Upper-stage Plane Beds Research Articles

Modelling Regime Changes of Dunes to Upper-Stage Plane Bed in Flumes and in Rivers

In this paper we derive a new morphological model, with an extended version of the sediment transport model for the mean step length (the average distance travelled by sediment particles), in which this mean step length depends on the mean bed shear stress. This model makes the step length increase with increasing flow, in line with previous experimental results. To account for suspension and the large-scale turbulent structures in rivers, the step length also depends explicitly on water depth. This approach enabled modelling of the transition from dunes to the upper-stage plane bed. It was shown that by increasing the step length, the lag between shear stress and bed load transport rate increases, and the dunes eventually become smoother and lower, until finally the dunes wash out. The newly adopted model approach is tested successfully with a synthetic data set from the literature, where plane bed conditions are indeed reached in the model, similar to the results of a more advanced model. It is shown that with increasing discharge, the flow increases, which leads to higher step length and to the washing out of the dunes. Although the present model still overestimates the dune height for river cases, the potential of the model concept for river dune dynamics, including the transition to upper-stage plane bed, is shown. The model results indicate that, if a transition to upper-stage plane bed occurs in a realistic river scenario, a reduction of the water depth of approximately 0.5 m can occur.

Current- and Wave-Generated Bedforms on Mixed Sand–Clay Intertidal Flats: A New Bedform Phase Diagram and Implications for Bed Roughness and Preservation Potential

The effect of bedforms on frictional roughness felt by the overlying flow is crucial to regional modelling of estuaries and coastal seas. Bedforms are also a key marker of palaeoenvironments. Experiments have shown that even modest biotic and abiotic cohesion in sand inhibits bedform formation, modifies bedform size, and slows bedform development, but this has rarely been tested in nature. This study used a comprehensive dataset recorded over a complete spring–neap cycle on an intertidal flat to investigate bedform dynamics controlled by a wide range of wave and current conditions, including wave–current angle and bed cohesion. A detailed picture of different bedform types and their relationship to the flow, be they equilibrium, non-equilibrium, or relict, was captured in a phase diagram that integrates wave-dominated, current-dominated, and combined flow bedforms. This phase diagram incorporates a wider range of flow conditions than previous phase diagrams, including bedforms related to near-orthogonal wave–current angles, e.g. ladderback ripples. Comparison with laboratory-derived phase diagrams indicates that washed-out ripples, lunate interference ripples and upper-stage plane beds replace the subaqueous dune field, which may be a key characteristic of intertidal flats. The field data also provide a means of predicting the bedform dimensions, which can be transferred to other areas and grain sizes. We show that an equation for the prediction of equilibrium bedform size is sufficient to predict the roughness, even though the bedforms are highly variable in character and only in equilibrium with the flow for half the time. Whilst the effect of cohesive clay is limited under active spring conditions, clay does play a role in reducing the bedform dimensions under quiescent neap conditions. We also investigated which combinations of waves, currents, and bed clay contents in the intertidal zone have the highest potential for bedform preservation in the geological record. This shows that combined wave–current bedforms have the lowest and equilibrium current ripples have the highest preservation potential, even in the presence of moderate and storm waves. Hence, the absence of wave ripples and combined-flow bedforms in sedimentary successions cannot be taken as evidence that waves were absent at the time of deposition.

Hydraulic control on the development of megaflood runup deposits

Runup deposits are veneers of alluvium that drape floodway valley side walls above the height of giant bars deposited during megafloods. Given sufficient sediment supply, the highest giant bars, deposited in re-entrants along the flood margins, tend to grow to close to the maximum time-averaged water level of the flood. However, considerable fluctuations in the water level, caused by sediment-charged floodwaters surging over shorter time-scales, are responsible for the higher runup deposits. Here, the theoretical calculations of the expected maximum runup heights are compared with surveyed heights of six runup deposits in the Chuja Valley, Altai, Siberia. The limitations and strengths of the theoretical approach are identified and modified parameters proposed that can be used to provide partial explanation for the differences between theory and observation. Conceptually, surging can be viewed as caused by four interrelated elements: (1) propagation of undular weir flow; (2) macroturbulence; (3) flow separation; and (4) standing, reflection and interference waves. The heights of the observed runup deposits primarily are related to the depth of the flood water above the bar tops and, to a lesser extent, the Froude number, but tend to lie below the maximum surge heights of the modelled flow. Changes in the effective geometry of the flow re-entrant, mediating flow patterns, as water depth increases is likely the cause of mismatch between theory and observation. Runup deposits may also lie at lower elevations than predicted because of sediment supply considerations and the return flow of surges ‘combing’ down deposits. Nonetheless, the difference between observed and predicted runup heights is often only a few tens of metres such that, for deep floods, runup deposits potentially are useful palaeostage indicators. The analysis also indicates that upper-stage plane beds do not dominate bar tops, rather bar top deposition was primarily to lower-stage plane beds, from dense suspensions.

