Fractal properties of simulated bed profiles in coarse-grained channels

Bed roughness characteristics in coarse-grained channels are fairly complex. A hierarchy of roughness elements can be observed, ranging from variable particle sizes and shapes and small-scale sedimentary structures, to large-scale bedforms such as riffle-pool sequences. The effects of these scales of roughness on the flow geometry still remain to be thoroughly investigated. The semivariogram has been suggested in the past as a means of quantifying bed roughness effects on streamflow, as well as for distinguishing between scales of roughness. However, field measurements are rather time-consuming. The low number of bed profiles measured in the field precludes the identification of generally applicable relationships between the statistical properties derived from the semivariograms (such as the Hausdorff dimensions and the scale of autocorrelation corresponding to each fractal band) and the bed configuration itself (geometrical and sedimentological properties). Simulation results of gravel-bed profiles are, therefore, presented in order to complement the original investigation of Robert (1988a). The simulation experiments, based on grain characteristics of sizes and shapes and on morphological properties of small-scale bedforms, yield very significant information on boundary roughness at the microscale and give insight into the interpretation of empirical semivariograms (derived from field measurements). Bed-material sorting, variable grain shapes, and height and spacing of cluster bedforms control the fractal dimensions obtained from the semivariograms, as well as the location of the break of slope and the range of the process.     

On the transition between 2D and 3D dunes

Sediment transport in sand-bedded alluvial channels is strongly conditioned by bedforms, the planimetric morphology of which can be either two- or three-dimensional. Experiments were undertaken to examine the processes that transform the bed configuration from two-dimensional (2D) dunes to three-dimensional (3D) dunes. A narrowly graded, 500 μm size sand was subjected to a 0·15 m deep, non-varying mean flow ranging from 0·30 to 0·55 m sec⁻¹ in a 1 m wide flume. Changes in the planimetric configuration of the bed were monitored using a high-resolution video camera that produced a series of 10 sec time-lapsed digital images. Image analysis was used to define a critical value of the non-dimensional span (sinuosity) of the bedform crestlines that divides 2D forms from 3D forms. Significant variation in the non-dimensional span is observed that cannot be linked to properties of the flow or bedforms and thus appears random. Images also reveal that, once 2D bedforms are established, minor, transient excesses or deficiencies of sand are passed from one bedform to another. The bedform field appears capable of absorbing a small number of such defects but, as the number grows with time, the resulting morphological perturbations produce a transition in bed state to 3D forms that continue to evolve, but are pattern-stable. The 3D pattern is maintained by the constant rearrangement of crestlines through lobe extension and starving downstream bedforms of sediment, which leads to bifurcation. The experiments demonstrate that 2D bedforms are not stable in this calibre sand and call into question the reliability of bedform phase diagrams that use crestline shape as a discriminator.     

Variability in bedform morphology and kinematics with transport stage

Bedform geometry is widely recognized to be a function of transport stage. Bedform aspect ratio (height/length) increases with transport stage, reaches a maximum, then decreases as bedforms washout to a plane bed. Bedform migration rates are also linked to bedform geometry, in so far as smaller bedforms in coarser sediment tend to migrate faster than larger bedforms in finer sediment. However, how bedform morphology (height, length and shape) and kinematics (translation and deformation) change with transport stage and suspension have not been examined. A series of experiments is presented where initial flow depth and grain size were held constant and the transport stage was varied to produce bedload dominated, mixed‐load dominated and suspended‐load dominated conditions. The results show that the commonly observed pattern in bedform aspect ratio occurs because bedform height increases then decreases with transport stage, against a continuously increasing bedform length. Bedform size variability increased with transport stage, leading to less uniform bedform fields at higher transport stage. Total translation‐related and deformation‐related sediment fluxes all increased with transport stage. However, the relative contribution to the total flux changed. At the bedload dominated stage, translation‐related and deformation‐related flux contributed equally to the total flux. As the transport stage increased, the fraction of the total load contributed by translation increased and the fraction contributed by deformation declined because the bedforms got bigger and moved faster. At the suspended‐load dominated transport stage, the deformation flux increased and the translation flux decreased as a fraction of the total load, approaching one and zero, respectively, as bedforms washed out to a plane bed.     

