A mixing-length model for predicting vertical velocity distribution in flows through emergent vegetation

Abstract

The vertical profiles of streamwise velocities are computed on flood plains vegetated with trees. The calculations were made based on a newly developed one-dimensional model, taking into account the relevant forces acting on the volumetric element surrounding the considered vegetation elements. A modified mixing length concept was used in the model. An important by-product of the model is the method for evaluating the friction velocities, and consequently bed shear stresses, in a vegetated channel. The model results were compared with the relevant experimental results obtained in a laboratory flume in which flood plains were covered by simulated vegetation.     

Influence of junction angle on three‐dimensional flow structure and bed morphology at confluent meander bends during different hydrological conditions

Recent field and modeling investigations have examined the fluvial dynamics of confluent meander bends where a straight tributary channel enters a meandering river at the apex of a bend with a 90° junction angle. Past work on confluences with asymmetrical and symmetrical planforms has shown that the angle of tributary entry has a strong influence on mutual deflection of confluent flows and the spatial extent of confluence hydrodynamic and morphodynamic features. This paper examines three‐dimensional flow structure and bed morphology for incoming flows with high and low momentum‐flux ratios at two large, natural confluent meander bends that have different tributary entry angles. At the high‐angle (90°) confluent meander bend, mutual deflection of converging flows abruptly turns fluid from the lateral tributary into the downstream channel and flow in the main river is deflected away from the outer bank of the bend by a bar that extends downstream of the junction corner along the inner bank of the tributary. Two counter‐rotating helical cells inherited from upstream flow curvature flank the mixing interface, which overlies a central pool. A large influx of sediment to the confluence from a meander cutoff immediately upstream has produced substantial morphologic change during large, tributary‐dominant discharge events, resulting in displacement of the pool inward and substantial erosion of the point bar in the main channel. In contrast, flow deflection is less pronounced at the low‐angle (36°) confluent meander bend, where the converging flows are nearly parallel to one another upon entering the confluence. A large helical cell imparted from upstream flow curvature in the main river occupies most of the downstream channel for prevailing low momentum‐flux ratio conditions and a weak counter‐rotating cell forms during infrequent tributary‐dominant flow events. Bed morphology remains relatively stable and does not exhibit extensive scour that often occurs at confluences with concordant beds. Copyright © 2014 John Wiley & Sons, Ltd.     

Flow in a tightly curving meander bend: effects of seasonal changes in aquatic macrophyte cover

The effects of aquatic macrophytes on flow and turbulence were studied in a tightly curving meander bend. Three field measurement campaigns were carried out within a one year period to capture effects of seasonal changes in macrophyte cover. They comprised three‐dimensional velocity measurements and mappings of vegetation cover and bathymetry. Flow accelerates and converges over the run into an axial pool in a jet‐like flow pattern bordered by outer and inner bank flow separation zones. The jet and widening of the cross‐section anticipate helical flow until the second half of the bend, where an asymmetric pool developed. Submerged vegetation at the riffles preserves the jet at much lower discharges during the summer period by concentrating high momentum fluid near the surface. Plants locally modify the velocity and stress patterns, reduce bed shear stresses, create zones of fine sediment accumulation and reinforce the bed and banks with roots and rhizomes. Plant patches colonising the banks and the point bar confine secondary flow cells laterally and affect shape and magnitude of the transverse flow profiles near their edges. The morphology of the bend was very stable over the observation period and neither bank erosion nor pool scouring occurred. However, fine sediments accumulate within vegetation patches and in the recirculation zones while the remaining open areas tend to erode slightly. With the decay of macrophytes in winter, sediment accumulations are mobilised again and the bathymetry levels, supporting cyclic models of morphologic change in vegetated bends. In the second part of the paper, semi‐empirical models for the three predominant flow types were tested and discussed; velocity and stress models of vegetated mixing layers and plane turbulent jets, and Rozovskii's model for the transverse flow in bends. Copyright © 2012 John Wiley & Sons, Ltd.     

