On interfacial instability as a cause of transverse subcritical bed forms
TL;DR: In this paper, the authors show that transverse waveforms on sand beds sheared by unidirectional currents can be initiated as an interfacial hydrodynamic instability of Kelvin-Helmholtz type when the current is sufficiently vigorous to produce general sediment movement, leading to the organization of the transport system into laterally extended, discrete bed forms.
Abstract: [1] Recent experimental results suggest there are at least two distinct bed form initiation processes. Bed forms may be generated from local bed defects that are propagated down and across stream by flow separation processes when sediment transport is patchy and sporadic. Alternatively, bed form development may occur over the whole bed at once when sediment transport is general and widespread. Herein, we critically test a simple model for this latter bed form initiation mode that was originally presented by H.-K. Liu in 1957 but not tested because of the complex nature of the measurements required. The theory is based on the idea that a moving sand bed might be likened to a dense fluid and that a hydrodynamic instability develops at the interface between the sediment transport layer and the near-bed fluid, leading to the organization of the transport system into laterally extended, discrete bed forms. Our predicted initial bed form lengths are within 10% of the lengths observed in a series of flume experiments, suggesting that transverse waveforms on sand beds sheared by unidirectional currents can be initiated as an interfacial hydrodynamic instability of Kelvin-Helmholtz type when the current is sufficiently vigorous to produce general sediment movement, that is, to create a sediment transport layer that acts as a pseudofluid with density composed of solid and fluid components.
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TL;DR: In this paper, 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.
Abstract: 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.
241 citations
TL;DR: In this paper, a new extended bed-form phase diagram is presented that summarizes the bedforms generated in mixtures of sand and mud under rapidly decelerated flows and defines the stability fields of a range of bed-forms generated under flows that have modified fluid dynamics owing to the presence of suspended sediment.
Abstract: The use of sedimentary structures as indicators of flow and sediment morphodynamics in ancient sediments lies at the very heart of sedimentology, and allows reconstruction of formative flow conditions generated in a wide range of grain sizes and sedimentary environments. However, the vast majority of past research has documented and detailed the range of bedforms generated in essentially cohesionless sediments that lack the presence of mud within the flow and within the sediment bed itself. Yet most sedimentary environments possess fine-grained sediments and recent work has shown how the presence of this fine sediment may substantially modify the fluid dynamics of such flows. It is increasingly evident that understanding the influence of mud, and the presence of cohesive forces, is essential to permit a fuller interpretation of many modern and ancient sedimentary successions. In this paper, the present state of knowledge on the stability of current- and wave-generated bedforms and their primary current stratification is reviewed, and a new extended bedform phase diagram is presented that summarizes the bedforms generated in mixtures of sand and mud under rapidly decelerated flows. This diagram provides a phase space using the variables of yield strength and grain mobility as the abscissa and ordinate axes, respectively, and defines the stability fields of a range of bedforms generated under flows that have modified fluid dynamics owing to the presence of suspended sediment within the flow. Our results also present unique data on a range of bedforms generated in such flows, whose recognition is essential to help interpret such deposits in the ancient sedimentary record, including the following: (1) heterolithic stratification, comprising alternating laminae or layers of sand and mud; (2) the preservation of low-amplitude bed-waves, large current ripples and bed scours with intrascour composite bedforms; (3) low-angle cross-lamination and long lenses and streaks of sand and mud formed by bed-waves; (4) complex stacking of reverse bedforms, mud layers and low-angle cross-lamination on the upstream face of bed scours; (5) planar bedding comprising stacked mud–sand couplets. Furthermore, the results shown herein demonstrate that flow variability is not required to produce deposits consisting of interbedded sand and muds, and that the nature of flaser, wavy and lenticular bedding ( sensu Reineck & Wunderlich 1968) may also need reconsideration in the deposits of such sediment-laden flows.
132 citations
TL;DR: In this paper, a coupled hydro-morphodynamic numerical model was developed for simulation of stratified, turbulent flow over a mobile sand bed. The model is based on the curvilinear immersed boundary approach of Khosronejad et al. and is applied to simulate sand wave initiation, growth and evolution in a mobile bed laboratory open channel.