Streamlined bedrock terrain and fast ice flow, Jakobshavns Isbrae, West Greenland: implications for ice stream and ice sheet dynamics

This study investigates the marginal subglacial bedrock bedforms of Jakobshavns Isbrae, West Greenland, in order to examine the processes governing bedform evolution in ice stream and ice sheet areas, and to reconstruct the interplay between ice stream and ice sheet dynamics. Differences in bedform morphology (roche moutonnee or whaleback) are used to explore contrasts in basal conditions between fast and slow ice flow. Bedform density is higher in ice stream areas and whalebacks are common. We interpret that this is related to higher ice velocities and thicker ice which suppress bed separation. However, modification of whalebacks by plucking occurs during deglaciation due to ice thinning, flow deceleration, crevassing and fluctuations in basal water pressure. The bedform evidence points to widespread basal sliding during past advances of Jakobshavns Isbrae. This was encouraged by increased basal temperatures and melting at depth, as well as the steep marginal gradients of Jakobshavns Isfjord which allowed rapid downslope evacuation of meltwater leading to strong ice/bedrock coupling and scouring. In contrast to soft-bedded ice stream bedforms, the occurrence of fixed basal perturbations and higher bed roughness in rigid bed settings prevents the basal ice subsole from maintaining a stable form which, coupled with secondary plucking, counteracts the development of bedforms with high elongation ratios. Cross-cutting striae and double-plucked, rectilinear bedforms suggest that Jakobshavns Isbrae became partially unconfined during growth phases, causing localised diffluent flow and changes in ice sheet dynamics around Disko Bugt. It is likely that Disko Bugt harboured a convergent ice flow system during repeated glacial cycles, resulting in the formation of a large coalesced ice stream which reached the continental shelf edge.     

Bedform spurs: a result of a trailing helical vortex wake

The formative conditions for bedform spurs and their roles in bedform dynamics and associated sediment transport are described herein. Bedform spurs are formed by helical vortices that trail from the lee surface of oblique segments of bedform crest lines. Trailing helical vortices quickly route sediment away from the lee surface of their parent bedform, scouring troughs and placing this bed material into the body of the spur. The geometric configuration of bedform spurs to their parent bedform crests is predicted by a cross‐stream Strouhal number. When present, spur‐bearing bedforms and their associated trailing helical wakes exert tremendous control on bedform morphology by routing enhanced sediment transport between adjacent bedforms. Field measurements collected at the North Loup River, Nebraska, and flume experiments described in previous studies demonstrate that this trailing helical vortex‐mediated sediment transport is a mechanism for bedform deformation, interactions and transitions between two‐dimensional and three‐dimensional bedforms.     

A unified model for bedform development and equilibrium under unidirectional,oscillatory and combined‐flows

The development of bedforms under unidirectional, oscillatory and combined‐flows results from temporal changes in sediment transport, flow and morphological response. In such flows, the bedform characteristics (for example, height, wavelength and shape) change over time, from their initiation to equilibrium with the imposed conditions, even if the flow conditions remain unchanged. These variations in bedform morphology during development are reflected in the sedimentary structures preserved in the rock record. Hence, understanding the time and morphological development in which bedforms evolve to an equilibrium stage is critical for informed reconstruction of the ancient sedimentary record. This article presents results from a laboratory flume study on bedform development and equilibrium development time conducted under purely unidirectional, purely oscillatory and combined‐flow conditions, which aimed to test and extend an empirical model developed in past work solely for unidirectional ripples. The present results yield a unified model for bedform development and equilibrium under unidirectional, oscillatory and combined‐flows. The experimental results show that the processes of bedform genesis and growth are common to all types of flows, and can be characterized into four stages: (i) incipient bedforms; (ii) growing bedforms; (iii) stabilizing bedforms; and (iv) fully developed bedforms. Furthermore, the development path of bedform; growth exhibits the same general trend for different flow types (for example, unidirectional, oscillatory and combined‐flows), bedform size (for example, small versus large ripples), bedform shape (for example, symmetrical or rounded), bedform planform geometry (for example, two‐dimensional versus three‐dimensional), flow velocities and sediment grain sizes. The equilibrium time for a wide range of bed configurations was determined and found to be inversely proportional to the sediment transport flux occurring for that flow condition.     