Flow separation at the inner (convex) and outer (concave) banks of constant‐width and widening open‐channel bends

There is a paucity of data and insight in the mechanisms of, and controls on flow separation and recirculation at natural sharply‐curved river bends. Herein we report on successful laboratory experiments that elucidate flow structure in one constant‐width bend and a second bend with an outer‐bank widening. The experiments were performed with both a flat immobile gravel bed and mobile sand bed with dominant bedload sediment transport. In the constant‐width bend with immobile bed, a zone of mainly horizontal flow separation (vertical rotational axis) formed at the inner bank that did not contain detectable flow recirculation, and an outer‐bank cell of secondary flow with streamwise oriented rotational axis. Surprisingly, the bend with widening at the outer bank and immobile bed did not lead to a transverse expansion of the flow. Rather, flow in the outer‐bank widening weakly recirculated around a vertical axis and hardly interacted with the inner part of the bend, which behaved as a constant‐width bend. In the mobile bed experiment, downstream of the bend apex a pronounced depositional bar developed at the inside of the bend and pronounced scour occurred at the outside. Moreover the deformed bed promoted flow separation over the bar, including return currents. In the constant‐width bend, the topographic steering impeded the generation of an outer‐bank cell of secondary flow. In the bend with outer‐bank widening, the topographic steering induced an outward expansion of the flow, whereby the major part of the discharge was conveyed in the central part of the widening section. Flow in the outer‐bank widening was highly three dimensional and included return currents near the bottom. In conclusion, the experiments elucidated three distinct processes of flow separation common in sharp bends: flow separation at the inner bank, an outer‐bank cell of secondary flow, and flow separation and recirculation in an outer‐bank widening. Copyright © 2012 John Wiley & Sons, Ltd.     

EXPERIMENTAL STUDY ON THE RELATION OF BED MORPHOLOGY WITH SURFACE FLOW IN MEANDER CHANNELS

1 INTRODUCTION The plane shape of a river channel is very important for river improvement planning, because it must allow floodwater to flow off safely. Natural rivers wind from side to side, which creates meandering forms. From the history of river impro…     

EXPERIMENTAL STUDY ON THE RELATIONA OF BED MORPHOLOGY WITH SURFACE FLOW IN MEANDER CHANNELS

Alternate bars have the property that they migrate downstream whenever floods occur. However, in meander channels whose bend angles are larger than a critical value, the migration of bars can be suppressed, and the positions of bank erosion and flood attack also will be steady. In this study, the bed morphology in flume channels with bends of various lengths and angles is investigated at various flow discharges, and the relation of bed morphology to surface flow is investigated in detail using fluid measuring software. An effort is made to obtain guidelines for the plane shape design of meander channels. Based on the experimental results of bed topography and measurement of surface flow direction and velocity distribution, from the viewpoint of bank erosion and the concentration and dispersion of flood flow the most suitable plane shape for meandering channels is suggested through which the migration of alternate bars is suppressed.     

Spatial and temporal intensification of lateral hyporheic flux in narrowing intra‐meander zones

Meander bends in alluvial rivers morphologically evolve towards meander cut‐off with narrowing intra‐meander necks, and this should steepen hydraulic gradients and intensify intra‐meander hyporheic flux. This research used dye tracking and head loss measurements in a 1 : 500 planimetrically scaled laboratory river table to quantify the spatial and temporal intensification of intra‐meander flux rates at two evolution ages. The younger meander bend, M1, had a sinuosity of 2.3, a river neck width of 0.39 cm, and 0.6% river slope, and the older meander bend, M3, had a sinuosity of 5.2, a river neck width of 0.12 cm, and 0.5% river slope. Flux into and out of the meander bend was estimated along the normalized curvilinear distance s*, with the meander neck at s* = 0.1 and s* = 0.9, the meander centroid at s* = 0.37 and s* = 0.63, and the apex at s* = 0.5. Between the meander centroid and neck, we documented a 60% spatial intensification for M1 and a 90% spatial intensification for M3. Between M1 and M3, we documented a 135% temporal intensification at the neck and a 100% intensification at the centroid. Our empirical spatial and temporal intensification rates involving the M1 and the M3 scenario were one to three times lower than theoretical rates derived from a river evolution model with equivalent M1 and M3 planimetry. Overestimation by the theoretical model was attributed to exaggerated head loss caused by the model neglecting groundwater contributions to river stage. Hyporheic exchange provides critical ecosystem services, and its spatial and temporal variation with meander evolution should be considered in river management. Copyright © 2012 John Wiley & Sons, Ltd.     