Abstract: We develop a coupled hydro-morphodynamic numerical model for carrying out large-eddy simulation of stratified, turbulent flow over a mobile sand bed. The method is based on the curvilinear immersed boundary approach of Khosronejad et al. (Adv. Water Resour., vol. 34, 2011, pp. 829–843). We apply this method to simulate sand wave initiation, growth and evolution in a mobile bed laboratory open channel, which was studied experimentally by Venditti & Church (J. Geophys. Res., vol. 110, 2005, F01009). We show that all the major characteristics of the computed sand waves, from the early cross-hatch and chevron patterns to fully grown three-dimensional bedforms, are in good agreement with the experimental data both qualitatively and quantitatively. Our simulations capture the measured temporal evolution of sand wave amplitude, wavelength and celerity with good accuracy and also yield three-dimensional topologies that are strikingly similar to what was observed in the laboratory. We show that near-bed sweeps are responsible for initiating the instability of the initially flat sand bed. Stratification effects, which arise due to increased concentration of suspended sediment in the flow, also become important at later stages of the bed evolution and need to be taken into account for accurate simulations. As bedforms grow in amplitude and wavelength, they give rise to energetic coherent structures in the form of horseshoe vortices, which transport low-momentum near-bed fluid and suspended sediment away from the bed, giving rise to characteristic ‘boil’ events at the water surface. Flow separation off the bedform crestlines is shown to trap sediment in the lee side of the crestlines, which, coupled with sediment erosion from the accelerating flow over the stoss side, provides the mechanism for continuous bedform migration and crestline rearrangement. The statistical and spectral properties of the computed sand waves are calculated and shown to be similar to what has been observed in nature and previous numerical simulations. Furthermore, and in agreement with recent experimental findings (Singh et al., Water Resour. Res., vol. 46, 2010, pp. 1–10), the spectra of the resolved velocity fluctuations above the bed exhibit a distinct spectral gap whose width increases with distance from the bed. The spectral gap delineates the spectrum of turbulence from the low-frequency range associated with very slowly evolving, albeit energetic, coherent structures induced by the migrating sand waves. Overall the numerical simulations reproduce the laboratory observations with good accuracy and elucidate the physical phenomena governing the interaction between the turbulent flow and the developing mobile bed.
105 citations
TL;DR: The authors reviewed three notable challenges that remain regarding fluvial dunes, namely scale-consistent linking of bed morphologies with turbulent flow fields, the intriguing question of what causes trains of highly-ordered sediment waves to form in beds of river sediments, and how to define the important characteristics of a dune-covered bed, including lengths, shapes, and their statistical nature.
Abstract: Research into fluvial dunes spans disciplines, studies at grain to reach scales, and methodological approaches that include theoretical, experimental, numerical and field investigations. Despite significant research efforts to date, it remains difficult to provide definitive answers to some fundamental questions regarding dunes. This paper reviews three notable challenges that remain regarding fluvial dunes, namely scale-consistent linking of bed morphologies with turbulent flow fields, the intriguing question of what causes trains of highly-ordered sediment waves to form in beds of river sediments, and how to define the important characteristics of a dune-covered bed, including lengths, shapes, and their statistical nature. In each case, the particular challenge is discussed and then recent research and ways forward are presented. Copyright © 2010 John Wiley & Sons, Ltd.
83 citations
TL;DR: In this article, the authors developed a numerical model to investigate the initial stages of erosion and the development of ripples produced by the THV system in the vicinity of a surface-mounted cylindrical pier.
