Shear velocity estimates in rough‐bed open‐channel flow

Shear velocity u_* is an important parameter in geophysical flows, in particular with respect to sediment transport dynamics. In this study, we investigate the feasibility of applying five standard methods [the logarithmic mean velocity profile, the Reynolds stress profile, the turbulent kinetic energy (TKE) profile, the wall similarity and spectral methods] that were initially developed to estimate shear velocity in smooth bed flow to turbulent flow over a loose bed of coarse gravel (D₅₀ = 1·5 cm) under sub‐threshold conditions. The analysis is based on quasi‐instantaneous three‐dimensional (3D) full depth velocity profiles with high spatial and temporal resolution that were measured with an Acoustic Doppler Velocity Profiler (ADVP) in an open channel. The results of the analysis confirm the importance of detailed velocity profile measurements for the determination of shear velocity in rough‐bed flows. Results from all methods fall into a range of ± 20% variability and no systematic trend between methods was observed. Local and temporal variation in the loose bed roughness may contribute to the variability of the logarithmic profile method results. Estimates obtained from the TKE and Reynolds stress methods reasonably agree. Most results from the wall similarity method are within 10% of those obtained by the TKE and Reynolds stress methods. The spectral method was difficult to use since the spectral energy of the vertical velocity component strongly increased with distance from the bed in the inner layer. This made the choice of the reference level problematic. Mean shear stress for all experiments follows a quadratic relationship with the mean velocity in the flow. The wall similarity method appears to be a promising tool for estimating shear velocity under rough‐bed flow conditions and in field studies where other methods may be difficult to apply. This method allows for the determination of u_* from a single point measurement at one level in the intermediate range (0·3 < h < 0·6). Copyright © 2013 John Wiley & Sons, Ltd.     

Laboratory flume studies of microflow environments of aquatic plants

The microflow environments of aquatic plants with reference to Myriophyllum and Hydrilla are simulated in a laboratory flume. A Nix Streamflow microflow meter was used to measure the mean velocity profiles of flow at different densities of plants, flow ranges and measurement positions. Each mean velocity profile consists of three hydrodynamic regimes (i.e. within‐canopy zone, above‐canopy zone and a transitional zone between them), which indicate the presence of two benthic boundary layers (internal and external ones). Out of 38 measured mean velocity profiles, most do not fit a logarithmic relationship. The following hydrodynamic parameters are used in characterizing the flow regimes: local shear velocity (u_*), roughness length (z_o), canopy roughness Reynolds number (Re_*), bed shear stress (τ_o) and laminar sublayer (σ). Copyright © 2002 John Wiley & Sons, Ltd.     

The effect of wave-induced turbulence on intertidal mudflats: Impact of boat traffic and wind

Semi-diurnal and fortnightly surveys were carried out to quantify the effects of wind- and navigation-induced high-energy events on bed sediments above intertidal mudflats. The mudflats are located in the upper fluvial part (Oissel mudflat) and at the mouth (Vasière Nord mudflat) of the macrotidal Seine estuary. Instantaneous flow velocities and mudflat bed elevation were measured at a high frequency and high resolution with an acoustic doppler velocimeter (ADV) and an ALTUS altimeter, respectively. Suspended particulate matter concentrations were estimated by calibrating the ADV acoustic backscattered intensity with bed sediments collected at the study sites. Turbulent bed shear stress values were estimated by the turbulent kinetic energy method, using velocity variances filtered from the wave contribution. Wave shear stress and maximum wave–current shear stress values were calculated with the wave–current interaction (WCI) model, which is based on the bed roughness length, wave orbital velocities and the wave period (T_S). In the fluvial part of the estuary, boat passages occurred unevenly during the surveys and were characterized by long waves (T_S>50 s) induced by the drawdown effect and by short boat-waves (T_S<10 s). Boat waves generated large bottom shear stress values of 0.5 N m⁻² for 2–5 min periods and, in burst of several seconds, larger bottom shear stress values up to 1 N m⁻². At the mouth of the estuary, west south-west wind events generated short waves (T_S<10 s) of H_S values ranging from 0.1 to 0.3 m. In shallow-water environment (water depth <1.5 m), these waves produced bottom shear stress values between 1 and 2 N m⁻². Wave–current shear stress values are one order of magnitude larger than the current-induced shear stress and indicate that navigation and wind are the dominant hydrodynamic forcing parameters above the two mudflats. Bed elevation and SPM concentration time series showed that these high energy events induced erosion processes of up to several centimetres. Critical erosion shear stress (τ_ce) values were determined from the SPM concentration and bed elevation measurements. Rough τ_ce values were found above 0.2 N m⁻² for the Oissel mudflat and about 1 N m⁻² for the Vasière Nord mudflat.     