Formation process of meandering channel by a 2D numerical simulation

A 2D depth-averaged model for hydrodynamic,sediment transport and river morphological adjustment is presented.The sediment transport submodel considers non-uniform sediment,bed surface armoring,impact of secondary flow on the direction of bed-load transport,and transverse slope of river bed.The bank erosion submodel incorporates a simple simulation method for updating bank geometry during either degradational or aggradational bed evolution.The model is applied to a 180°bend with a constant radius under unsteady flow conditions,and to Friedkin’s laboratory meander channels.The results are in acceptable agreement with measurements,confirming the two dimensional model’s potential in predicting the formation of river meandering and improving understanding of patterning processes.Future researches are needed to clarify some simplifications and limitations of the model.     

Chute channel dynamics in large,sand‐bed meandering rivers

Meander bends of many large, sand‐bed meandering rivers are partitioned by chute channels that convey permanent flow, and co‐exist with the mainstem for decades. As a first step toward understanding the dynamics and morphodynamic implications of these ‘bifurcate meander bends’, this study applied binary logistic regression analysis to determine whether it is possible to predict chute initiation based on attributes of meander bend character and dynamics. Regression models developed for the Strickland River, Papua New Guinea, the lower Paraguay River, Paraguay/Argentina, and the Beni River, Bolivia, revealed that the probability of chute initiation at a meander bend is a function of the bend extension rate (the rate at which a bend elongates in a direction perpendicular to the valley axis trend). Image analyses of all rivers and field observations from the Strickland suggest that the majority of chute channels form during scroll–slough development. Rapid extension is shown to favour chute initiation by breaking the continuity of point bar deposition and vegetation encroachment at the inner bank, resulting in widely‐spaced scrolls with intervening sloughs that are positively aligned with primary over‐bar flow. The rivers plot in order of increasing chute activity on an empirical meandering‐braided pattern continuum defined by potential specific stream power (ω_pv) and bedload calibre (D₅₀). Increasing stream power is considered to result in higher bend extension rates, with implications for chute initiation. In addition, chute stability is shown to depend on river sediment load relative to flow discharge (Qs/Q), such that while the Beni may plot in the region of highly braided rivers by virtue of a high potential specific stream power, the formation of stable chute channels is suppressed by the high sediment load. This tendency is consistent with previous experimental studies, and results in a planform that is transitional between single‐thread meandering and braided. Copyright © 2011 John Wiley & Sons, Ltd.     

Flow-induced vegetation uprooting in a meandering bend:Experimental investigation

Vegetation uprooting is a complex process which depends on many interrelated factors. In this paper,attention is focused on the flow-induced uprooting in river bends, where the flow characteristics vary as effected by the channel’s curvature and its continuous changing in the downstream direction. Results are presented by an experimental work done in a high-amplitude meandering flume with mature herbaceous vegetation on the bed. In the first part of the paper, the variation along the bend of the...     

A model of equilibrium bed topography for meander bends with erodible banks

Channel curvature produces secondary currents and a transverse sloping channel bed, along which the depth increases towards the outer bank. As a result deep pools tend to form adjacent to the outer bank, promoting bank collapse. The interaction of sediment grains with the primary and secondary flow and the transverse sloping bed also causes meanders to move different grain sizes in different proportions and directions, resulting in a consistent sorting pattern. Several models have been developed to describe this process, but they all have the potential to over‐predict pool depth because they cannot account for the influence of erodible banks. In reality, bank collapse might lead to the development of a wider, shallower cross‐section and any resulting flow depth discrepancy can bias associated predictions of flow, sediment transport, and grain‐size sorting. While bed topography, sediment transport and grain sorting in bends will partly be controlled by the sedimentary characteristics of the bank materials, the magnitude of this effect has not previously been explored. This paper reports the development of a model of flow, sediment transport, grain‐size sorting, and bed topography for river bends with erodible banks. The model is tested via intercomparison of predicted and observed bed topography in one low‐energy (5·3 W m^?2 specific stream power) and one high‐energy (43·4 W m^?2) study reach, namely the River South Esk in Scotland and Goodwin Creek in Mississippi, respectively. Model predictions of bed topography are found to be satisfactory, at least close to the apices of bends. Finally, the model is used in sensitivity analyses that provide insight into the influence of bank erodibility on equilibrium meander morphology and associated patterns of grain‐size sorting. The sensitivity of meander response to bank cohesion is found to increase as a function of the available stream power within the two study bends. Copyright © 2002 John Wiley & Sons, Ltd.     