Experimental investigation of low-angle dune morphodynamics

Dunes commonly dominate the bed of sandy rivers and they are of central importance in predicting flow resistance and water levels. In the present study, we show that by using light-weight polystyrene particles as substrate in a laboratory setting, promising morphodynamic similarity is obtained between dunes in shallow flow (flume) and deep flow (field) conditions. In particular, results from our flume experiments show that dune lee-side angles, which are crucial in turbulence production and energy dissipation, better approximate dune lee-side angles observed in natural channels. Furthermore, dune height evolution towards upper stage plane bed observed in the present experimental study, closely follows dune height evolution as observed in world’s large rivers.

On the effect of segregation on intense bimodal bed load

Open-channel two-phase flow above a granular mobile bed is studied experimentally and theoretically. In the two-phase flow, water serves as a carrying liquid for plastic grains transported as collisional contact load in the upper-stage plane bed regime. The investigation evaluates friction- and transport characteristics of the flow under the condition of intense collisional transport of grains and links them with the internal structure of the two-phase flow. The paper focusses on the effect of bimodal solids (mixed two fractions of grains of similar density and different size and shape) on the flow characteristics and internal structure. Hence, experimental results obtained for the bimodal mixture are compared with results for individual grain fractions. The experiments show that the bimodal character of the transported solids affects the layered internal structure of the flow as a result of fraction segregation due primarily to gravity (kinetic) sieving during transport. The segregation also affects the friction- and transport characteristics of intense bed load. In the paper, the effects are described and quantified.

THRESHOLDS OF UPPER-STAGE PLANE BED REGIME FOR INTENSE BED LOAD IN OPEN CHANNEL

Results are discussed of laboratory experiments on criteria determining the transition between the regime of dunes and the upper stage plane bed (UPB) regime and the transition between the UPB regime and the regime of wavy flow. The experiments were carried for 3 fractions of plastic material and two fractions of glass beads in a broad range of flow conditions (different discharges of water and solids and longitudinal bed slopes) in a tilting flume.The experiments reveal that, contrary to expectations, a constant value of the Shields parameter is not an appropriate criterion for the transition between the dune regime and the UPB regime. Instead, the criterion seems to be well represented by a constant value of the longitudinal bed slope. The transition between the UPB regime and the wavy regime is found at a constant value of the densimetric Froude number. Relatively high values of Froude number at the threshold are due primarily to the presence of the collisional transport layer which protects the bed from an influence of undulating water surface.

