Transverse Bed Research Articles

The effects of transverse bed topography variations in ice‐flow models

A suite of ice‐flow models is subject to a performance test designed to investigate treatment of flow over variable basal topography. Using transfer functions developed by Gudmundsson (2003) and numerical models of various complexity, this study demonstrates that a widely used flowband model has strong limitations associated with its underlying assumptions, and thus should be applied only in specific geometrical settings. Its performance can be significantly improved by using the laterally averaged basal topography instead of centerline topography. In applications where spatial variability of flow fields is important, hybrid ice‐flow models can be a viable alternative to flowband models. In addition, analysis of horizontal distributions of the various ice‐flow characteristics (e.g., surface elevation, velocity, and horizontal stress components) shows that field observations that focus on assessing these parameters only along the centerline of ice flow could be misleading. These results also suggest that such spatial variability needs to be taken into account when designing field surveys of ice flow.

Periodic bedrock ridges on Mars

Evidence for sediment transport and erosion by wind is widespread over the surface of Mars today and was likely a major geomorphic process for much of its geological past. Although Martian surface features resembling aeolian dunes and ripples have been recognized since the Mariner and Viking missions, such features have been interpreted previously as active, indurated, or exhumed sedimentary forms. Here we report evidence based on High Resolution Imaging Science Experiment images that show some megaripple forms are eroded into cohesive substrate rather than being composed of loose granular material or fossilized dunes. Exposure of stratigraphic continuity within layered, cohesive material extending crest to trough through features with mean wavelengths of 18 to 51 m demonstrates the primarily erosional formation of what we term periodic bedrock ridges (PBRs). Hence some surfaces on Mars previously considered to be covered by wind‐deposited material are actually wind‐carved exposures that offer windows into Martian history. PBRs lack the distinctive streamlining associated with wind‐parallel yardangs and comparison of PBR orientation to yardangs, megayardangs, and active sedimentary dunes in the same vicinity confirm that these PBRs formed transverse to prevailing winds. Observed wavelengths of PBRs are comparable to those predicted by a simple model for erosional wavelengths of periodic transverse bed forms owing to the spacing of flow separations within the flow. Recognition of these transverse aeolian erosional forms brings up the question of how widespread Martian PBRs are and how many have been misinterpreted as active or indurated (fossilized) sedimentary dunes.

Processes governing the flow redistribution in sharp river bends

Insight is provided in hydrodynamic processes governing the velocity redistribution in sharp river bends based on simulations of three recent experiments by means of Blanckaert and de Vriend's (2003, 2010) reduced-order nonlinear model without curvature restrictions. This model successfully simulated the flow redistribution and the secondary flow in all three experiments. The results indicate that the flow redistribution is primarily governed by topographic steering, curvature variations and secondary flow, in a broad range of different configurations, including mildly to sharply curved bends, narrow to shallow bends, smooth to rough bends, bends with additional complexities such as horizontal recirculation zones or patches of riverbed vegetation. The relative importance of these three dominant processes is case dependent, and controlled by the parameters Cf−1H/B, R/B and streamwise curvature variations. The first parameter characterizes a river reach, whereas the second and third parameters are characteristics of individual bends. Major differences exist between the hydrodynamic processes in mildly and sharply curved bends. First, velocity redistribution induced by curvature variations is negligible in mildly curved bends, but the dominant process in sharp bends. This result is relevant, because most meander models are based on the assumption of weak-curvature variations. Second, nonlinear hydrodynamic interactions play a dominant role in sharp bends, where mild-curvature models overpredict the secondary flow and in some cases even falsely identify it as the dominant process governing the velocity redistribution, which leads to unsatisfactory flow predictions. The reduction in secondary flow strength provoked by the nonlinear hydrodynamic interactions is accompanied by a reduction in the transverse bed slope, which reduces the effect of topographic steering.