Spatial variability of three‐dimensional Reynolds stresses in a developing channel bend

Experimental results of the mean flow field and turbulence characteristics for flow in a model channel bend with a mobile sand bed are presented. Acoustic Doppler velocimeters (ADVs) were used to measure the three components of instantaneous velocities at multiple cross sections in a 135° channel bend for two separate experiments at different stages of clear water scour conditions. With measurements at multiple cross sections through the bend it was possible to map the changes in both the spatial distribution of the mean velocity field and the three Reynolds shear stresses. Turbulent stresses are known to contribute to sediment transport and the three‐dimensionality inherent to flow in open channel bends presents a useful case for determining specific relations between three‐dimensional turbulence and sediment entrainment and transport. These measurements will also provide the necessary data for validating numerical simulations of turbulent flow and sediment transport. The results show that the magnitude and distribution of three‐dimensional Reynolds stresses increase through the bend, with streamwise‐cross stream and cross stream‐vertical components exceeding the maximum principal Reynolds stress through the bend. The most intriguing observation is that near‐bed maximum positive streamwise‐cross stream Reynolds stress coincides with the leading edge of the outer bank scour hole (or thalweg), while maximum cross stream‐vertical Reynolds stress (in combination with high negative streamwise‐cross stream Reynolds stress near the bend apex) coincides with the leading edge of the inner bank bar. Maximum Reynolds stress and average turbulent kinetic energy appear to be greater and more localized over the scour hole before final equilibrium scour is reached. This suggests that the turbulent energy in the flow is higher while the channel bed is developing, and both lower turbulent energy and a broader distribution of turbulent stresses near the bed are required for cessation of particle mobilization and transport. Copyright © 2010 John Wiley & Sons, Ltd.     

Three‐dimensional flow structure and patterns of bed shear stress in an evolving compound meander bend

Compound meander bends with multiple lobes of maximum curvature are common in actively evolving lowland rivers. Interaction among spatial patterns of mean flow, turbulence, bed morphology, bank failures and channel migration in compound bends is poorly understood. In this paper, acoustic Doppler current profiler (ADCP) measurements of the three‐dimensional (3D) flow velocities in a compound bend are examined to evaluate the influence of channel curvature and hydrologic variability on the structure of flow within the bend. Flow structure at various flow stages is related to changes in bed morphology over the study timeframe. Increases in local curvature within the upstream lobe of the bend reduce outer bank velocities at morphologically significant flows, creating a region that protects the bank from high momentum flow and high bed shear stresses. The dimensionless radius of curvature in the upstream lobe is one‐third less than that of the downstream lobe, with average bank erosion rates less than half of the erosion rates for the downstream lobe. Higher bank erosion rates within the downstream lobe correspond to the shift in a core of high velocity and bed shear stresses toward the outer bank as flow moves through the two lobes. These erosion patterns provide a mechanism for continued migration of the downstream lobe in the near future. Bed material size distributions within the bend correspond to spatial patterns of bed shear stress magnitudes, indicating that bed material sorting within the bend is governed by bed shear stress. Results suggest that patterns of flow, sediment entrainment, and planform evolution in compound meander bends are more complex than in simple meander bends. Moreover, interactions among local influences on the flow, such as woody debris, local topographic steering, and locally high curvature, tend to cause compound bends to evolve toward increasing planform complexity over time rather than stable configurations. Copyright © 2016 John Wiley & Sons, Ltd.     