Sand flux and wind profiles in the saltation layer above a rounded dune top

The near-bed airflow and the movement of sand dune sediments by wind are fundamental dune geomorphological processes.This research measured the wind profiles and sand mass flux on the rounded top of a transverse dune at the southern edge of the Tengger Desert to examine how to best predict the vertical profile of sand flux.This work also tested the accuracy of previously developed models in predicting the apparent roughness length during saltation.Results show that mass flux vertical distribution over the dune top is underestimated by an exponential function,overestimated by a power function,but closely matches the predictions made using the LgstcDoseRsp function.Given suitable values ofα,βandγaccording to the grain size composition,S?rensen equation with the peaked shape of the mass transport curve will well predict the dimensionless mass flux qg/ρu*3against dimensionless shear velocity u*/u*t.The modified Charnock model works best of the previously published models tested,with an R2of 0.783 in predicting the enhanced roughness over the moving sand surface,as opposed to an R2of0.758 for the Owen model and an R2of 0.547 for the Raupach model.For the rounded dune top in this study,C m=0.446±0.016.     

Aeolian sediment flux decay: Non-linear behaviour on developing deflation lag surfaces

Wind tunnel simulations of the effect of non-erodible roughness elements on sediment transport show that the flux ratio q/q_s, shear velocity U*, and roughness density λ are co-dependent variables. Initially, the sediment flux is enhanced by kinetic energy retention in relatively elastic collisions that occur at the roughness element surfaces, but at the same time, the rising surface coverage of the immobile elements reduces the probability of grain ejection. A zone of strong shearing stress develops within 0·03 to 0·04 m of the rough bed because of a relative straightening of velocity profiles which are normally convex with saltation drag. This positive influence on fluid entrainment is opposed by declining shear stress partitioned to the sand bed. Similarly, because the free stream velocity U_f is fixed while U_* increases, velocity at height z and particle momentum gain from the airstream decline, leading eventually to lower numbers of particles ejected on average at each impact. When the ratio of the element basal area to frontal area σ is approximately equal to 3·5, secondary flow effects appear to become significant, so that the dimensionless aerodynamic roughness parameter Z₀/h and shear stress on the exposed sand bed T_s decrease. It is at this point that grain supply to the airstream and saltation drag appear to be significantly reduced, thereby intensifying the reduction in U_*. The zone of strong fluid shear near the bed dissipates.     

Effects of a fully submerged boulder within a boulder array on the mean and turbulent flow fields: Implications to bedload transport

The objective of this coupled experimental and numerical study is to provide insight into the mean and turbulent flow fields within an array of fully submerged, isolated, immobile boulders. Our study showed that the velocity defect law performed well for describing the mean flow around the boulder within the array. A prerequisite, however, was to accurately estimate the spatial variability of u* around the boulder, which was achieved via the boundary characteristics method. The u* exhibited considerable spatial variability within the array and form roughness was shown to be up to 2 times larger than the skin roughness in the boulder near-wake region. Because the boulders bear a significant amount of the flow shear, the available bed shear stress for entrainment of the mobile sediment, ?? _ols , near the boulders was roughly 50% lower than the ambient ?? _ols . The ?? _ols variability induced by the boulders could lead to a threefold overestimation of the sediment transport rate.     

A theoretical investigation of bed-form shapes

The deformation of movable boundaries under the action of an applied turbulent shear stress is well known. The resulting bed forms often are highly organized and nearly two-dimensional, which makes them an intriguing focus of study considering that they are generated in both steady and oscillatory turbulent flows. Many past studies share a common approach in which an infinitesimal perturbation is prescribed and the resulting growth or decay patterns are examined. In this approach, the bed forms are usually sinusoidal and the perturbation analysis does not provide a theoretical prediction of equilibrium bed-form geometry. An alternative approach is suggested here in which the forcing terms (pressure and stress) are prescribed parametrically and the governing equations are solved for the flow velocity and the associated boundary deformation. Using a multilayered approach, in which the bottom boundary layer is divided into a discrete, yet, arbitrary number of finite layers, analytical solutions for the horizontal current and bed profile are derived. The derivations identify two nondimensional parameters, p₀/u₀² and ₀/kh₀u₀², which modulate the amplitude of the velocity fluctuations and boundary deformation. For the case of combined pressure and stress divergence anomalies, the magnitude of the front face and lee slopes exhibit an asymmetry that is consistent with observed bed forms in steady two-dimensional flows.Responsible Editor: Jens Kappenberg     