Modelling the equilibrium bed topography of submarine meanders that exhibit reversed secondary flows

Submarine meandering channels formed by turbidity currents are common; however, their location on the ocean floor and their inactive status make it difficult to measure process dynamics and bed morphology. Conceptual models have, therefore, instead been developed by analogy with the well understood mechanics of fluvial bends. However, unlike fluvial currents, in turbidity currents the downstream velocity maximum typically occurs near the bed and recent experimental and theoretical studies suggest that, under certain hydraulic and morphological conditions, this forces the secondary flow to exhibit the reverse sense to that encountered in fluvial bends. Herein the possible morphological implications of a reversal of secondary flow are explored by modelling the force balance on sediment grains moving through either (i) field and laboratory submarine meander bends that are known to exhibit ‘reversed’ secondary flows, or (ii) inactive submarine meander bends where the nature of the secondary flow in the formative turbidity currents can be inferred to be reversed. Exploratory simulations are undertaken for a single hypothetical submarine bend with morphological properties based on nine relic meanders observed on the floor of the Gulf of Alaska. Reconstructions of secondary flow properties within the Gulf of Alaska bends indicate that they likely exhibited reversed secondary flows. Results of the exploratory simulations indicate that, unlike typical fluvial meanders, the transverse bed profile gradient of the hypothetical bend is very low and the point bar is located downstream of the bend apex.

Sediment transport in an active erodible channel bend of Brahmaputra river

Spatial variation of sediment transport in an alluvial sand-bed river bend needs to be understood with its influencing factors such as bank erosion, secondary current formation, land spur and bed-material characteristics. In this study, detailed hydrographic surveys with Acoustic Doppler Current Profiler (ADCP) were conducted at an active erodible river bend to measure suspended load, velocity, bathymetric profile and characteristics of the bed material. Study indicates the presence of multi-thread flow in the channel bend. Local variation of sediment transport is primarily controlled by active bank erosion, land spur and sand bar formation. Vertical distribution of suspended sediment concentration follows a power function with normalized depth. Average bed-material concentration at the reach level is computed from observed sediment profiles, and is compared against various sediment transport functions. Results show that the sediment transport function suggested by Yang gives better predictions for this reach. Transverse bed slopes at critical survey transects were computed from the bathymetric data and evaluated with analytical approaches. Out of three analytical approaches used, Odgaard’s approach estimates the bed slopes fairly close to the observed one. These two functions are suitable in the Brahmaputra river for further morphological studies.

Meander dynamics: A nonlinear model without curvature restrictions for flow in open‐channel bends

Despite the rapid evolution of computational power, simulation of meander dynamics by means of reduced and computationally less expensive models remains practically relevant for investigation of large‐scale and long‐term processes, probabilistic predictions, or rapid assessments. Existing meander models are invariantly based on the assumptions of mild curvature and slow curvature variations and fail to explain processes in the high‐curvature range. This article proposes a nonlinear model for meander hydrodynamics without curvature restrictions. It provides the distribution of the main flow, the magnitude of the secondary flow, the direction of the bed shear stress, and the curvature‐induced additional energy losses. It encompasses existing mild curvature models, remains valid for straight flow, and agrees satisfactorily with experimental data from laboratory experiments under conditions that are more demanding than sharp natural river bends. The proposed model reveals the mechanisms that drive the velocity redistribution in meander bends and their dependence on the river's roughness Cf, the flow depth H, the radius of curvature R, the width B, and bathymetric variations. It identifies Cf−1H/R as the major control parameter for meander hydrodynamics in general and the relative curvature R/B for sharp curvature effects. Both parameters are small in mildly curved bends but O(1) in sharply curved bends, resulting in significant differences in the flow dynamics. Streamwise curvature variations are negligible in mildly curved bends, but they are the major mechanisms for velocity redistribution in sharp bends. Nonlinear feedback between the main and secondary flow also plays a dominant role in sharp bends: it increases energy losses and reduces the secondary flow, the transverse bed slope, and the velocity redistribution.