A New Phase Diagram for Combined-Flow Bedforms

Abstract Combined-flows, which involve a combination of unidirectional and wave-induced oscillatory flow, are omnipresent in coastal and lacustrine environments. Despite the extensive progress made in understanding the bedforms generated by such flows in past studies, there still remains a wide range of unexplored flow conditions where the bedform geometry, and hence consequent sedimentary structures, have not been explored, especially for strong unidirectional flows (greater than 0.30 m s−1) and intermediate oscillation periods (between 2 and 8 seconds). To address this gap in our knowledge, the stability of bedforms in a 0.25 mm diameter sand bed was studied under pure unidirectional, pure-oscillatory, and combined-flow conditions with oscillation periods of 4, 5, and 6 s. The maximum orbital velocity (Uo) was varied from 0.00 to 1.00 m s−1 while the unidirectional component (Uu) was varied from 0 to 0.50 m s−1. The experimental data collected under unidirectional flows stronger than 0.30 m s−1 allows expansion of current understanding of the bed configurations for current-dominated combined-flows, where the phase boundary between combined-flow bedforms and current ripples was uncertain. Under these flow conditions, ten distinctive bedform states can be recognized: no motion (NM), 2D symmetric ripples (2D SR), 3D symmetric ripples (3D SR), 3D symmetric dunes (3D SR), 3D asymmetric ripples (3D AR), 3D quasi-asymmetric ripples (3D QAR), 3D asymmetric dunes (3D AD), 3D current ripples (3D CR), 3D current dunes (3D CD), and upper-stage plane bed (USPB). Each of these bedform stages is described, quantified, and characterized in dimensional phase diagrams. A complete re-evaluation of the nomenclature for combined-flow bedforms is proposed, which includes their planform and cross-sectional geometry, in order to better represent the bed morphologies. This new nomenclature also unifies past research on bedforms in both unidirectional and oscillatory flows and thus presents a new synopsis of bedforms developed under such flows. One of the main changes proposed that allows integration with the nomenclature used in unidirectional flows is the reclassification of large ripples as dunes. Furthermore, the introduction of the planform and cross-sectional geometries as properties by which to classify bedforms leads to the definition of a stable phase space for two-dimensional symmetrical ripples and three-dimensional quasi-asymmetrical ripples. These new data and analysis allow proposition of a new unified phase diagram for combined-flows.

Unsteady two-dimensional paleohydraulic reconstruction of extreme floods over the last 4000 yr in Segura River, southeast Spain

Summary Floods in the Almadenes Canyon (Segura River, southeast Spain) have been reconstructed using unsteady two-dimensional shallow water modelling. Slackwater deposits, archaeological age dating and hydraulic modelling allowed us to reconstruct some of the oldest extreme floods reported in Spain. The paleoreconstruction was performed for the first time in three steps: retrodicted flood discharges for the most recent flood (AD 900) were quantified comparing the simulated Shields and Froude numbers with respect to characteristic values for the existence of ripples and upper-stage plane bed at a cave that served as a shelter for humans; ensuing velocity, Shields and Froude maps were then used as a forward predictor allowing the finding of additional paleostage indicators far from the shelter; finally, new PSIs were employed to verify the reliability of the reconstruction. In doing so, better insight into the paleoflood landscape was derived from consideration of the association of bedforms and modelled hydraulic conditions. The present study, assuming a stable geometry of the bedrock canyon during the Late Holocene, extends the estimation of flow discharge magnitudes to ca. 4000 yr BP ranging from 500 m 3 /s in the oldest floods (3700 yr BP) up to 700–1000 m 3 /s in the most recent (AD 900).

Evidence of Bedform Superimposition and Flow Unsteadiness In Unit-Bar Deposits, South Saskatchewan River, Canada

Abstract Unit-bar deposits are ubiquitous components of river-channel deposits and strongly influence their hydrological properties, yet they are not easy to interpret. This paper concerns details of the internal structures of six unit bars from the South Saskatchewan River, Canada, that were investigated using trenches, epoxy resin peels, and 900 MHz ground-penetrating radar (GPR) profiles. The composition of unit bars depends on flow unsteadiness and superimposed bedforms. Flow unsteadiness causes changes in the mean grain size of the sediment in transport, but is expressed primarily as a change in the type and direction of migration of smaller ripple- and dune-scale bedforms superimposed on unit bars. Superimposed bedforms with heights that exceed 25% of the host bedform height reduce their host’s slope and generate inclined sets. Host bedforms with smaller superimposed bedforms form angle-of-repose cross strata with a visible pre-sorting pattern. The relationship between the formative host- and superimposed bedforms and such pre-sorted cross strata can be used to interpret numerous aspects of the three-dimensional geometries of the bedforms. Such detailed interpretations rely on: (i) regularly spaced fine-grained drapes deposited during the passage of troughs of superimposed bedforms, (ii) grain-size sorting patterns generated by sorting within the superimposed bedforms before deposition, (iii) grain-size sorting during deposition by grainfall and intermittent grainflows down the bar lee-slope, and (iv) the presence and nature of low-angle reactivation surfaces. The detailed interpretations revealed that the deposits of dam-related floods were significantly smaller than the deposits of individual unit bars in this study. The unsteady flow and sediment transport conditions are reflected by changes in the structural composition of the unit bars. Reactivation surfaces associated with flow unsteadiness, as opposed to those formed by large superimposed bedforms, were characterized by changes in mean grain size, the buildup of sediment at the base of the bar lee slope, and changes in structures formed by superimposed bedforms. Reactivation surfaces generated by large superimposed bedforms indicate that bedform preservation is likely increased in areas of flow deceleration. The trough deposits of exposed unit bars contained bubble sand, planar laminae due to upper-stage plane beds, and low-angle inclined laminae due to antidunes. These structures indicate that unit-bar troughs can act as ephemeral channels. The composition of the investigated unit bars thus emphasizes the interplay between flow unsteadiness and bed morphology in the formation of sedimentary structures in river channels. Sediment surfaces generate visible GPR reflections where the thickness and contrast in electrical properties of the sediment layers are sufficiently large. Most cross-stratified sets were represented only by reflections from the base of the set, and not by high-angle inclined reflections from the cross strata. The local absence of reflections from cross strata is attributed to the lack of contrast in electrical properties of the well-sorted cross strata and their limited thickness relative to the radar wavelength. In contrast to cross strata, reactivation surfaces formed by large superimposed bedforms and flow unsteadiness were commonly associated with distinct inclined reflections.

