An empirical model for the development and equilibrium morphology of current ripples in fine sand

A flume study on the development and equilibrium morphology of current ripples in fine sand (D₅₀ = 0·238 mm) was performed to extend an empirical model for current ripple stability in 0·095 mm sand to larger grain sizes. The results of the flume experiments agree with the very fine sand model that current ripple development from a flat bed is largely independent of flow velocity. At all flow velocities, ripples evolve from incipient, through straight, sinuous and non-equilibrium linguoid, to equilibrium linguoid plan morphology. The time needed to achieve an equilibrium linguoid plan form is related to an inverse power of flow velocity and ranges from several minutes to more than hundreds of hours. Average equilibrium height and length are 17·0 mm and 141·1 mm respectively. These values are about 20% larger than in very fine sand. Equilibrium ripple height and length are proportional to flow velocity near the stability field of dunes. In the same velocity range, a characteristic grouping of ripples with smaller ripples migrating on the upstream face of larger ripples was observed. Bed-form development shows a conspicuous two-phase behaviour at flow velocities < 0·49 m s^?1. In the first phase of development, ripple height and length increase along an exponential path, similar to that at higher flow velocities, thus reaching intermediate equilibrium values of 14·8 mm and 124·5 mm respectively. After some time, however, a second phase commences, that involves a rapid increase in bed-form size to the typical equilibrium values for 0·238 mm sand. A comparison with literature data shows that the results obtained for 0·238 mm sand agree reasonably well with other flume studies at similar grain size. Yet considerable variability in the relationships between ripple dimensions and flow strength ensues from, among others, underestimation of equilibrium time, shallow flow depths and differences in sediment texture.     

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

An 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.     

Time as an independent variable for current ripples developing towards linguoid equilibrium morphology

Flume experiments show that current ripples on very fine sand surfaces always develop towards a linguoid shape with constant height and wavelength provided that sufficient time is allowed for their formation. Straight and sinuous current ripples only reflect intermediate stages in ripple development and may be regarded as non-equilibrium bedforms. The time period which current ripples require to reach linguoid equilibrium morphology is related to an inverse power of flow velocity. In the transitional stage from current ripples to upper stage plane bed (i.e. washed-out ripple stage) only the equilibrium wavelength remains constant, whereas equilibrium height rapidly decreases to zero. Our observations imply that bed-roughness parameters in sediment transport calculations can be simplified when equilibrium conditions are attained, and that inferences about flow energy from the dimensions of current ripples in very fine sand need to be regarded with caution.     

浅水非线性波作用下沙纹床面底层流动特性试验研究

通过水槽试验研究浅水非线性波作用下沙纹床面底层流动特性,利用CCD图像技术观测分析非对称沙纹的形成和演化规律。利用声学多普勒测速仪(ADV)测量非对称沙纹底床上的流场,得到了不同波高、周期、水深条件下的沙纹峰顶和谷底断面的瞬时速度。试验结果分析表明,浅水非线性波作用下床面上形成非对称沙纹,其近底流速具有较强紊动特性,随着距床面距离的增大紊动强度逐渐减弱。在水流方向改变时,沙纹背部具有明显漩涡运动。沙纹背后形成的漩涡能起到维持沙纹的作用。浅水非线性波作用下,沙纹的形成原因主要是床面泥沙颗粒在非对称流动和床面近壁粘性底层中漩涡结构动力作用下,作受迫摆动、推移所致。     

Initiation of ripple marks under oscillating water

It was observed that a monolayer of glass beads which were scattered sparsely on a rigid plane floor grew into regular waves of particles under oscillatory water flow. The relative displacement of two nearby particles due to viscous fluid forces seems to be responsible for the initiation of these particle waves. It was also observed that the similar particle waves were formed on the initially flat surface of a thick sand bed and subsequently developed into oscillatory sand ripples of a common type. On the basis of these observations, it is suggested that the particle waves may be the basic cause of the initiation of general ripple marks under oscillatory flow.     