Abstract: [1] Bed load transport and erosion in fine sediment beds are mainly driven by the dynamics of the near-bed turbulent flow. In situations when the shear stress is not sufficiently high to produce significant transport, the presence of an obstacle can initiate erosion and trigger the development of bed forms, which are produced by the emergence of the turbulent horseshoe vortex (THV) system. We develop a numerical model to investigate the initial stages of erosion and the development of ripples produced by the THV system in the vicinity of a surface-mounted cylindrical pier. The flow is simulated using the detached eddy simulation approach, which has been shown to accurately resolve most of the turbulent stresses produced by the THV. To compute the erosion, the Exner equation is coupled to a new bed load transport model that directly incorporates the effect of the instantaneous flow field on sediment transport. The morphodynamic model is integrated simultaneously with the flow equations using an arbitrary Lagrangian-Eulerian method for moving boundaries. Even though the time rate of scour is slower compared to the observations, the computed results exhibit essentially all the dynamics of erosion, including the emergence of ripples reported in the experiments of Dargahi (1990). The bed forms show similar velocities as reported in the experiments and are shown to be statistically similar to ripples measured in laboratory experiments and in nature. To our knowledge, this is the first three-dimensional simulation to capture the ripple dynamics that evolve naturally from the nonlinear interactions between the flow and the bed.
76 citations
References
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TL;DR: The theory of kinematic waves is applied to the problem of estimating how a ‘hump’, or region of increased concentration, will move along a crowded main road, and is applicable principally to traffic behaviour over a long stretch of road.
Abstract: This paper uses the method of kinematic waves, developed in part I, but may be read independently. A functional relationship between flow and concentration for traffic on crowded arterial roads has been postulated for some time, and has experimental backing (§2). From this a theory of the propagation of changes in traffic distribution along these roads may be deduced (§§2, 3). The theory is applied (§4) to the problem of estimating how a ‘hump’, or region of increased concentration, will move along a crowded main road. It is suggested that it will move slightly slower than the mean vehicle speed, and that vehicles passing through it will have to reduce speed rather suddenly (at a ‘shock wave’) on entering it, but can increase speed again only very gradually as they leave it. The hump gradually spreads out along the road, and the time scale of this process is estimated. The behaviour of such a hump on entering a bottleneck, which is too narrow to admit the increased flow, is studied (§5), and methods are obtained for estimating the extent and duration of the resulting hold-up. The theory is applicable principally to traffic behaviour over a long stretch of road, but the paper concludes (§6) with a discussion of its relevance to problems of flow near junctions, including a discussion of the starting flow at a controlled junction. In the introductory sections 1 and 2, we have included some elementary material on the quantitative study of traffic flow for the benefit of scientific readers unfamiliar with the subject.
3,911 citations
TL;DR: In this article, the authors describe the formation of low-speed streaks in the region very near the wall, which interact with the outer portions of the flow through a process of gradual lift-up, then sudden oscillation, bursting, and ejection.
Abstract: Extensive visual and quantitative studies of turbulent boundary layers are described. Visual studies reveal the presence of surprisingly well-organized spatially and temporally dependent motions within the so-called ‘laminar sublayer’. These motions lead to the formation of low-speed streaks in the region very near the wall. The streaks interact with the outer portions of the flow through a process of gradual ‘lift-up’, then sudden oscillation, bursting, and ejection. It is felt that these processes play a dominant role in the production of new turbulence and the transport of turbulence within the boundary layer on smooth walls.Quantitative data are presented providing an association of the observed structure features with the accepted ‘regions’ of the boundary layer in non-dimensional co-ordinates; these data include zero, negative and positive pressure gradients on smooth walls. Instantaneous spanwise velocity profiles for the inner layers are given, and dimensionless correlations for mean streak-spacing and break-up frequency are presented.Tentative mechanisms for formation and break-up of the low-speed streaks are proposed, and other evidence regarding the implications and importance of the streak structure in turbulent boundary layers is reviewed.