Conditions for formation of massive turbiditic sandstones by primary depositional processes

It can be shown from bedform stability diagrams, that each turbidity current, regardless of whether its density is low or high, or whether its history is simple (e.g., surging flow) or complex (e.g., sustained flow), should pass through a final waning phase in which flow conditions are prone to bedform development. Yet, many thick deep-marine sandstones of supposed turbidity-current origin are totally devoid of tractional structures, such as plane-parallel lamination and ripple cross-lamination. TDURE, a mathematical model for the calculation of duration of sediment deposition from high-density turbidity currents (HDTCs), is used to show that the absence of Bouma T b and T c divisions cannot be explained by rapid temporal flow deceleration only. The model calculations imply that discernible tractional structures are formed, even at residence times within the upper-stage plane bed and ripple stability regimes of several seconds and several tens of seconds, respectively. Therefore, other explanations have to be sought for the absence of lamination in turbiditic massive sandstones. These include incompatible grain size, post-depositional removal or obstruction of lamination by bioturbation and liquefaction, and erosion of laminated divisions followed by rapid burial.

Subaqueous gravel dunes

ABSTRACT Gravel dunes are rarely reported owing to comparative rarity of occurrence and generic confusion with antidunes and classes of gravel bars. A compilation of data from the literature for sediments with a median size greater than 2 mm shows that dunes have been developed in the laboratory in median grain sizes up to 28.6 mm. For field conditions, there are data for grain sizes up to 60 mm. Equilibrium and non-equilibrium gravel dunes range in length from less than 0.6 m to greater than 100 m. Heights range from less than 0.1 m to 16 m. Height and length data for the steepest three-dimensional (3-D) gravel dunes are consistent with the H:L function reported by Ashley (1990) for equilibrium dunes developed in sand. For a broad range of dune length, 3-D gravel dunes are steeper than two-dimensional (2-D) dunes, but for L > 100 m and H > 8 m there are too few data to draw any conclusion. Ashley's H:L function does not apply to a broad range of 2-D gravel dunes. A separate well defined function is proposed to describe the H:L relationship for 2-D gravel dunes of maximum steepness. There are few data on the hydrodynamic development of gravel dunes. As a guide, gravel dunes develop for a range of Froude numbers up to 0.75 given that the nondimensional mean bed shear stress () exceeds circa 0.1. Dunes reach their maximum height at = 0.25 and have reduced in height when = 0.3. Froude numbers of 0.84 and above lead to crestal flattening, dune diminution, and eventual replacement by antidunes or upper-stage plane beds. However, owing to lag effects, transitional bedforms have been recorded for Froude numbers near the critical value of 1. The development of gravel dune steepness from lower-stage plane bed through to upper-stage plane bed is well described in only one case, by Dinehart (1992a). Fredsoe's (1975) function for equilibrium dune steepness applies reasonably well to Dinehart's steepest dunes. Allen's (1984) bedform existence field based on and a characteristic grain size of the bed sediment has been extended from 5 mm to include bedstocks as coarse as 33 mm.