Topographic steering, flow recirculation, velocity redistribution, and bed topography in sharp meander bends

The bed topography and associated flow field are investigated in a laboratory configuration with parameters that are representative for sharp natural meander bends. Zones of inward mass transport are characterized by a quasi‐linear transverse bed profile, whereas zones of outward mass transport, induced by pronounced curvature variations, are characterized by a quasi‐horizontal shallow point bar at the inside of the bend, a deep pool at the outside, and an increase in overall cross‐sectional area. These quasi‐bilinear bed profiles can be attributed to the curvature‐induced secondary flow that is confined to the pool. Topographic steering, mainly due to mass conservation, concentrates the major part of the discharge over the deepest zones of the bend. But the pattern of depth‐averaged velocities, which is relevant with respect to the development of the bed topography, does not show maximum values over the deepest zones. A term‐by‐term analysis of the depth‐averaged streamwise momentum equation reveals that the water surface gradient is the principal mechanism with respect to flow velocity redistribution, although inertia and secondary flow are also processes of dominant order of magnitude. A required condition for the occurrence of adverse pressure gradients and flow recirculation due to planform curvature variations is established. A different type of flow recirculation, due to a subtle feedback between the flow and the bed topography, occurs over the point bar. The neglect of the influence of vertical velocities impinging on the bed in models for sediment transport is identified as a major shortcoming in the modeling of the morphodynamics of meandering river channels.

Investigation on the Dimensions and Shape of a Submerged Vane for Sediment Management in Alluvial Channels

A submerged vane is a flow-training facility mounted vertically on the channel bed to control the sediment movement in the channel cross section, and has been utilized in various applications, such as prevention of bank erosion, sediment exclusion at water intakes, and deepening channels for navigation. The performance of a submerged vane is related to its dimensions and shape. This study aims to investigate a vane's sediment control effectiveness as a function of its size and shape, with the expectation of an optimal combination of dimensions and shape. A model for the calculation of the transverse bed profile in a cross section of a straight alluvial channel induced by a single submerged vane is developed. The model is utilized to investigate the performances for three types of vanes: (1) rectangular plates with various height and length; (2) tapered plates with linear decreasing in length from the base to the top; and (3) plates of parallelogram with the top of the plates swept forward or backward. Design guidelines and suggestions on the dimensions and shape of the vane are provided based on the results.

A three-dimensional k-ɛ-k p model in curvilinear coordinates for sediment movement and bed evolution

To aim at the substitution of the magnitude and direction of water flow movement near bed for those of bed load transport in solid-liquid two-phase one-fluid model, and to simulate the effect of secondary flow on transverse bed load transport in channel bends and the effect of bed slope on bed load transport in a better way, a three-dimensional k-ɛ-kp solid-liquid two-phase two-fluid model in curvilinear coordinates is solved numerically with a finite-volume method on an adaptive grid for studying water- sediment movements and bed evolution in a 120° channel bend. Numerical results show that the trajectories of solid-phase deviate from those of liquid-phase in the channel bend, and the deviation increases with the increase of the particle diameters. The calculated bed deformation by the k-ɛ-kp model is in better agreement with measured bed deformation than those by one-fluid model. It is proved that the k-ɛ-kp model can simulate the effect of secondary flow on lateral bed load transport with the higher accuracy than the one-fluid model.

Modeling Bed Changes in Meandering Rivers Using Triangular Finite Elements

A two-dimensional depth-averaged model was used for the simulation of scour and deposition in sand-bed meandering channels with fixed banks. The model employs unstructured meshes based on triangular elements and incorporates the effects of curvature-induced helical flow and transverse bed slope in the direction of bed-load sediment transport. The model was tested using experimental data from a well-known laboratory curved channel and a full scale meandering river. The numerical results agreed well with observed data, demonstrating that the model can reproduce the main features of bed profiles along meandering rivers, such as the formation of point bars and pools.