Turbulence characteristics of flow past submerged vanes

Submerged vanes are hydrofoils utilized to manage the sediment transport through the river by generating the turbulence in the flow in the form of helical currents.The vanes are placed in the flow with respect to its direction at angle of 10°to 40°.In the current study,an attempt has been made to study the effect of the introduction of vanes in form of rows on parameters like turbulence intensities,Reynolds stresses,turbulent kinetic energy,anisotropy index,and the velocity profile of the flow.It is observed that the profile of variation of turbulence intensities,turbulent kinetic energy,vertical Reynolds stress and velocity over three different marked verticals on a transect are nearly identical whereas a large scatter is observed in the variation of transverse Reynolds stress over the vertical of the aforementioned vertical locations.This observation suggests that flow turbulence is homogeneous over the vertical while scattering in the variation of the transverse Reynolds stress component may be attributed to the presence of secondary currents in the flow.After introducing rows of submerged vanes,the bed turbulence is reduced,hence,helping reduce many scour related phenomenon.It is also observed that a vortex occurred at 0.85 times the height of the vane and the variation of turbulence quantities in the presence of vanes shows the existence of a peak in these quantities.It is observed that as flow moves away from the vane rows,due to the interaction of vortices and the action of vorticity,vortices dampens down and the flow regains homogeneity.After the introduction of submerged vane rows,bed shear stress reduces as fluid from the surface replaces the slow-moving fluid near the bed due to the secondary currents generated by the vanes leading to reduction in the magnitude of turbulence intensities,Reynolds stresses,and turbulent kinetic energy near the bed.The anisotropy index is observed to increase near the bed as induced secondary currents enhanced the turbulence production in the near bed region.All the profiles of parameters obtained in the current study show the existence of a peak or inflexions at a height of 0.85 H from bed(Where,H is the height of the submerged vane).Profiles of parameters obtained in the current study suggest that as the vorticity dampens the vane-generated secondary currents,the scattering in the profiles along the vertical reduces and profiles are observed to regain the variation which they had before the introduction of vane rows,suggesting that flow turbulence has regained its homogeneity.     

Parameterization of near-bed processes under collinear wave and current flows from a two-phase sheet flow model

Sediment transport models require appropriate representation of near-bed processes. We aim here to explore the parameterizations of bed shear stress, bed load transport rate and near-bed sediment erosion rate under the sheet flow regime. To that end, we employ a one-dimensional two-phase sheet flow model which is able to resolve the intrawave boundary layer and sediment dynamics at a length scale on the order of the sediment grain. We have conducted 79 numerical simulations to cover a range of collinear wave and current conditions and sediment diameters in the range 210–460 μm$\mathrm{\mu }\mathrm{m}$. The numerical results confirm that the intrawave bed shear stress leads the free stream velocity, and we assess an explicit expression relating the phase lead to the maximum velocity, wave period and bed roughness. The numerical sheet flow model is also used to provide estimates for the bed load transport rate and to inspect the near-bed sediment erosion. A common bed load transport rate formulation and two typical reference concentration approaches are assessed. A dependence of the bed load transport rate on the sediment grain diameter is observed and parameterized. Finally, the intrawave near-bed vertical sediment flux is further investigated and related to the time derivative of the bed shear stress.     

Bank‐toe processes in incised channels: the role of apparent cohesion in the entrainment of failed bank materials

