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.     

Turbulence characteristics of flows passing through a tetrahedron frame in a smooth open-channel

The turbulence characteristics of flows passing through a tetrahedron frame were investigated by using a 2-dimensional fiber-optic laser Doppler velocimeter (2-D FLDV). Experiments for uniform flows with different bed slopes under both submerged and un-submerged conditions were carried out in a re-circulating flume with glass side walls. The experimental bed was a smooth fixed bed. It was observed that with the tetrahedron frame the mean longitudinal velocity decrease in the retardation zone. However, both the longitudinal and the vertical turbulence intensities are larger than those for the undisturbed approach flow. The tetrahedron frame may reduce the probability of sediment entrainment by retarding the flow and reducing the boundary shear stress. In addition, it may induce sediment deposition in a sediment laden flow by changing the flow direction and increasing the energy dissipation.     

Velocity and turbulence variations at the edge of saltmarshes

Saltmarsh vegetation significantly influences tidal currents and sediment deposition by decelerating the water velocity in the canopy. In order to complement previous field results, detailed profiles of velocity and turbulence were measured in a laboratory flume. Natural Spartina anglica plants were installed in a 3 m length test section in a straight, recirculating flume. Different vegetation densities, water depths and surface velocities were investigated. The logarithmic velocity profile, which existed in front of the vegetation, was altered gradually to a skimming-flow profile, typical for submerged saltmarsh vegetation. The flow reduction in the denser part of the canopy also induced an upward flow (the current was partially deflected by the canopy). The skimming flow was accompanied by a zone of high turbulence co-located with the strongest velocity gradient. This gradient moved upward and the turbulence increased with distance from the edge of the vegetation. Below the skimming flow, the velocity and the turbulence were low. The structure of the flow in the canopy was relatively stable 2 m into the vegetation. The roughness length (z₀) of the vegetation depends only on the vegetation characteristics, and is not sensitive to the current velocity or the water depth. Both the reduced turbulence in the dense canopy and the high turbulence at the top of the canopy should increase sediment deposition. On the other hand, the high turbulence zone just beyond the vegetation edge and the oblique upward flow may produce reduced sedimentation; a phenomenon that was observed near the vegetation edge in the field.     

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.     

Mean and turbulent flow fields in a simulated ice‐covered channel with a gravel bed: some laboratory observations

Northern rivers experience freeze‐up over the winter, creating asymmetric under‐ice flows. Field and laboratory measurements of under‐ice flows typically exhibit flow asymmetry and its characteristics depend on the presence of roughness elements on the ice cover underside. In this study, flume experiments of flows under a simulated ice cover are presented. Open water conditions and simulated rough ice‐covered flows are discussed. Mean flow and turbulent flow statistics were obtained from an Acoustic Doppler Velocimeter (ADV) above a gravel‐bed surface. A central region of faster flow develops in the middle portion of the flow with the addition of a rough cover. The turbulent flow characteristics are unambiguously different when simulated ice covered conditions are used. Two distinct boundary layers (near the bed and in the vicinity of the ice cover, near the water surface) are clearly identified, each being characterized by high turbulent intensity levels. Detailed profile measurements of Reynolds stresses and turbulent kinetic energy indicate that the turbulence structure is strongly influenced by the presence of an ice cover and its roughness characteristics. In general, for y/d > 0·4 (where y is height above bed and d is local flow depth), the addition of cover and its roughening tends to generate higher turbulent kinetic energy values in comparison to open water flows and Reynolds stresses become increasingly negative due to increased turbulence levels in the vicinity of the rough ice cover. The high negative Reynolds stresses not only indicate high turbulence levels created by the rough ice cover but also coherent flow structures where quadrants one and three dominate. Copyright © 2012 John Wiley & Sons, Ltd.     

Turbulent flow structure in a gravel-bed river: Markov chain analysis of the fluctuating velocity profile

Three electromagnetic current meter probes were deployed in a Canadian gravel-bed river to obtain simultaneous records at 10 Hz of streamwise (u) and vertical (v) velocity components at three heights above the bed. By looking at the positive and negative signs of the instantaneous fluctuations from the time-average values of each velocity component at each height, the fluctuating velocity profile of u or v can be treated as a Markov chain with eight states and its statistical properties can be tested against null hypotheses based on the absence of spatial structure. We report results of this novel approach. The most common states of the u profile were those with either higher-than-average or lower-than-average velocities at all heights; these ‘high speed’ and ‘low speed’ states persisted for up to 3 s. The most common v profiles were all-upwards or all-downwards, but these persisted for shorter times than the high speed and low speed u profiles. Analysis of transition probabilities shows statistically significant tendencies for acceleration from the low speed u profile, and change from all-upwards to all-downwards v profile, to take place progressively from the uppermost probe downwards, in a sweep-like way. Deceleration from the high speed to low speed u profile and change from all-downwards to all-upwards v profile (burst-like behaviour) do not show such clear patterns. The results are interpreted in terms of the advection of inverted wedges of relatively high-momentum fluid, followed by more chaotic structures. A separate set of flow visualization experiments over a mixed gravel bed in a flume supports the presence of advected wedge structures, the decelerating part of the sequence corresponding to irregular ejections of near-bed fluid.     