2D stream hydrodynamic, sediment transport and bed morphology model for engineering applications

AbstractA 2D depth‐averaged hydrodynamic, sediment transport and bed morphology model named STREMR HySeD is presented. The depth‐averaged sediment transport equations are derived from the 3D dilute, multiphase, flow equations and are incorporated into the hydrodynamic model STREMR. The hydrodynamic model includes a two‐equation turbulence model and a correction for the mean flow due to secondary flows. The suspended sediment load can be subdivided into different size classes using the continuum (two‐fluid) approach; however, only one bed sediment size is used herein. The validation of the model is presented by comparing the suspended sediment transport module against experimental measurements and analytical solutions for the case of equilibrium sediment‐laden in a transition from a rigid bed to a porous bed where re‐suspension of sediment is prevented. On the other hand, the bed‐load sediment transport and bed evolution numerical results are compared against bed equilibrium experimental results for the case of a meander bend. A sensitivity analysis based on the correction for secondary flow on the mean flow including the effect of secondary flow on bed shear stresses direction as well as the downward acceleration effect due to gravity on transverse bed slopes is performed and discussed. In general, acceptable agreement is found when comparing the numerical results obtained with STREMR HySeD against experimental measurements and analytical solutions. Copyright © 2007 John Wiley & Sons, Ltd.

STUDY ON NUMERICAL SIMULATION AND FACTOR ANALYSIS OF FLUSHING RIVER MOUTH BAR

A 2D River morphology model with a curvilinear grid is developed to simulate the flushing river mouth bar occurred at the Ara River in July 2004. In the hydrodynamic model, the 2D free surface flow is calculated by the Saint Venant equations which are solved by an implicit finite difference technique and the ADI method. In the morphological model, the Van Rijin's model is used to evaluate sediment transport including bed load and suspended load. The helical flow and the transverse bed slope modify the bed load sediment transport. The bed level change is computed by a sediment continuity equation of the bank erosion model. The model is validated by comparison with the observations of water level variations and the riverbed topography at the mouth. A factor analysis is conducted to evaluate the effects of discharge, tide level, and grain size. The result shows that differences of sea elevation and peak discharge have significant effects on a process of morphological change at the river mouth.

Simulating sine-generated meandering channel evolution with an analytical model

An analytical model to simulate the evolution of a meandering channel was developed based on the analytical solution of flow field in a sine-generated meandering channel and application of the bank erosion model by Duan et al. The flow-field solution was derived from two-dimensional, depthaveraged, steady-flowequations in channel-fitted, curvilinear orthogonal coordinates where the transverse bed slopewas treated as a variable increasing with channel sinuosity. The flow-field solution indicated that the location where the shift of maximum velocity zone from the convex to concave banks in sine-generated channels varies with the transverse bed slope and the strength of secondary current. The rate of bank erosion was calculated as a gradient function of the longitudinal sediment transport rate and strength of the secondary flow rather than being proportional to the magnitude of excessive near-bank velocity or shear stress. This model replicated the evolution of meandering channels from mildly to highly sinuous ones. Simulation results showed the migration of meandering channel is a combination of downstream translation, lateral extension, expansion, and downstream and upstream rotation. Low-sinuous free meanders migrate rapidly toward downstream. As the sinuosity increases, downstream translation diminishes, and meandering loops expand laterally with its head rotating toward downstream and then upstream. The simulated results indicated the gradient of the longitudinal sediment transport rate is essential in modeling meandering evolution.

Comparison of discrete elemental modelling to experimental data regarding mixing of solids in the transverse direction of a rotating kiln

Finnie et al. [Finnie, G.J., Kruyt, N.P., Ye M., Zeilstra, C., Kuipers, J.A.M., 2005. Longitudinal and transverse mixing in rotary kilns: a discrete element method approach. Chemical Engineering Science 60, 4083–4091] developed a discrete elemental model to simulate the mixing of solids in a rotary kiln. It is interesting to analyse and compare their results to those obtained through experimental observations such as those by Henein et al. [Henein, H., Brimacombe, J.K., Watkinson, A.P., 1983. Experimental study of transverse bed motion in rotary kilns. Metallurgical Transactions B 14B, 191–205] Van Puyvelde et al. [Van Puyvelde, D.R., Young, B.R., Wilson, M.A., Schmitd, S.J., 1999. Experimental determination of transverse mixing kinetics in a rolling drum by image analysis. Powder Technology 106, 183–191; 2000. Modelling transverse mixing in a rolling drum. Canadian Journal of Chemical Engineering 78, 635–642] and Mellmann [Mellmam, J., 2001. The transverse motion of solids in rotating cylinders—forms of motion and transition behavior. Powder Technology 118, 251–270].