Bedform climbing in theory and nature

Where bedforms migrate during deposition, they move upward (climb) with respect to the generalized sediment surface. Sediment deposited on each lee slope and not eroded during the passage of a following trough is left behind as a cross-stratified bed. Because sediment is thus transferred from bedforms to underlying strata, bedforms must decrease in cross-sectional area or in number, or both, unless sediment lost from bedforms during deposition is replaced with sediment transported from outside the depositional area. Where sediment is transported solely by downcurrent migration of two-dimensional bedforms, the mean thickness of cross-stratified beds is equal to the decrease in bedform cross-sectional area divided by the migration distance over which that size decrease occurs; where bedforms migrate more than one spacing while depositing cross-strata, bed thickness is only a fraction of bedform height. Equations that describe this depositional process explain the downcurrent decrease in size of tidal sand waves in St Andrew Bay, Florida, and the downwind decrease in size of transverse aeolian dunes on the Oregon coast. Using the same concepts, dunes that deposited the Navajo, De Chelly, and Entrada Sandstones are calculated to have had mean heights between several tens and several hundreds of metres.     

Supply‐limited bedform patterns and scaling downstream of a gravel–sand transition

A distinct suite of sand bedforms has been observed to occur in laboratory flows with limited sand supply. As sand supply to the bed progressively increases one observes sand ribbons, discrete barchans and, eventually, channel spanning dunes; but there are relatively few observations of this sequence from natural river channels. Furthermore, there are few observations of transitions from limited sand supply to abundant supply in the field. Bedforms developed under limited, but increasing, sand supply downstream of the abrupt gravel–sand transition in the Fraser River, British Columbia, are examined using multi‐beam swath‐bathymetry obtained at high flow. This is an ideal location to study supply‐limited bedforms because, due to a break in river slope, sand transitions from washload upstream of the gravel–sand transition to bed material load downstream. Immediately downstream, barchanoid and isolated dunes are observed. Most of the bedform field has gaps in the troughs, consistent with sand moving over a flat immobile or weakly mobile gravel bed. Linear, alongstream bedform fields (trains of transverse dunes formed on locally thick, linear deposits of sand) exhibit characteristics of sand ribbons with superimposed bedforms. Further downstream, channel spanning dunes develop where the bed is composed entirely of sand. Depth scaling of the dunes does not emerge in this data set. Only where the channel has accumulated abundant sand on the bed do the dunes exhibit scaling congruent with previous data compilations. The observations suggest that sediment supply plays an important, but often overlooked, role in bedform scaling in rivers.     

淹没植物明渠床面冲淤及其对水流运动的影响

植物的存在改变了河流水动力特性,造成独特的床面冲淤态势。利用实验室水槽模拟含淹没植物的河道,对床面形态和紊流统计特性参数进行测量,研究不同类型紊流作用下的床面冲淤特征以及床面起伏对流动的影响。结果表明:床面剪切紊流条件下,床面形态为马蹄坑-沙沟/沙脊与沙波复合分布,床面变形加剧了流速沿水深不均匀分布并促进水流动量交换;在自由剪切混合层紊流条件下,床面形态为植物根部马蹄形冲坑及其后方沙沟、沙脊交错分布,床面变形对流动的影响并不显著;“类二重紊流”条件下,床面形态同样表现为马蹄坑-沙沟/沙脊-沙波复合,床面变形促进植物层内部的水流动量交换、抑制紊动清扫,抑制植物层外部的动量交换、促进紊动喷射。     

Formation and preservation of open-framework gravel strata in unidirectional flows