Thickness of sets of cross strata and planar strata as a function of formative bed-wave geometry and migration, and aggradation rate

Cross strata and planar strata (formed by the migration of ripples and dunes or low-relief bed waves on upper-stage plane beds, respectively) are the most common internal structures in fluvial sands and sandstones. The thickness of cross sets or planar laminae at a given location is controlled by (1) aggradation rate relative to downstream migration rate of bed waves and (2) the succession of bed waves of varying height passing the location. A quantitative understanding of this relationship is now appearing, based on new theory and experimental studies with ripples, dunes, and upper-stage plane beds. In many cases, the effects of control 1 can be ignored. In such cases, only the largest bed waves in a population form cross sets or planar laminae; the ratio of mean cross-set thickness/mean height of formative bed waves is less than 0.4, and the ratio of mean cross-set thickness/mean height of all bed waves is less than 0.5. A simple quantitative model (a modified form of the Paola-Borgman model) is presented for predicting the height distributions of bed waves (ripples, dunes, low-relief bed waves) from the thickness distributions of cross sets or planar laminae. If the aggradation rate is appreciable, more of the smaller bed waves in a population can form cross sets or planar laminae, and the preservation ratios increase (to 1 in the case of supercritical climbing-ripple cross strata). In this case, it is necessary to determine the angle of climb and length of the bed waves in order to use the model to predict bed-wave height distributions.

Washed-Out Ripples: Their Equilibrium Dimensions, Migration Rate, and Relation to Suspended-Sediment Concentration in Very Fine Sand

The transition from linguoid ripples to upper-stage plane bed under steady, uniform flow conditions in very fine sand (D 50 = 0.108 mm) was studied quantitatively using a flume. The transitional ripples, referred to as washed-out ripples, are symmetrical to slightly asymmetrical bed forms with a convex-up profile and low-angle foresets in the direction of the main flow. The washed-out ripples are stable between 10 degrees C-equivalent depth-averaged flow velocities of 0.75 m/s and 0.91 m/s. With increasing velocity in this range the 10 degrees C-equivalent average equilibrium height of the bed forms decreases from 12 mm to zero, the 10 degrees C-equivalent average equilibrium spacing decreases slightly from 138 mm to 103 mm, and the 10 degrees C-equivalent average migration rate increases from 1 mm/s to 3 mm/s. The changes in morphology and migration rate with increasing flow velocity from linguoid ripples to washed-out ripples result from a spatial shift of the locus of maximum sediment flux from the bed-form crest to the downstream wake region. The shift follows the increasing concentration of sediment particles in a near-bed traction carpet above the sediment surface. With increasing flow velocity the volumetric suspended sediment concentration at 0.01 m above ripple crests increases from 0.9% at the lower boundary to 1.6% at the upper boundary of the washed-out-ripple stability field.

The development of small scale bedforms in tidal environments: an empirical model for unsteady flow and its applications

ABSTRACTDimensions and plan morphology of current ripples are generally considered to vary with flow velocity and grain size. Recently, however, it has been shown that for sand of D50=0.095 and 0.238 mm the equilibrium dimensions are identical at all velocities within the stability field of ripples and that the plan form of equilibrium ripples is linguoid. On this basis, an empirical unsteady flow model has been developed and tested with flume experiments in order to predict ripple development in natural depositional environments. The model includes the development of washed‐out ripples and upper stage plane bed. The unsteady flow model explains the development and preservation of small scale bedforms in various tidal environments more accurately than previous models. Such bedforms can serve, therefore, as indicators of prevailing hydrodynamic conditions.

A flume study on the development and equilibrium morphology of current ripples in very fine sand

ABSTRACTAn empirical model is constructed for the development and equilibrium dimensions of small scale, unidirectional bedforms in sand with a median grain size of 0·095 mm, based on a series of steady flow experiments in a flume. Current ripples always attain a linguoid plan morphology with constant average height (13·1 mm) and wavelength (115·7 mm), provided that sufficient time is allowed for their formation. The development pattern of these ripples on a flat bed is independent of flow velocity, and involves four stages: (1) incipient ripples; (2) straight and sinuous ripples; (3) non‐equilibrium linguoid ripples, and (4) equilibrium linguoid ripples. Straight and sinuous ripples are non‐equilibrium bedforms at all flow velocities. The time needed to reach equilibrium dimensions is related to the inverse power of flow velocity and ranges from several minutes to more than hundreds of hours. At flow velocities where washed ripples are stable, the equilibrium wavelength is similar to that of equilibrium linguoid ripples, but the equilibrium height rapidly decreases from 13·1 mm to zero towards upper stage plane bed conditions.The results of the flume experiments correspond reasonably well with those of previous studies, provided that various complicating factors, such as different experimental methods, different sediment characteristics, shallow flow depths and non‐equilibrium runs, are accounted for.