Depositional processes,bedform development and hybrid bed formation in rapidly decelerated cohesive (mud–sand) sediment flows

Flows with high suspended sediment concentrations are common in many sedimentary environments, and their flow properties may show a transitional behaviour between fully turbulent and quasi‐laminar plug flows. The characteristics of these transitional flows are known to be a function of both clay concentration and type, as well as the applied fluid stress, but so far the interaction of these transitional flows with a loose sediment bed has received little attention. Information on this type of interaction is essential for the recognition and prediction of sedimentary structures formed by cohesive transitional flows in, for example, fluvial, estuarine and deep‐marine deposits. This paper investigates the behaviour of rapidly decelerated to steady flows that contain a mixture of sand, silt and clay, and explores the effect of different clay (kaolin) concentrations on the dynamics of flow over a mobile bed, and the bedforms and stratification produced. Experiments were conducted in a recirculating slurry flume capable of transporting high clay concentrations. Ultrasonic Doppler velocity profiling was used to measure the flow velocity within these concentrated suspension flows. The development of current ripples under decelerated flows of differing kaolin concentration was documented and evolution of their height, wavelength and migration rate quantified. This work confirms past work over smooth, fixed beds which showed that, as clay concentration rises, a distinct sequence of flow types is generated: turbulent flow, turbulence‐enhanced transitional flow, lower transitional plug flow, upper transitional plug flow and a quasi‐laminar plug flow. Each of these flow types produces an initial flat bed upon rapid flow deceleration, followed by reworking of these deposits through the development of current ripples during the subsequent steady flow in turbulent flow, turbulence‐enhanced transitional flow and lower transitional plug flow. The initial flat beds are structureless, but have diagnostic textural properties, caused by differential settling of sand, silt and cohesive mud, which forms characteristic bipartite beds that initially consist of sand overlain by silt or clay. As clay concentration in the formative flow increases, ripples first increase in mean height and wavelength under turbulence‐enhanced transitional flow and lower transitional plug‐flow regimes, which is attributed to the additional turbulence generated under these flows that subsequently causes greater lee side erosion. As clay concentration increases further from a lower transitional plug flow, ripples cease to exist under the upper transitional plug flow and quasi‐laminar plug flow conditions investigated herein. This disappearance of ripples appears due to both turbulence suppression at higher clay concentrations, as well as the increasing shear strength of the bed sediment that becomes more difficult to erode as clay concentration increases. The stratification within the ripples formed after rapid deceleration of the transitional flows reflects the availability of sediment from the bipartite bed. The exact nature of the ripple cross‐stratification in these flows is a direct function of the duration of the formative flow and the texture of the initial flat bed, and ripples do not form in cohesive flows with a Reynolds number smaller than ca 12 000. Examples are given of how the unique properties of the current ripples and plane beds, developing below decelerated transitional flows, could aid in the interpretation of depositional processes in modern and ancient sediments. This interpretation includes a new model for hybrid beds that explains their formation in terms of a combination of vertical grain‐size segregation and longitudinal flow transformation.     

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.     

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

Dimensions 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.     

Effect of velocity hiatuses in oscillatory flow on migration and geometry of ripples: wave‐flume experiments

A series of wave‐flume experiments was conducted to closely look at characteristics of geometry and migration of wave‐generated ripples, with particular reference to the effect of velocity ‘hiatuses’ during which the near‐bed flow velocity becomes much smaller than the threshold of sediment movement. Three types of wave patterns were generated: two types for simulating waves with intervening velocity hiatuses; and regular waves for comparison purposes. In the former two types, two different wavelengths of water waves were generated alternately in the course of a wave test: the wave with a longer wavelength was set large enough to mobilize the bottom sediment, whereas the wave with a shorter wavelength was set too small to mobilize the sediment. The former two types were designed to be different in sequence of convexity and concavity of wave patterns. The sequence with the convex–concave longer wave and successive convex–concave shorter wave was described as a ‘zero‐up‐crossing’ wave pattern, and the inverse sequence was described as a ‘zero‐down‐crossing’ wave pattern. The ripples developed under oscillatory flow with intervening hiatuses manifested the following characteristics in geometry and migration. (i) The morphological characteristics of ripples, namely wavelength, height and the ripple steepness, are unaffected by the intervening hiatuses of velocity. (ii) The directions of ripple migration under the zero‐up‐crossing and zero‐down‐crossing wave patterns corresponded well with the directions of the flow immediately before onset of the hiatuses. (iii) The observation of sand particle movement on the ripple surface indicated that, under the zero‐up‐crossing waves, the velocity hiatus prevents the entrained sediment cloud from being thrown onshore, and thus the sediment grains thrown onshore are fewer than those thrown offshore. As a result of the sediment movement over one wave‐cycle, the net sediment transport is directed offshore under the zero‐up‐crossing wave pattern. (iv) The velocity of ripple migration was highly correlated with acceleration skewness. Under most of the zero‐up‐crossing (zero‐down‐crossing) wave patterns, flow acceleration skewed negative (positive) and ripples migrated offshore (onshore).     