Modeling width adjustment in meandering channels

Widening in sinuous channels occurs when the retreat of the outer bank exceeds the advance of the opposite bank. An analytical model is presented to simulate width adjustment in meandering channels of non-cohesive bank material resulting from bank erosion of two interactive processes: basal erosion and bank collapse. Bank collapse refers to the avalanche of non-cohesive material in the upper part of bank above water surface resulting from over-steepening of the bank surface due to basal erosion. The rate of basal erosion, including lateral erosion and bed degradation, is calculated as a function of the longitudinal gradient of sediment transport rate and strength of secondary flow. The transverse bed slope is treated as a variable that increases as channel sinuosity increases until the transverse bed slope reaches its maximum value. By simplifying the bank-collapse process for non-cohesive materials, the present study shows that the rate of bank-line retreat is determined by lateral erosion rate, near-bank bed-degradation rate, sediment grain size, and difference between flow depth and bank height. The time-dependent widening processes of two meandering channels in the laboratory are selected to test applicability of the model. The result shows that the simulated bank lines at individual time intervals closely match the experimental measurements. Whether the sinuosity of a meandering channel will increase or decrease is primarily determined by didtribution of the lngitudinal gradient of sediment transport rate along the channel.

Threshold of sediment motion on combined transverse and longitudinal sloping beds

Theoretical and experimental investigations are presented on the threshold of noncohesive sediment motion under a steady-uniform stream flow on a combined transverse (across the flow direction) and longitudinal (streamwise direction) sloping bed. Theoretical analysis of the equilibrium of a sediment particle lying on a combined transverse and longitudinal sloping bed shows that the critical shear stress ratio (ratio of critical shear stress for a sloping bed to that for a horizontal bed) is a function of the transverse bed slope, longitudinal bed slope, angle-of-repose of sediment particles and lift-drag ratio. As in laboratory flume study, the uniform flow is difficult to establish in a steeply sloping channel and is impossible to obtain in an adversely sloping channel, experiments were conducted in two inverted semicircular ducts (closed-conduit flow) for three sizes of uniform sediments. The critical shear stresses for experimental runs were determined considering side-wall correction. The experimental results correspond closely with the results obtained using the present model. The model can be applicable to both the channel beds and banks.

Bed load at low Shields stress on arbitrarily sloping beds: Alternative entrainment formulation

According to the Bagnold hypothesis for equilibrium bed load transport, a necessary constraint for the maintenance of equilibrium bed load transport is that the fluid shear stress at the bed must be reduced to the critical, or threshold, value associated with incipient motion of grains. It was shown in a companion paper [Seminara et al., 2002], however, that the Bagnold hypothesis breaks down when applied to equilibrium bed load transport on beds with transverse slopes above a relatively modest value that is well below the angle of repose. An investigation of this failure resulted in a demonstration of its lack of validity even for nearly horizontal beds. The constraint is here replaced with an entrainment formulation, according to which a dynamic equilibrium is maintained by a balance between entrainment of bed grains into the bed load layer and deposition of bed load grains onto the bed. The entrainment function is formulated so that the entrainment rate is an increasing function of the excess of the fluid shear stress at the bed over the threshold value. The formulation is implemented with the aid of a unique set of laboratory data that characterizes equilibrium bed load transport at relatively low shear stresses for streamwise angles of bed inclination varying from nearly 0° to 22°. The formulation is shown to provide a description of bed load transport on nearly horizontal beds that fits the data as well as that resulting from the Bagnold constraint. The entrainment formulation has the added advantage of not requiring the unrealistically high dynamic coefficient of Coulomb friction resulting from the Bagnold constraint. Finally, the entrainment formulation provides reasonable and consistent results on finite streamwise and transverse bed slopes, even those at which the Bagnold formulation breaks down completely.