The morphology and dynamics of low amplitude bedwaves upon upper stage plane beds and the preservation of planar laminae

ABSTRACTExperimental studies of subcritical, unidirectional flow over upper stage plane beds of medium grained sand reveal the ubiquitous presence of low amplitude bedwaves. Flow depth was 0·11 m, mean flow velocities were 0·86–1·0 m s−1, shear velocities were 0·058–0·71 m s−1 and dimensionless shear stresses were 0·56–0·87. Bedwaves are asymmetrical in profile and range from 0·75 to 11 mm in height (mainly 2–6 mm), from 0·7 to 1·3 m in wavelength and have mean celerities of 10 mm s−1. Flow records suggest that the bedwaves are associated with accelerating flow over the bedwave crests and flow which decelerates and diverges laterally over the troughs. High resolution bed profiling during aggradation of the bed combined with subsequent box coring illustrates that these bedwaves are responsible for the planar laminae characteristic of upper stage plane beds. Lamina preservation is dependent upon the mean aggradation rate and the sequence of bedwaves of different height crossing any point; individual laminae are more readily preserved at higher aggradation rates where the possibility of reworking by later bedwaves is reduced. Laminae are recognized by small changes in grain size and commonly a fining upwards at the top of laminae which is generated by fine grained material infiltrating a lower lamina in the leeside of a bedwave.

Flow resistance under conditions of intense gravel transport

A study of flow resistance was undertaken in a channelized reach of the North Fork Toutle River, downstream of Mount St. Helens, Washington. Hydraulic and sediment transport data were collected in flows with velocities up to 3 m/s and shear stresses up to 7 times the critical value needed for bed load transport. Details of the flow structure as revealed in vertical velocity profiles indicate that weak bed load transport over a plane gravel bed has little effect on flow resistance. The plane gravel bed persists up to stresses ∼3 times critical, at which point, irregular bed forms appear. Bed forms greatly increase flow resistance and cause velocity profiles to become distorted. The latter arises as an effect of flows becoming depth‐limited as bed form amplitude increases. At very high rates of bed load transport, an upper stage plane bed appeared. Velocity profiles measured in these flows match the law of the wall closely, with the equivalent roughness being well represented by ks = 3D84 of the bed load. The effects noted here will be important in very large floods or in rivers that are not free to widen, such as those cut into bedrock.

Flow, sediment transport and bedform dynamics over the transition from dunes to upper-stage plane beds: implications for the formation of planar laminae

Flow, sediment transport and bedform dynamics over the transition from dunes to upper-stage plane beds: implications for the formation of planar laminae

Parallel lamination developed from upper-stage plane beds: A model based on the larger coherent structures of the turbulent boundary layer

The larger coherent flow structures of free-surface turbulent currents scale on flow thickness and mean velocity, and are probably upstream-sloping horse-shoe vortices. Coupled to them is a spatial pattern of bed shear stress which, as it moves with the downstream-convected structures, seems capable of generating travelling bed waves on a deformable upper-stage plane sand bed. The wave height is on the order of a few millimetres, but the horizontal dimensions can measure decimetres or metres, increasing with flow thickness. As the bed shear stress is a maximum in the wave troughs, the sand preserved within the body of each wave is expected to be normally graded texturally. The body of each wave constitutes a graded lamina, a portion of which has some chance of permanent preservation under conditions of long-term net deposition. The scale and grading of these hypothetical laminae are consistent with the textural features and dimensions of parallel laminations associated with upper-stage plane beds observed from the field. The model is not applicable to wave swash-backwash laminations, and does not describe the case where slowly moving, steep-faced flat bars generate laminae.