Detection and reconstruction of large‐scale coherent flow structures in gravel‐bed rivers

Large‐scale flow structures (LSFS) in the streamwise direction are important features of gravel‐bed river flows, because they may contribute to sediment transport and gas exchange. In the present study, these structures are detected using Huang's empirical mode decomposition and reconstructed with phase‐averaging techniques based on a Hilbert transform of the velocity signal. The analysis is based on the fluctuating component of 15 quasi‐instantaneous velocity profiles measured with a three‐dimensional (3D) acoustic Doppler velocity profiler (ADVP) in an armoured gravel‐bed river with a low relative submergence of 2.9 (ratio between flow depth and bed grain diameter). LSFS were identified in most of the measured profiles and consistently showed similar features. We were able to characterize the geometry of these large‐scale coherent structures: the front has a vertical linear shift in the time domain and a vertical profile corresponding to a first quarter moon with the apex situated at z/h ≈ 0.4. In the vertical, the front scales with flow depth h, and in the streamwise direction, LSFS scale with three to seven times the mean flow depth. On the bed, the effect of LSFS is a periodic non‐linear variation of the friction velocity on average between 0.90 and 1.10 times the mean value. A model for the friction velocity cycle resulting from LSFS oscillation is presented. Copyright © 2014 John Wiley & Sons, Ltd.     

Experimental investigation on local shear stress and turbulence intensities over a rough non-uniform bed with and without sediment using 2D particle image velocimetry

The current work focuses on locally resolving velocities,turbulence,and shear stresses over a rough bed with locally non-uniform character.A nonporous subsurface layer and fixed interfacial sublayer of gravel and sand were water-worked to a nature-like bed form and additionally sealed in a hydraulic flume.Two-dimensional Particle Image Velocimetry(2 D-PIV) was applied in the vertical plane of the experimental flume axis.Runs with clear water and weak sediment transport were done under slightly supercritical flow to ensure sediment transport conditions without formation of considerable sediment deposits or dunes.The study design included analyzing the double-averaged flow parameters of the entire measurement domain and investigating the flow development at 14 consecutive vertical subsections.Local geometrical variabilities as well the presence of sediment were mainly reflected in the vertical velocity component.Whereas the vertical velocity decreased over the entire depth in presence of sediment transport,the streamwise velocity profile was reduced only within the interfacial sublayer.In the region with decelerating flow conditions,however,the streamwise velocity profile systematically increased along the entire depth extent.The increase in the main velocity(reduction of flow resistance)correlated with a decrease of the turbulent shear and main normal stresses.Therefore,effects of rough bed smoothening and drag force reduction were experimentally documented within the interfacial sublayer due to mobile sediment.Moreover,the current study leads to the conclusion that in nonuniform flows the maximum Reynolds stress values are a better predictor for the bed shear stress than the linearly extrapolated Reynolds stress profile.This is an important finding because,in natural flows,uniform conditions are rare.     

Effect of slope angle of an artificial pool on distributions of turbulence

Experiments were carried out over a 2-dimentional pool with a constant length of 1.5 m and four different slopes.The distributions of velocity,Reynolds stress and turbulence intensities have been studied in this paper.Results show that as flow continues up the exit slope,the flow velocity increases near the channel bed and decreases near the water surface.The flow separation was not observed by ADV at the crest of the bed-form.In addition,the length of the separation zone increases with the increasing of entrance and exit slopes.The largest slope angle causes the maximum normalized shear stress.Based on the experiments,it is concluded that the shape of Reynolds stress distribution is generally dependent on the entrance and exit slopes of the pool.Also,the shape of Reynolds stress distribution is affected by both decelerating and accelerating flows.Additionally,with the increase in the slope angle,secondary currents are developed and become more stable.Results of the quadrant analysis show that the momentum between flow and bed-form is mostly transferred by sweep and ejection events.     