자연하천 만곡부의 횡방향 안정하상을 위한 한계속도

본 연구에서는 자연하천의 만곡수로에서 종방향 유속으로 인해 현재보다 더 이상 횡 방향 경사의 변형이 일어나지 않아 세굴이 감소하고 하상이 횡방향으로 안정한 상태를 유지할 수 있는 적정 유속의 한계인 한계속도를 제시하였다. 한계속도의 이론 유도는 하상횡경모형의이론적 배경이 되는 운동량모멘트방정식으로부터 얻은 하상면 횡방향전단력성분과 이에 대응하는 하상전단력과의 힘의 평형으로부터 유도되었다. 이론식의 검증을 위해 4개 자연하천수로의 실측자료론 적용하여 계산치와 실측치를 비교한 결과 잘 일치하였다. 적용결과에서 보정계수와 만곡수로의 평균입자 Froude수는 밀접한 상관관계를 갖고 있는 것으로 나타났다. In this study, an equation is proposed to estimate the limit velocity for lateral stable bed in a curved channel stream. The stable bed on lateral direction is satisfied when there is no more deformation occurs on the transverse bed slope and non-scouring condition in a bend. A theoretical equation for limit velocity is derived using a transverse bed slope model. So, the limit velocity has its theoretical background in the equilibrium of two forces, lateral shear force at the bed due to longitudinal flow and the corresponding lateral bed shear force. To verify the equation, data from four natural river channels were used. There is good agreement between the calculated values using this equation and the measured values. The corrections in equation was found to be correlated with the averaged particle Froude number.

Model testing of submerged vanes in strongly curved narrow channel bends

This paper reports on a laboratory study that examines the effectiveness of submerged vanes for the control of erosion in strongly curved narrow channel bends. All previous researches on submerged vanes were performed in either straight or weakly curved channels that were hydraulically "wide". Submerged vanes are thin rectangular-shaped low-profile foils, typically set at small angles to the main current and arranged in either single or multiple parallel arrays in the longitudinal direction. When installed in a channel bend they induce a helicoidal vortex that interacts with and weakens the centrifugally induced secondary current. The latter effect leads to reduced local erosion near the bend's outer bank. Physical model testing was performed to determine the effects of several parameters affecting submerged vane performance, including submerged vane height H, length L, angle to main flow direction α, vane streamwise spacing δs, vane transverse spacing from outer bank δn, and bend angle φ. Submerged vanes effectively stabilize channel bend erosion by reducing the scour depth at the outer bank, generating positive transverse bed slope at the outer bank, and by reducing the net sediment loss through the channel. In general, an increase in vane height tends to shift the thalweg away from the outer bank; an increase in vane length tends to reduce the general erosion through the channel.Key words: submerged vanes, riverbank stabilization, bottom vanes, narrow channels, bank protection, bank stabilization, channel bends.

Shallow wakes generated on smooth and rough surfaces

This study deals with the behavior of shallow turbulent wakes generated on smooth and rough surfaces. The wake generator used is a flat plate placed normal to the flow. Experiments were conducted at flow depths of 40 and 80 mm. The boundary layer thickness in the approaching flow occupies 60–75% of the flow depth. The Reynolds number based on the plate width and approaching freestream velocity varies from 13.0 × 103 to 14.5 × 103. Velocity measurements were carried out in the near-wake region (1–10 plate widths) using a laser-Doppler anemometer. The mean velocity distributions at various axial stations collapse onto a single curve by a proper choice of the length and velocity scales. It is important to note that a sense of self-similarity is attained even in the near-wake region. Attempts were made to clarify the relative effects of the transverse shear and bed friction in shallow open channel wakes.