Features of cross-stratified units due to random and other changes in bed forms

Because cross-stratified units depend upon the movement of bed forms, any change in the shape, size and direction of travel of the forms is reflected in the geometry of the units, notably in their relative length, breadth and thickness, mode of termination upstream and downstream, and internal discontinuities. Most models of cross-stratification so far published are unsatisfactory because they ignore the fact that real bed forms are subject to change. The changes are thought to occur at two levels of detail independently. Those at the coarser level depend on the essential non-uniformity, unsteadiness and multi-directionality of natural flows, when assessed on a suitably large scale. At the finer level, change is related to the random behaviour of individual bed forms as they interact with the adjacent flow, and it proceeds even when the flow is an equilibrium one overall. Flume experiments on current ripples show that many features of cross-stratified units can be explained by the random behaviour of bed forms. The finite streamwise length of such units, and their upstream and downstream erosional termination, is governed by the life-span (finite) of individual ripples and by the extent of net deposition on the bed. Internal discontinuities, closely resembling features described as reactivation structures, were also found to depend on the relative motion of ripples, no change of flow discharge and stage being involved. The degree of relative motion in the ripple assemblages was substantial, as measured by the fluctuating component of the ripple celerity.     

Zur Geometrie von Wellenrippeln in Sanden unterschiedlicher Korngröße

Field research of wave generated bed forms within complex sediment size distributions near the inlet of a tidal lagoon at the northern coast of Brittany has stimulated an experimental study in a laboratory wave tank. Several sediment mixtures, most of them with bimodal grain size distributions, were exposed to different monochromatic shallow water waves. The observations and measurements included the dynamics of the water waves and the generation, shape, and size of oscillatory bed forms. The experiments confirm the known relationship between grain size and ripple size. In addition it is shown that coarse sand, added to a preexisting fine bed material leads to an increasing asymmetry of ripples. There is some suggestion that the variability of ripple heights is reduced by higher contents of coarse sand. Bimodal sediment size distributions obviously do not cause unusual geometry of ripples — at least within the range of the experimental tests. The different sand size modes move together in one phase, forming structures with more or less homogeniously distributed bed material. Differentiation of sediment sorting does of course occur, but this is in the range of the whole test section. Finally the experiments allowed to test the validity of some wave formulas. The own experiments are compared with some results from field and laboratory studies of other authors.     

Time-sequence observations of wave-formed sand ripples on an ocean shoreface

Analysis of an 18-day time-lapse film record of shoreface ripple development, with concurrent measurements of near-bottom flow and surface waves, provides new insight on equilibrium bedform conditions, adjustment of ripple planform to variable hydrodynamics, and ripple migration behaviour. The study was conducted in approximately 10 m water depth, 1 km off Martinique Beach on the Atlantic coast of Nova Scotia (Canada), under low-energy summer wave conditions. Significant wave-height and peak period during the study averaged 0–7 m and 8 s, respectively, with extremes up to 1–7 m and 11 s during passage of three weak weather disturbances. Six mutually exclusive ripple types have been defined: (1) short-wavelength regular ripples; (2) variable bifurcated ripples; (3) variable terminated ripples; (4) short-crested ripples; (5) long-wavelength regular ripples; and (6) chaotic ripples. Ripple wavelength ranged from 0–07 m to 0–24 m and displayed a strong Reynolds number dependence. Together with other published field data, the results suggest a lower limit of γ=0–06 m for the wavelength of wave ripples in ocean shoreface environments. Ripple orientation ranged through 38° and responded rapidly to changes in wave approach direction, but did not conform to the orientation of the adjacent shoreline. Ripples were observed to migrate both on- and off-shore (with and against the wave advance direction) at rates up to ±0–1 m h^-1, associated with net flows other than wave-induced onshore asymmetry and mass transport. Migration (mainly of ripple types 1 and 2) occurred during the peak of storm events, but showed no obvious correlation with measured near-bottom flow magnitude or direction. Ripple behaviour demonstrates equilibrium with prevailing dynamic conditions when straight-crested rippie types 1 and 5 are present. Disequilibrium in orientation or dimensions is expressed by increasing sinuosity, bifurcation and crest termination in types 2,3,4 and 6.     