Lateral sediment transport by bedforms in a meander bend

Bedforms and their migration are among the most important features determining bed load transport on point bars in sand-bedded rivers. A case study has been carried out in the Danish river Gels Å in a bend with equilibrium point bar topography. Bedforms (dunes) were repeatedly surveyed to determine the bedform migration on the point bar surface. Bedforms occur in two categories in the bend: primary dunes and secondary dunes migrating transversely in the troughs between primary dunes. The study shows that the migration of these bedforms can account for the entire lateral transport known to concentrate the transport in the convex half of the cross section at the bend exit. The bedform transport is induced by both dune categories, partly by turning of the primary dunes towards the convex bank and partly by the migration of secondary dunes. In certain areas, the two categories operate together and thus make the lateral transport particularly large; it is shown that almost 60 per cent of the entire lateral transport in the bend takes place within less than 30 per cent of the streamwise extent of the point bar.     

Modeling depth-averaged velocity and bed shear stress in compound channels with emergent and submerged vegetation

This paper presents an approach to modeling the depth-averaged velocity and bed shear stress in compound channels with emergent and submerged vegetation. The depth-averaged equation of vegetated compound channel flow is given by considering the drag force and the blockage effect of vegetation, based on the Shiono and Knight method (1991) [40]. The analytical solution to the transverse variation of depth-averaged velocity is presented, including the effects of bed friction, lateral momentum transfer, secondary flows and drag force due to vegetation. The model is then applied to compound channels with completely vegetated floodplains and with one-line vegetation along the floodplain edge. The modeled results agree well with the available experimental data, indicating that the proposed model is capable of accurately predicting the lateral distributions of depth-averaged velocity and bed shear stress in vegetated compound channels with secondary flows. The secondary flow parameter and dimensionless eddy viscosity are also discussed and analyzed. The study shows that the sign of the secondary flow parameter is determined by the rotational direction of secondary current cells and its value is dependent on the flow depth. In the application of the model, ignoring the secondary flow leads to a large computational error, especially in the non-vegetated main channel.     

Stochastic erosion of composite banks in alluvial river bends

The erosion of composite river banks is a complex process involving a number of factors including fluvial erosion, seepage erosion, and cantilever mass failure. To predict the rate of bank erosion with these complexities, a stochastic bank erosion model is suitable to define the probability distribution of the controlling variables. In this study, a bank erosion model in a river bend is developed by coupling several bank erosion processes with an existing hydrodynamic and morphological model. The soil erodibility of cohesive bank layers was measured using a submerged jet test apparatus. Seasonal bank erosion rates for four consecutive years at a bend in the Brahmaputra River, India, were measured by repeated bankline surveys. The ability of the model to predict erosion was evaluated in the river bend that displayed active bank erosion. In this study, different monsoon conditions and the distribution functions of two variables were considered in estimating the stochastic bank erosion rate: the probability of the soil erodibility and stochastic stage hydrographs for the nth return period river stage. Additionally, the influences of the deflection angle of the streamflow, longitudinal slope of river channel, and bed material size on bank erosion rate were also investigated. The obtained stochastic erosion predictions were compared with the observed distribution of the annual‐average bank erosion rate of 45 river bends in the Brahmaputra River. The developed model appropriately predicted the short‐term morphological dynamics of sand‐bed river bends with composite banks. Copyright © 2014 John Wiley & Sons, Ltd.     

Biomorphodynamic modelling of inner bank advance in migrating meander bends

We propose a bio-morphodynamic model at bend cross-sectional scale for the lateral migration of river meander bends, where the two banks can migrate separately as a result of the mutual interaction between river flow, sediments and riparian vegetation, particularly at the interface between the permanently wet channel and the advancing floodplain. The model combines a non-linear analytical model for the morphodynamic evolution of the channel bed, a quasi-1D model to account for flow unsteadiness, and an ecological model describing riparian vegetation dynamics. Simplified closures are included to estimate the feedbacks among vegetation, hydrodynamics and sediment transport, which affect the morphology of the river-floodplain system. Model tests reveal the fundamental role of riparian plants in generating bio-morphological patterns at the advancing floodplain margin. Importantly, they provide insight into the biophysical controls of the ‘bar push’ mechanism and into its role in the lateral migration of meander bends and in the temporal variations of the active channel width.     