Neural network modelling for mean velocity and turbulence intensities of steep channel flows

The main purpose of this study is to evaluate the potential of simulating the profiles of the mean velocity and turbulence intensities for the steep open channel flows over a smooth boundary using artificial neural networks. In a laboratory flume, turbulent flow conditions were measured using a fibre‐optic laser doppler velocimeter (FLDV). One thousand and sixty‐four data sets were collected for different slopes and aspect ratios at different locations. These data sets were randomly split into two subsets, i.e. training and validation sets. The multi‐layer functional link network (MFLN) was used to construct the simulation model based on the training data. The constructed MFLN models can almost perfectly simulate the velocity profile and turbulence intensity. The values of correlation coefficient (γ) are close to one and the values of root mean square error (RMSE) are close to zero in all conditions. The results demonstrate that the MFLN can precisely simulate the velocity profiles, while the log law and Reynolds stress model (RSM) are less effective when used to simulate the velocity profiles close to the side wall. The simulated longitudinal turbulence intensities yielded by the MFLN were also fairly consistent with the measured data, while the simulated vertical turbulence intensities by the RSM were not consistent with the measured data. Copyright © 2007 John Wiley & Sons, Ltd.     

A bed‐load transport model for rough turbulent open‐channel flows on plane beds

Data from flume studies are used to develop a model for predicting bed‐load transport rates in rough turbulent two‐dimensional open‐channel flows moving well sorted non‐cohesive sediments over plane mobile beds. The object is not to predict transport rates in natural channel flows but rather to provide a standard against which measured bed‐load transport rates influenced by factors such as bed forms, bed armouring, or limited sediment availability may be compared in order to assess the impact of these factors on bed‐load transport rates. The model is based on a revised version of Bagnold's basic energy equation i_bs_b = e_bω, where i_b is the immersed bed‐load transport rate, ω is flow power per unit area, e_b is the efficiency coefficient, and s_b is the stress coefficient defined as the ratio of the tangential bed shear stress caused by grain collisions and fluid drag to the immersed weight of the bed load. Expressions are developed for s_b and e_b in terms of G, a normalized measure of sediment transport stage, and these expressions are substituted into the revised energy equation to obtain the bed‐load transport equation i_b = ω G ^3·4. This equation applies regardless of the mode of bed‐load transport (i.e. saltation or sheet flow) and reduces to i_b = ω where G approaches 1 in the sheet‐flow regime. That i_b = ω does not mean that all the available power is dissipated in transporting the bed load. Rather, it reflects the fact that i_b is a transport rate that must be multiplied by s_b to become a work rate before it can be compared with ω. It follows that the proportion of ω that is dissipated in the transport of bed load is i_bs_b/ω, which is approximately 0·6 when i_b = ω. It is suggested that this remarkably high transport efficiency is achieved in sheet flow (1) because the ratio of grain‐to‐grain to grain‐to‐bed collisions increases with bed shear stress, and (2) because on average much more momentum is lost in a grain‐to‐bed collision than in a grain‐to‐grain one. Copyright © 2006 John Wiley & Sons, Ltd.     

Studies on emergent flow over vegetative channel bed with downward seepage

Experimental observations in a tilting flume having a bed covered with rice plants (Oryza sativa) are used to analyse the flow characteristics of flexible emergent vegetation with downward seepage. The flow velocity for no-seepage and with seepage is reduced by, on average, 52% and 33%, respectively, as the flow reaches the downstream end with vegetation. Higher Reynolds stress occurs at the start of the vegetation zone; hence, bed material transport occurs in this region. The results indicate that the bed is no longer the primary source of turbulence generation in vegetated flow; rather it is dominated by turbulence generated by the vegetation stems. The local effect of the presence of vegetation causes variations in the hydrodynamic characteristics along the vegetated portion of the channel, which leads to erosion and deposition in the vegetation zone. The experiments show that vegetation can provide considerable stability to channels by reducing channel erosion even with downward seepage.     

Flow structure over a wavy bed with vegetation cover

On the basis of experiments carried out in flume with a wavy bed with vegetation cover, flow velocity, turbulence intensities and Reynolds stress distributions are investigated. The wavy bed was similar to dune in this study. The fixed artificial dunes were constructed over the bed and artificial vegetation put over them in a laboratory flume. An Acoustic Doppler Velocimeter and spatially-averaged method were applied to determine turbulent flow components and shear velocity. Results were compared with a gravel bedform. It was observed that vegetation cover influences considerably the flow structure and displays clearly the flow separation and reattachment point. The law of the wall was not valid within the vegetation cover, but it was fitted well to the zone above the vegetation cover within the inner layer. For a wavy bed having the same dimensions, shear velocity and friction factor over vegetation cover are 1.7 and 2.6 times of those for the gravel bedform, respectively. The results of laboratory study were compared with those of river study.     

Velocity distribution in a gradually accelerating free surface flow

This study investigates the interaction of the vertical velocity v and the streamwise velocity u in a gradually accelerating flow. The analytical result shows that the momentum of uv driven by the mean velocities in a non-uniform flow is not negligible. This additional momentum directly results in the concave profiles of Reynolds shear stress in gradually accelerating flows, a departure from the expected linear profile. Consequently, this momentum causes the maximum velocity to be located below the free surface, i.e., the dip-phenomenon. This paper investigated the interactions of the Reynolds shear stress, non-zero vertical velocity and dip-phenomenon, it is found that the non-zero vertical velocity causes the dip-phenomenon. The approach is tested using the experimental data of Song and others, and good agreements between the predicted and measured velocity profiles have been achieved.     