Numerous processes may instigate bank retreat and the consequent collection of failed cohesive materials at the bank toe. Cohesion between the failed material and the substrate can provide additional strength to resist direct fluvial entrainment. Failed, cohesive material can act as a form of natural bank‐toe protection by consuming and diverting flow energy that may otherwise be used to further scour the basal zone of incising channels. Investigations in Goodwin Creek, Mississippi, have revealed the existence of apparent cohesion between failed, cohesive blocks and their underlying surface. The method used to assess this cohesion involved a pulley system mounted on a tripod and supporting a load cell. Mean and maximum apparent‐cohesion values of 1·08 kPa and 2·65 kPa, respectively, were measured in this way, identifying a source that bonds blocks to the underlying surface. Cohesion values and types vary spatially and temporally. Tensiometric tests beneath blocks suggest that cohesion resulting from matric suction alone may be as much as 3·5 kPa in summer and 1·8 kPa in winter. Apparent cohesion is believed to have been sufficient to help prevent removal of the largest blocks by a peak flow of 66·4m³&sol;s on 23 September 1997. Maximum excess shear stress required to entrain a D₇₅ block can be augmented by as much as 97% by the presence of apparent cohesion at the block–substrate interface when compared with a condition with zero apparent cohesion at the block underside. Given these findings, it is no longer sufficient to estimate block entrainment in the basal area from block size or bed roughness alone, as in a Shields‐type approach. Copyright © 2001 John Wiley & Sons, Ltd.     

Effect of non‐uniformity of flow on velocity and turbulence intensities over a cobble‐bed

Non‐uniform flows encompassing both accelerating and decelerating flows over a cobble‐bed flume have been experimentally investigated in a flume at a scale of intermediate relative submergence. Measurements of mean longitudinal flow velocity u, and determinations of turbulence intensities u′, v′, w′, and Reynolds shear stress ?u_fw_f have been made. The longitudinal velocity distribution was divided into the inner zone close to the bed and the outer zone far from the bed. In the inner zone of the boundary layer (near the bed) the velocity profile closely followed the ‘Log Law’; however, in the outer zone the velocity distribution deviated from the Log Law consistently for both accelerating and decelerating flows and the changes in bed slopes ranging from ?2% to + 2% had no considerable effect on the outer zone. For a constant bed slope (S = ±0·015), the larger the flow rate, the smaller the turbulence intensities. However, no detectable pattern has been observed for u′, v′ and w′ distributions near the bed. Likewise, for a constant flow rate (Q = 0·040 m³/s), with variation in bed slope the longitudinal turbulent intensity profile in the longitudinal direction remained concave for both accelerating and decelerating flows; whereas vertical turbulent intensity (w′) profile presented no specific form. The results reveal that the positions of maximum values of turbulence intensities and the Reynolds shear stress depend not only on the flow structure (accelerating or decelerating) but also on the intermediate relative submergence scale. Copyright © 2009 John Wiley & Sons, Ltd.     

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.     

Hydraulic properties of concentrated flow of a bank gully in the dry‐hot valley region of southwest China

To quantify spatiotemporal variation in hydraulic properties of bank gully concentrated flow, a series of scour experiments were run under water discharge rates ranging from 30 to 120 l min^?1. Concentrated flows were found to be turbulent and supercritical in the upstream catchment area and downstream gully beds. As discharge increased, values of the soil erosion rate, Reynolds number (Re), shear stress, stream power, and flow energy consumption (ΔE) increased while values of the Froude number (Fr) and the Darcy–Weisbach friction factor (resistance f ) did not. With the exception of gully headcut collapse under discharge rates of 60, 90, and 120 l min^?1, a declining power function trend (P < 0.05) in the soil erosion rate developed in the upstream catchment area, headcuts, and downstream gully beds. However, increasing trends were observed in temporal variations of hydraulic properties for downstream gully beds and the upstream catchment area. Despite significant differences in temporal variation between the soil erosion rate and hydraulic property values, relative steady state conditions of the soil erosion rate and ΔE were attained following an initial period of adjustment in the upstream catchment area, headcuts, and downstream gully beds under different discharge rates. A logarithmic growth of flow energy consumption per unit soil loss (ΔE_u) was observed in bank gullies and the upstream catchment area as the experiment progressed, further illustrating the actual reason behind the discrepancy in temporal variation between soil erosion rates and ΔE. Results demonstrate that ΔE can be used to estimate headcut erosion soil loss, but further quantitative studies are required to quantify coupling effects between hydraulic properties and vertical variation in soil mechanical properties on temporal variation for bank gully soil erosion rates. Copyright © 2015 John Wiley & Sons, Ltd.     

Study on the stability of non-cohesive river bank

Frequent bank collapse in nature highlights the need to study the mechanism of bank stability. This paper presents a theoretical analysis and a flume experimental study on the interaction of hydrodynamic conditions and non-cohesive banks of meandering and straight rivers. No bank collapse occurs if the bank angle is smaller than a critical value. The critical angle is a function of a dimensionless parameter K_UD, which is directly proportional to the square of flow velocity near river bed and inversely proportional to the median diameter of bank material. Furthermore, the critical angle reduces with flow velocity and is higher in meandering rivers than in straight rivers. Formulas for estimating the threshold of bank stability are obtained by curve fitting method with experimental data. The results agree with the data measured in the middle and lower reaches of the Yangtze River.     