Scour holes and ripples occur below the hydraulic smooth to rough transition of movable beds

Scour holes often form in shallow flows over sand on the beach and in morphodynamic scale experiments of river reaches, deltas and estuarine landscapes. The scour holes are on average 2 cm deep and 5 cm long, regardless of the flow depth and appear to occur under similar conditions as current ripples: at low boundary Reynolds numbers, in fine sand and under relatively low sediment mobility. In landscape experiments, where the flow is only about 1 cm deep, such scours may be unrealistically large and have unnatural effects on channel formation, bar pattern and stratigraphy. This study tests the hypotheses that both scours and ripples occur in the same conditions and that the roughness added by sediment saltation explains the difference between the ripple–dune transition and the clear‐water hydraulic smooth to rough transition. About 500 experiments are presented with a range of sediment types, sediment mobility and obstructions to provoke scour holes, or removal thereof to assess scour hole persistence. Most experiments confirm that ripples and scour holes both form in the ripple stability field in two different bedform stability diagrams. The experiments also show that scours can be provoked by perturbations even below generalized sediment motion. Moreover, the hydraulic smooth to rough transition modified with saltation roughness depending on sediment mobility was similar in magnitude and in slope to ripple–dune transitions. Given uncertainties in saltation relations, the smooth to rough transitions modified for movable beds are empirically equivalent to the ripple–dune transitions. These results are in agreement with the hypothesis that scours form by turbulence caused by localized flow separation under low boundary Reynolds numbers, and do not form under generalized flow separation over coarser particles and intense sediment saltation. Furthermore, this suggests that ripples are a superposition of two independent forms: periodic bedforms occurring in smooth and rough conditions plus aperiodic scours occurring only in hydraulic smooth conditions.     

Ripple formation in combined transdirectional steady and oscillatory flow

Measurements are described of the geometry of ripples formed on beds of sand exposed to a steady current at right angles to an oscillatory flow. Four different sands were studied. The oscillation was produced by an oscillating tray set into the bed of a steady-flow flume. It was observed that straight-crested ripples formed by oscillatory flow would usually develop a ‘serpentine’ form when the superimposed steady current exceeded a certain limit. For amplitudes of the tray velocity U_∞ less than about 0.38 m s^-1 this limit corresponded to U_∞/ū_*c>31, where ū_*c is the shear velocity measured just upstream of the oscillating tray. It is suggested that the serpentine form is caused by the interaction of vortices carried back and forth between adjacent ripples. On this assumption, the wavelength of the serpentine form would be proportional to the product of period of oscillation and near-bed steady current velocity. The present measurements appear to support this hypothesis although there is also evidence that the wavelength is influenced by preferred spacing patterns between vortices. The measurements also show the ratio of the amplitude of the serpentine form to its wavelength to be approximately constant. Empirical relationships are derived relating ripple geometry to flow and sediment properties. It is observed that the influence of Reynolds number and sediment properties on the geometry is very weak. It is suggested that this is typical of ripples formed with relatively low sediment transport rates. It is also found that, under the present experimental conditions, the ripple spacing in the direction of oscillation is almost independent of the magnitude of the steady current and in close agreement with the wavelengths previously measured in an oscillating water tunnel. This suggests that the additional inertia effects associated with oscillating tray rigs were not sufficient to affect bed geometry under the present test conditions.     

Flows above oscillatory ripples

The flows above ripples of glass beads and ripple models have been visualized in an oscillatory water tunnel. Some ripples were observed to form without flow separation. Two types of vortices, the standing vortices without flow separation and the separation vortices have been observed, and their similarity is discussed.     