Open‐framework gravel (OFG) in river deposits is important because of its exceptionally high permeability, resulting from the lack of sediment in the pore spaces between the gravel grains. Fluvial OFG occurs as planar strata and cross strata of varying scale, and is interbedded with sand and sandy gravel. The origin of OFG has been related to: (1) proportion of sand available relative to gravel; (2) separation of sand from gravel during a specific flow stage and sediment transport rate (either high, falling or low); (3) separation of sand from gravel in bedforms superimposed on the backs of larger bedforms; (4) flow separation in the lee of dunes or unit bars. Laboratory flume experiments were undertaken to test and develop these theories for the origin of OFG. Bed sediment size distribution (sandy gravel with a mean diameter of 1·5 mm) was kept constant, but flow depth, flow velocity and aggradation rate were varied. Bedforms produced under these flow conditions were bedload sheets, dunes and unit bars. The fundamental cause of OFG is the sorting of sand from gravel associated with flow separation at the crest of bedforms, and further segregation of grain sizes during avalanching on the steep lee side. Sand in transport near the bed is deposited in the trough of the bedform, whereas bed‐load gravel avalanches down the leeside and overruns the sand in the trough. The effectiveness of this sorting mechanism increases as the height of the bedform increases. Infiltration of sand into the gravel framework is of minor importance in these experiments, and occurs mainly in bedform troughs. The geometry and proportion of OFG in fluvial deposits are influenced by variation in height of bedforms as they migrate, superposition of small bedforms on the backs of larger bedforms, aggradation rate, and changes in sediment supply. If the height of a bedform increases as it migrates downstream, so does the amount of OFG. Changes in the character of OFG on the lee‐side of unit bars depend on grain‐size sorting in the superimposed bedforms (dunes and bedload sheets). Thick deposits of cross‐stratified OFG require high bedforms (dunes, unit bars) and large amounts of aggradation. These conditions might be expected to occur during high falling stages in the deeper parts of river channels adjacent to compound‐bar tails and downstream of confluence scours. Increase in the amount of sand supplied relative to gravel reduces the development of OFG. Such increases in sand supply may be related to falling flow stage and/or upstream erosion of sandy deposits.     

A quantitative, three-dimensional depositional model of gravelly braided rivers

A quantitative, three‐dimensional depositional model of gravelly, braided rivers has been developed based largely on the deposits of the Sagavanirktok River in northern Alaska. These deposits were described using cores, wireline logs, trenches and ground‐penetrating radar profiles. The origin of the deposits was inferred from observations of: (1) channel and bar formation and migration and channel filling, interpreted from aerial photographs; (2) water flow during floods; and (3) the topography and texture of the river bed at low‐flow stage. This depositional model quantitatively represents the geometry of the different scales of strataset, the spatial relationships among them and their sediment texture distribution. Porosity and permeability in the model are related to sediment texture. The geometry of a particular type and scale of strataset is related to the geometry and migration of the bedform type (e.g. ripples, dunes, bedload sheets, bars) associated with deposition of the strataset. In particular, the length‐to‐thickness ratio of stratasets is similar to the wavelength‐to‐height ratio of associated bedforms. Furthermore, the wavelength and height of bedforms such as dunes and bars are related to channel depth and width. Therefore, the thickness of a particular scale of strataset (i.e. medium‐scale cross‐sets and large‐scale sets of inclined strata) will vary with river dimensions. These relationships between the dimensions of stratasets, bedforms and channels mean that this depositional model can be applied to other gravelly fluvial deposits. The depositional model can be used to interpret the origin of ancient gravelly fluvial deposits and to aid in the characterization of gravelly fluvial aquifers and hydrocarbon reservoirs.     