Effect of changes in fine‐grained matrix on bedload sediment transport in a gravel‐bed river

While clay and silt matrices of gravel‐bed rivers have received attention from ecologists concerned variously with the deteriorating environments of benthic and hyporheic organisms, their impact on sediment entrainment and transport has been explored less. A recent increase of such a matrix in the bed of Nahal Eshtemoa, an ephemeral river of the northern Negev, has more than doubled the boundary shear stress needed to initiate bedload, from 7 N m^‐2 (τ^* = 0.027) during the flash floods of 1991–2001 to 15 N m^‐2 (τ^* = 0.059) during those of 2008–2009. The relation between bedload flux and boundary shear stress continues to be well‐defined, but it is displaced. The matrix now contains a significant amount of silt and clay size material. The reasons for the increased entrainment threshold of bedload are explored. Large‐scale laser scanning of the dry bed reveals a reduction in grain‐scale morphological roughness, while artificial in situ tests of matrix integrity indicate considerable cohesion. The implications for adopting bed material sampling strategies that account for matrix development are assessed. Copyright © 2012 John Wiley & Sons, Ltd.     

Transport of nonsorbing solutes in a streambed with periodic bedforms

Previous studies of hyporheic zone focused largely on the net mass transfer of solutes between stream and streambed. Solute transport within the bed has attracted less attention. In this study, we combined flume experiments and numerical simulations to examine solute transport processes in a streambed with periodic bedforms. Solute originating from the stream was subjected to advective transport driven by pore water circulation due to current–bedform interactions as well as hydrodynamic dispersion in the porous bed. The experimental and numerical results showed that advection played a dominant role at the early stage of solute transport, which took place in the hyporheic zone. Downward solute transfer to the deep ambient flow zone was controlled by transverse dispersion at the later stage when the elapsed time exceeded the advective transport characteristic time t_c (= L/u_c with L being the bedform length and u_c the characteristic pore water velocity). The advection-based pumping exchange model was found to predict reasonably well solute transfer between the overlying water and streambed at the early stage but its performance deteriorated at the later stage. With dispersion neglected, the pumping exchange model underestimated the long-term rate and total mass of solute transfer from the overlying water to the bed. Therefore both advective and dispersive transport components are essential for quantification of hyporheic exchange processes.     

Analytic stage–discharge formulae for flow in straight trapezoidal open channels

Analytic stage–discharge formulae are derived for flow in straight trapezoidal channels, based on the 2D analytic velocity distribution in open channels given by Shiono and Knight [Shiono K, Knight DW, Turbulent open-channel flows with variable depth across the channel. J Fluid Mech 1991;222:617–46]. A simple hand-calculation method is provided. Legendre incomplete elliptic integrals of the first and second kinds and a binomial series expansion are used in the derivation of these analytic formulae, together with physically based hydraulic parameters, such as local friction factor (f), dimensionless eddy viscosity (λ) and secondary flow (Γ). The stage–discharge results obtained from the formulae are shown to be in good agreement with experimental data, as are the corresponding analytic velocity and boundary shear stress distributions. The influences of f, λ and Γ on the stage–discharge relationship are also discussed.     

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.     

Density and undrained shear strength of bed sediment from ND-CPT

The density and the undrained shear strength (s _u) of bed sediments at either side of the Isahaya Bay dike in the Ariake Sea, Japan, were investigated using nuclear density cone penetration tests (ND-CPTs). The nuclear density cone penetrometer (ND-CP) was operated from a boat, conducting 71 ND-CPTs. Furthermore, 26 undisturbed samples were obtained for soil density and s _u measurements to calibrate the ND-CPT data. The results show that the density and s _u obtained from in situ with the ND-CPTs agree well with those from the laboratory tests on undisturbed samples, and the obtained density profiles show good repeatability. The vertical variation in density and s _u of the bed sediment can be obtained from the ND-CPT results. The relations between the density and s _u show that s _u increases with an increase in density, but that this relation is site specific. The values of s _u show an exponentially growing trend and the values of log s _u show a linearly increasing trend with density. The vertical distribution of the bed sediments can be described using the density values obtained with the ND-CPT.