Lagoon–tidal flat sedimentation in an epeiric sea: Proterozoic Bhander Group,Son Valley,India

The Bhander Group, the uppermost stratigraphic unit of the Proterozoic Vindhyan Supergroup in Son Valley, exhibits in its upper part a 550 m thick, muddy siliciclastic succession characterized by features indicative of deposition in a wave‐affected coastal, lagoon–tidal flat environment suffering repeated submergence and emergence. The basic architecture of the deposit is alternation of centimetre‐ to decimetre‐thick sheet‐like interbeds of coarser clastics (mainly sandstone) and decimetre‐thick mudstones. The coarser interlayers are dominated by a variety of ripple‐formed laminations. The preserved ripple forms on bed‐top surfaces and their internal lamination style suggest both oscillatory and combined flows for their formation. Interference, superimposed, ladder‐back and flat‐topped ripples are also common. Synsedimentary cracks, wrinkle marks, features resembling rain prints and adhesion structures occur in profusion on bed‐top surfaces. Salt pseudomorphs are also present at the bases of beds. The mudstone intervals represent suspension settlement and show partings with interfaces characterized by synsedimentary cracks. It is inferred that the sediments were deposited on a coastal plain characterized by a peritidal (supratidal–intertidal) flat and evaporative lagoon suffering repeated submergence and emergence due to storm‐induced coastal setup and setdown in addition to tidal fluctuations. The 550 m thick coastal flat succession is surprisingly devoid of any barrier bar deposits and also lacks shoreface and shelfal strata. The large areal extent of the coastal flat succession (c. 100,000 km²) and its great thickness indicate an extremely low‐gradient epeiric basin characterized by an extensive coastal flat sheltered from the deeper marine domain. It is inferred that the Bhander coastal flat was protected from the open sea by the Bundelkhand basement arch to the north of the Vindhyan basin, instead of barrier bars. Such a setting favoured accumulation of a high proportion of terrigenous mud in the coastal plain, in contrast to many described examples from the Proterozoic. Copyright © 2001 John Wiley & Sons, Ltd.     

Flow and turbulence structure across the ripple–dune transition: an experiment under mobile bed conditions

Current knowledge of flow and turbulent processes acting across the sand bed continuum is still unable to unequivocally explain the mechanism(s) by which ripples become dunes. Understanding has been improved by comparative high-resolution studies undertaken over fixed bedforms at different stages in the continuum. However, these studies both ignore the role of mobile sediment and do not examine flow structure during the actual transition from ripples to dunes. The aims of the paper are: (i) to describe flow and turbulence characteristics acting above mobile bedforms at several stages across the transition; and (ii) to compare these data with those arising from experiments over fixed ripples and dunes. Laboratory experiments are presented that examine the turbulence structure across seven distinct stages of the transition from ripples to dunes. Single-point acoustic Doppler velocimeter sampling at three flow heights above a developing mobile boundary was undertaken. Time-averaged statistics and the instantaneous quadrant record reveal distinct changes in flow structure either side of the change from ripples to dunes. Initially, shear-related, high-frequency vortex shedding dominates turbulence production. This increases until two-dimensional (2D) dunes have formed. Thereafter, turbulence intensities and Reynolds stress decline and three-dimensional dunes exhibit values found over 2D ripples. This is the result of shear layer dampening which occurs when the topographically-accelerated downstream velocity increases at a faster rate than flow depth. Activity at reattachment increases due to high velocity fluid imparting high mass and momentum transfer at the bed and/or wake flapping. Suspended sediment may also play a role in turbulence dampening and bed erosion. Ejections dominate over sweeps in terms of event frequency but not magnitude. Strong relationships between inward interactions and sweeps, and ejections and outward interactions, suggest that mass and momentum exchanges are dependent upon activity in all four quadrants. The results contradict the notion present in most physical models that larger bedforms exhibit most shear layer activity. Consequently an improved model for the ripple–dune transition is proposed.     

Undular hydraulic jumps and the formation of backlash ripples on beaches

Field observations are made of the formation of backwash ripples on the beach face, formed by undular hydraulic jumps generated by backwash down the beach face colliding with wave bores. Measured ripple wavelengths range from set averages of 48 to 70 cm. Within a particular set of ripples the spacing tends to decrease in the offshore direction. These observations are compared with laboratory experiments where undular jumps are generated in a flume, and with a computer simulation model which calculates both the flow within an undular hydraulic jump and the resulting sediment transport which gives rise to the backwash ripples. The computer model involves a numerical solution of the Bousssinesq equations which govern the fluid flow, and sediment transport equations which relate the sand transport rate to the local mean flow velocity. The model permits a study of the detailed time-history of the undular jump development and the formation of the backwash ripples and shows good agreement with the field observations of backwash ripples, predicting an offshore decrease in their spacings. The laboratory experiments showed a similar result so long as the Froude number of the supercritical flow before the jump occurs is small (c. 1–4). Small differences between the computer model and experiments arose principally from the neglect of internal friction and surface tension in the model.