Morphodynamics and sedimentary structures of bedforms under supercritical‐flow conditions: New insights from flume experiments

Supercritical‐flow phenomena are fairly common in modern sedimentary environments, yet their recognition and analysis remain difficult in the stratigraphic record. This fact is commonly ascribed to the poor preservation potential of deposits from high‐energy supercritical flows. However, the number of flume data sets on supercritical‐flow dynamics and sedimentary structures is very limited in comparison with available data for subcritical flows, which hampers the recognition and interpretation of such deposits. The results of systematic flume experiments spanning a broad range of supercritical‐flow bedforms (antidunes, chutes‐and‐pools and cyclic steps) developed in mobile sand beds of variable grain sizes are presented. Flow character and related bedform patterns are constrained through time‐series measurements of bed configurations, flow depths, flow velocities and Froude numbers. The results allow the refinement and extension of some widely used bedform stability diagrams in the supercritical‐flow domain, clarifying in particular the morphodynamic relations between antidunes and cyclic steps. The onset of antidunes is controlled by flows exceeding a threshold Froude number. The transition from antidunes to cyclic steps in fine to medium‐grained sand occurs at a threshold mobility parameter. Sedimentary structures associated with supercritical bedforms developed under variable aggradation rates are revealed by means of combining flume results and synthetic stratigraphy. The sedimentary structures are compared with examples from field and other flume studies. Aggradation rate is seen to exert an important control on the geometry of supercritical‐flow structures and should be considered when identifying supercritical bedforms in the sedimentary record.     

An empirical model of subcritical bedform migration

The ability to predict bedform migration in rivers is critical for estimating bed material load, yet there is no relation for predicting bedform migration (downstream translation) that covers the full range of conditions under which subcritical bedforms develop. Here, the relation between bedform migration rates and transport stage is explored using a field and several flume data sets. Transport stage is defined as the non‐dimensional Shields stress divided by its value at the threshold for sediment entrainment. Statistically significant positive correlations between both ripple and dune migration rates and transport stage are found. Stratification of the data by the flow depth to grain‐size ratio improved the amount of variability in migration rates that was explained by transport stage to ca 70%. As transport stage increases for a given depth to grain‐size ratio, migration rates increase. For a given transport stage, the migration rate increases as the flow depth to grain‐size ratio gets smaller. In coarser sediment, bedforms move faster than in finer sediment at the same transport stage. Normalization of dune migration rates by the settling velocity of bed sediment partially collapses the data. Given the large amount of variability that arises from combining data sets from different sources, using different equipment, the partial collapse is remarkable and warrants further testing in the laboratory and field.     

A Surface Model for Aeolian Dune Topography

A surface model for aeolian bedform topography is adapted from a surface model of subaqueous bedform topography. The aeolian bedform surface model is developed using a uniform grid with a cell-centered finite volume approximation of the sediment continuity equation. The resulting modeling framework approximates the dynamic motions of aeolian bedform topography driven by bedform field boundary conditions. The numerical model is applied to simulate bedforms growing from unimodal and bimodal transport regimes from both a fixed elevation (sediment source area) and within a domain with fully periodic boundary conditions. The rates at which modeled aeolian bedforms grow and morphologically mature are sensitive to the chosen boundary conditions. Video files of model simulations and source code for the presented aeolian bedform surface modeling framework are available in supplemental materials. The aeolian bedform surface model code is malleable and readily modified for exploratory study of dynamic bedform topography that inherits morphological traits from aeolian bedform field boundary conditions.     

Bedforms produced by fine, cohesionless, granular and flakey sediments under subcritical water flows

Experiments have been conducted in a 10 m long laboratory flume to investigate the bedforms which develop from fine, cohesionless sediment beds. Two grades of near uniformly sized silica grains (of median nominal diameters 15 and 66 μm) and six grades of micaceous flakes (ranging in median nominal diameter from 15.5 to 76 μm) were used. A steady subcritical water discharge, which was increased in steps after several hours, was applied to a flat bed of each grade. The developing bedform sequence for fine granular beds was identified as many small-sized primary ripples, isolated primary, transverse primary, secondary ripples and then possibly dunes; this development was almost the same as that observed for coarser grains. The sequence for fine flake beds differed from grains. Only the single bedform type of parting lineations was observed; with increased discharge, the lineations began to oscillate and eventually enter into fluid suspension. The low discharge parallel lineations were thought to be generated by ‘streaks’ or lanes of transversely alternate high and low velocity fluid which have been reported to exist in the viscous sub-layer of a turbulent-smooth boundary, whilst the higher discharge wandering lineations were attributed to low velocity streak ‘bursts’.     