Channel morphologic processes of a highly sinuous bend approaching neck cutoff by bank erosion in the middle Yangtze River

The distal reach of the Lower Jingjiang River(LJR)in the middle of the Yangtze River consists of five adjacent bends,among which the Qigongling Bend is a U-shaped meander with a mean sinuosity of 2.2 and the narrowest neck 525 m in width.This bend is slowly approaching neck cutoff owing to progressive bank erosion.An abnormal phenomenon has occurred in this bend since the Three Gorges Reservoir(TGR)began to operate in 2003 which is erosion in the inner bank zone and deposition in the outer bank zone.This problem has not been fully understood because of the interplay of changes in water-sediment,bank erosion,and artificial bank revetment.In this study,aerial and remote sensing images,hydrological data,channel topography,and an existing bank erosion model are used to reveal channel morphodynamics of this bend and the trend of the potential neck cutoff induced by bank erosion.The study results show that the clear water released from the TGR has provided by forcefully eroded the point bar of inner bank but failed to scour the outer bank due to the protection of bank revetment since the 1990 s.Thus far,the outer bank zone near the bend apex has increasingly widened in conjunction with the formation of 2 emerging sand bars.Consequently,the thalweg of the main channel has laterally shifted toward the inner bank by roughly 800 m.More severely,the rate of bank retreat on the upstream side of the bend neck was about 4.5 m/yr in 2010-2019,but the downstream side of this neck was experienced slight deposition.Bank erosion could be accelerated by progressively increasing erosion and eventually trigger the occurrence of neck cutoff in the next few decades,thereby significantly altering the quasi-equilibrium regime of channel morphodynamics in the LJR.     

Rates,distributions and mechanisms of change in meander morphology over decadal timescales,River Dane,UK

This paper analyses types and rates of change in river meander morphology and the links between mechanisms of change and emergent behaviour of planform morphology. It uses evidence of four dates of aerial photography combined with annual field mapping and ground photography to examine the morphological changes and mechanisms of change in a series of bends on an active meandering river, the River Dane in NW England, over a 25 year period. This unique data set allows insight into the spatial and temporal variability of bank line movement and component processes. Bank lines were mapped photogrametrically from air photos of 1984, 1996, 2001 and 2007 and the digitised courses compared in ArcGIS to produce calculations of erosional and depositional areas and rates. Most bends exhibit morphological change that largely follows the autogenic sequence, identified in qualitative models of meander development, from low sinuosity curves through simple symmetric and asymmetric bends to compound forms with lobe development in the apex region. Rates of erosion and bankline movement increase through this sequence until the compound phase. Relationships of amounts of movement to various curvature measures of bend morphology are complex. Several new loops, distinct from compound bend behaviour, have developed during the study period in formerly straight sections. Mechanisms of morphological change are illustrated for four types of bends: new, rapid growth bend; sharp‐angled bend with mid‐channel bar development; symmetric migrating bend; and simple to compound bend development. The changes take place in phases that are not simply related to discharge but to inherent sequences and feedbacks in development of bars and bend morphology and timescales for these are identified. Overall, emergent behaviour of systematic planform change, moderated by channel confinement and boundary features, is produced from spatially and temporally varied channel processes. Copyright © 2010 John Wiley & Sons, Ltd.     

Dynamic mechanism of turbulent flow in meandering channels: considerations for deflection angle

To find turbulent flow structure inside meandering channels, three physical models of river meanders representing strongly curved bend, mild bend and elongated symmetrical meander loop were tested in this paper. Instantaneous velocity data in three dimensions were measured using Micro-ADV at different cross sections of these models. Depth averaged velocity vectors, streamwise velocity, secondary currents, turbulent and mean flow kinetic energy were investigated with respect to the sediment deposition pattern. In order to gain more regarding the force acting the sediment particles, three dimensional velocity fluctuations were analyzed in detailed inside the elongated symmetrical meander loop. Occurrence frequency, transition probability and angle of attack for different events were also computed for the points close to the bed. Of the present results, the importance of sweeps and ejections on sediment deposition can be detected. Further, distribution of bursting events is presented through the water column and compared the results with the previous works. Importantly, occurrence of fluctuating velocities in three dimensions at different locations inside the river meanders in addition to the effect of mean flow and turbulent components is responsible for sediment transport. Streamwise velocity distribution through the depth is also compared with some previous mathematical models. Researchers seeking the better control over the river morphology can apply this method without sacrificing much time and cost. This study is also included some insights to be pursued by future works.