths of about 600 mm and heights of a few tens of millimetres to wavelengths of hundreds of metres and heights of over ten metres. The smallest are larger than the biggest ripples. Dunes can form in a range of grain sizes from fine gravels to fine sands, but they are less well developed in finer deposits and do not occur in very fine sands or silts. This grain size limitation is thought to be related to the increased suspended load in the flow if the finer grain sizes are dominant: the suspended load suppresses turbulence in the flow and flow separation does not occur. The formation of dunes also requires flow to be sustained for long enough for the structure to build up, and to form cross-bedding the dune must migrate. Dunescale cross-bedding therefore cannot be generated by short-lived flow events. Dunes are most commonly encountered in river channels, deltas, estuaries and shallow marine environments where there are relatively strong, sustained flows.

Bar forms

Bars are bedforms occurring within channels that are of a larger scale than dunes: they have width and height dimensions of the same order of magnitude as the channel within which they are formed. Bars can be made up of sandy sediment, gravelly material or mixtures of coarse grain sizes. In a sandy channel the surfaces of bar forms are covered with subaqueous dune bedforms, which migrate over the bar surface and result in the formation of units of cross-bedded sands. A bar form deposit is therefore typically a cross-bedded sandstone as a lens-shaped body. The downstream edge of a bar can be steep and develop its own slip-face, resulting in large-scale cross-stratification in both sandstones and conglomerates. Bars in channels are classified in terms of their position within the channel (side and alternate bars at the margins, mid-channel bars in the centre and point bars on bends: and their shape.

Plane bedding and planar lamination

Horizontal layering in sands deposited from a flow is referred to as plane bedding in sediments and produces a sedimentary structure called planar lamination in sedimentary rocks. Current ripples only form if the grains are smaller than the thickness of the viscous sublayer: if the bed is rough, the small-scale flow separation required for ripple formation does not occur and the grains simply roll and saltate along the surface. Plane beds form in coarser sands at relatively low flow velocities (close to the threshold for movement), but as the flow speed increases dune bedforms start to be generated. The horizontal planar lamination produced under these circumstances tends to be rather poorly defined. 
Plane bedding is also observed at higher flow velocities in very fine- to coarse-grained sands: ripple and dune bedforms become washed out with an increase in flow speed as the formation of flow separation is suppressed at higher velocities. These plane beds produce well-defined planar lamination with laminae that are typically 5–20 grains thick. The bed surface is also marked by elongate ridges a few grain diameters high separated by furrows oriented parallel to the flow direction. This feature is referred to as primary current lineation (often abbreviated to ‘pcl’) and it is formed by sweeps within the viscous sublayer that push grains aside to form ridges a few grains high which lie parallel to the flow direction. The formation of sweeps is subdued when the bed surface is rough and primary current lineation is therefore less well defined in coarser sands. Primary current lineation is seen on the surfaces of planar beds as parallel lines of main grains which form very slight ridges, and may often be rather indistinct.

Supercritical flow

Flow may be considered to be subcritical, often with a smooth water surface, or supercritical, with an uneven surface of wave crests and troughs. These flow states relate to a parameter, the Froude number (Fr), which is a relationship between the flow velocity (y) and the flow depth (h), with ‘g’ the acceleration due to gravity. The Froude number can be considered to be a ratio of the flow velocity to the velocity of a wave in the flow. When the value is less than one, the flow is subcritical and a wave can propagate upstream because it is travelling faster than the flow. If the Froude number is greater than one this indicates that the flow is too fast for a wave to propagate upstream and the flow is supercritical. In natural flows a sudden change in the height of the surface of the flow, a hydraulic jump, is seen at the transition from thin, supercritical flow to thicker, subcritical flow. 
Where the Froude number of a flow is close to one, standing waves may temporarily form on the surface of the water before steepening and breaking in an upstream direction. Sand on the bed develops a bedform surface parallel to the standing wave, and as the flow steepens sediment accumulates on the upstream side of the bedform. These bedforms are called antidunes, and, if preserved, antidune cross-bedding would be stratification dipping upstream. However, such preservation is rarely seen because as the wave breaks, the antidune bedform is often reworked, and as the flow velocity subsequently drops the sediment is reworked into upper stage plane beds by subcritical flow. Well-documented occurrences of antidune cross-stratification are known from pyroclastic surge deposits, where high velocity flow is accompanied by very high rates of sedimentation.

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