2,753 citations
DOI•
01 Sep 1950
Abstract: CONTENTS Page Introduction. 1 Approach to the problem. _ 3 Limitation of the bed-load function _ _ _ 4 The undetermined function 4 The alluvial stream. 5 The sediment mixture 6 Hydraulics of the alluvial channel. 7 The friction formula 7 The friction factor 8 Resistance of the bars 9 The laminar sublayer 10 The transition between hydraulically rough and smooth beds_ 12 The velocity fluctuations 13 Suspension 14 The transportation rate of suspended load 17 Integration of the suspended load. _ 17 Numerical integration of suspended load 19 Limit of suspension. 24 The bed layer 24 Practical calculation of suspended load___ ____ 25 Numerical example 26 Page Bed-load concept 29 Some constants entering the laws of bed-load motion: 31 The bed-load equation 32 The exchange time 33 The exchange probability 34 Determination of the probability V 35 Transition between bed load and. suspended load 38 The necessary graphs 40 Flume tests with sediment mixtures.. 42 Sample calculation of a river reachl 44 Choice of a river reach 45 Description of a river reach_____ 45 Application of procedure to Big Sand Creek, Miss 46 Discussion of calculations 60 Limitations of the method____ 65 Summary. 67 Literature cited 68 Appendix 69 List of symbols. 69 Work charts _ 71
1,677 citations
Book•
01 Jan 1993
TL;DR: A review of open channel turbulence, focusing especially on certain features stemming from the presence of the free surface and the bed of a river, can be found in this paper, where the statistical theory of turbulence and coherent structures in open channel flows and boundary layers are discussed.
Abstract: A review of open channel turbulence, focusing especially on certain features stemming from the presence of the free surface and the bed of a river. Part one presents the statistical theory of turbulence; Part two addresses the coherent structures in open-channel flows and boundary layers.
1,446 citations
TL;DR: In this article, the theory of a distinctive type of wave motion, which arises in any one-dimensional flow problem when there is an approximate functional relation at each point between the flow q and concentration k (quantity passing a given point in unit time) and q remains constant on each kinematic wave.
Abstract: In this paper and in part II, we give the theory of a distinctive type of wave motion, which arises in any one-dimensional flow problem when there is an approximate functional relation at each point between the flow q (quantity passing a given point in unit time) and concentration k (quantity per unit distance). The wave property then follows directly from the equation of continuity satisfied by q and k. In view of this, these waves are described as 'kinematic', as distinct from the classical wave motions, which depend also on Newton's second law of motion and are therefore called 'dynamic'. Kinematic waves travel with the velocity $\partial $q/$\partial $k, and the flow q remains constant on each kinematic wave. Since the velocity of propagation of each wave depends upon the value of q carried by it, successive waves may coalesce to form 'kinematic shock waves'. From the point of view of kinematic wave theory, there is a discontinuous increase in q at a shock, but in reality a shock wave is a relatively narrow region in which (owing to the rapid increase of q) terms neglected by the flow-concentration relation become important. The general properties of kinematic waves and shock waves are discussed in detail in section 1. One example included in section 1 is the interpretation of the group-velocity phenomenon in a dispersive medium as a particular case of the kinematic wave phenomenon. The remainder of part I is devoted to a detailed treatment of flood movement in long rivers, a problem in which kinematic waves play the leading role although dynamic waves (in this case, the long gravity waves) also appear. First (section 2), we consider the variety of factors which can influence the approximate flow-concentration relation, and survey the various formulae which have been used in attempts to describe it. Then follows a more mathematical section (section 3) in which the role of the dynamic waves is clarified. From the full equations of motion for an idealized problem it is shown that at the 'Froude numbers' appropriate to flood waves, the dynamic waves are rapidly attenuated and the main disturbance is carried downstream by the kinematic waves; some account is then given of the behaviour of the flow at higher Froude numbers. Also in section 3, the full equations of motion are used to investigate the structure of the kinematic shock; for this problem, the shock is the 'monoclinal flood wave' which is well known in the literature of this subject. The final sections (section section 4 and 5) contain the application of the theory of kinematic waves to the determination of flood movement. In section 4 it is shown how the waves (including shock waves) travelling downstream from an observation point may be deduced from a knowledge of the variation with time of the flow at the observation point; this section then concludes with a brief account of the effect on the waves of tributaries and run-off. In section 5, the modifications (similar to diffusion effects) which arise due to the slight dependence of the flow-concentration curve on the rate of change of flow or concentration, are described and methods for their inclusion in the theory are given.
1,336 citations