Pyroclastic dune bedforms: macroscale structures and lateral variations. Examples from the 2006 pyroclastic currents at Tungurahua (Ecuador)

Pyroclastic currents are catastrophic flows of gas and particles triggered by explosive volcanic eruptions. For much of their dynamics, they behave as particulate density currents and share similarities with turbidity currents. Pyroclastic currents occasionally deposit dune bedforms with peculiar lamination patterns, from what is thought to represent the dilute low concentration and fluid‐turbulence supported end member of the pyroclastic currents. This article presents a high resolution dataset of sediment plates (lacquer peels) with several closely spaced lateral profiles representing sections through single pyroclastic bedforms from the August 2006 eruption of Tungurahua (Ecuador). Most of the sedimentary features contain backset bedding and preferential stoss‐face deposition. From the ripple scale (a few centimetres) to the largest dune bedform scale (several metres in length), similar patterns of erosive‐based backset beds are evidenced. Recurrent trains of sub‐vertical truncations on the stoss side of structures reshape and steepen the bedforms. In contrast, sporadic coarse‐grained lenses and lensoidal layers flatten bedforms by filling troughs. The coarsest (clasts up to 10 cm), least sorted and massive structures still exhibit lineation patterns that follow the general backset bedding trend. The stratal architecture exhibits strong lateral variations within tens of centimetres, with very local truncations both in flow‐perpendicular and flow‐parallel directions. This study infers that the sedimentary patterns of bedforms result from four formation mechanisms: (i) differential draping; (ii) slope‐influenced saltation; (iii) truncative bursts; and (iv) granular‐based events. Whereas most of the literature makes a straightforward link between backset bedding and Froude‐supercritical flows, this interpretation is reconsidered here. Indeed, features that would be diagnostic of subcritical dunes, antidunes and ‘chute and pools’ can be found on the same horizon and in a single bedform, only laterally separated by short distances (tens of centimetres). These data stress the influence of the pulsating and highly turbulent nature of the currents and the possible role of coherent flow structures such as Görtler vortices. Backset bedding is interpreted here as a consequence of a very high sedimentation environment of weak and waning currents that interact with the pre‐existing morphology. Quantification of near‐bed flow velocities is made via comparison with wind tunnel experiments. It is estimated that shear velocities of ca 0·30 m.s^?1 (equivalent to pure wind velocity of 6 to 8 m.s^?1 at 10 cm above the bed) could emplace the constructive bedsets, whereas the truncative phases would result from bursts with impacting wind velocities of at least 30 to 40 m.s^?1.     

Sedimentary architecture of an ancient linear megadune (Barremian,Neuquén Basin): Insights into the long‐term development and evolution of aeolian linear bedforms

Linear aeolian bedforms are the most abundant bedform type in Earth's dune fields, and are very common in the Solar System. Despite their abundance, the long‐term development of these bedforms and its impact upon the resulting sedimentary architecture in the geological record is still poorly understood. The aim of this paper is to study the exposed record of an ancient linear megadune in order to discuss its development and the factors that impact the sedimentary architecture of aeolian linear bedforms. The outcrops of the ancient Troncoso Sand Sea (Barremian, Neuquén Basin, Argentina) provide a unique opportunity to study a preserved megadune record with an external body geometry that confirms its linear morphology. Architectural analysis reveals significant differences in cross‐stratified set bodies and bounding surfaces’ features and allows for the identification of three architectural complexes within the bedform's record. Analysis of deterministic models, sedimentary body relative chronology and distribution suggest that these architectural complexes result from distinctive phases in bedform development. It also clearly shows that construction of the megadune was achieved by expansion from a core, and that its development was characterized by sustained growth and strong longitudinal dynamics, without net accumulation. This study indicates how sustained bedform growth, rather than accretion, can be a critical factor conditioning linear bedform architecture towards a more ‘classic’ (bimodal bounding surface and cross‐bedding dip directions) concentric sedimentary architecture style. Furthermore, this research reveals how this style of architecture could only be relatively common in the geological record when related to bedform topography preservation.