Characteristics of turbulence over the semi-fixed desert area north of Xinjiang,China

As the largest fixed and semi-fixed desert in China, the Gurbantünggüt Desert undergoes a long period of snow cover in the winter and the rapid growth of ephemeral plants in the spring, presenting obvious seasonal changes in the underlying desert surface type, which can lead to variation in the turbulence of the near-surface boundary layer turbulence over the desert. In this study, gradient tower data and eddy covariance data from 2017 were analysed to investigate the turbulence characteristics of the different surface boundary layers in the hinterland of the Gurbantünggüt Desert. The results indicate that stable atmospheric conditions in the desert occur exclusively during the early morning and at night in the desert, and the onset and duration of this stable state varies seasonally. Two regimes of intermittent turbulence occur during the night, a weak turbulent regime that occurs when the wind speed is less than the threshold and a strong turbulent regime when the wind speed exceeds the threshold, and different wind speed thresholds were observed at each level. These parameters follow a seasonal pattern of summer (July) > spring (April) > autumn (October) > winter (January) in terms of magnitude. The mean turbulence intensities of the along-wind, cross-wind and vertical wind are 0.5, 0.47 and 0.14, respectively, with I_u > I_v > I_w. The normalized standard deviation of the wind velocity components (σ_u, σ_v and σ_w) generally satisfies a 1/3 power-law relation. Our results show that the night-time turbulence regime classification for the Gurbantünggüt Desert strongly depends on meteorological and orographic features, and the intermittent turbulent events have the non-stationarity of the flow in common. The results can contribute to the study of land surface processes, climate change and desertification in inland arid desert areas.     

Experiment on morphological and hydraulic adjustments of step-pool unit to flow increase

Exceptional flood events with a return period of about 50 years can be destructive to step-pool channel segments. However, field investigations and flume experiments have not examined the hydraulic and morphological feedbacks of step-pool morphology during unsteady hydrographs of exceptional flood events. We performed a series of flume experiments with a manually constructed step model, perturbed with three hydrographs that varied in the rate of water supply change. The bed texture, topography, flow regimes, surface flow field and water depth were characterized and measured as the flow rate was increased during the experiments. A distinct pool feature emerged downstream of the manually constructed step when the flow rate exceeded the threshold scaled to the peaks of ordinary flood events in well-graded mountain streams. The pool feature was modified in several different ways with flow rate increase. The bed surface steadily coarsened, micro-bedforms developed and became more pronounced, the bed topography became more spatially complex based on analysis using the Hurst exponent, and last, pool depth steadily increased. Pool modification was also linked to the flow regime: the impinging jet regime led to grain size segmentation in the pool while the jump regime contributed to decelerating flow velocity. The steeper rising limb of hydrograph led to a less developed pool feature, with smaller sized micro-bedforms in the pool bottom to outlet, and higher discharge threshold for distinct coarsening and scouring in the pool. The estimated energy dissipation within the step-pool unit decreased as a power function from low to high flow, quantified as the ratio h_c/H_S, where h_c is the critical water depth and H_S is scour depth. Our results highlight the interaction between morphology, hydraulics, and energy dissipation of step-pool unit and the crucial role of hydrograph shape on the interaction during flow increase © 2019 John Wiley & Sons, Ltd.     

The impact of plant morphology on flow structure: comparative analysis of two types of submerged flexible macrophyte

ABSTRACT

The presence of aquatic vegetation in riverine and lacustrine environments alters the mean and turbulent flow structure and thus impacts the fate and transport of sediment and contaminants. Turbulent flows through Vallisneria natans (V. natans) and Potamogeton malaianus (P. malaianus) were investigated in a laboratory flume. The impact of plant morphology on mean velocity profile and turbulence distribution was analysed and discrepancies in flow alteration caused by different types of macrophyte were highlighted. Results show that a dense canopy of submerged macrophyte leads to a velocity profile featuring a counter velocity gradient in the lower part of the canopy. Negative Reynolds stress and its local maximum were observed there. Discrepancies in flow structure caused by different morphologies of both tested plants were further identified. With smaller frontal area in the lower part of the canopy, P. malaianus causes a much bigger gradient and local maximum in the velocity profile, and thus a larger local stress maximum than V. natans. The mean velocity gradient around the top of canopy, the Reynolds stress and the turbulence kinetic energy at the canopy interface are smaller than for the flow through the V. natans canopy. Larger reduction of the mean velocity within the V. natans canopy makes the suspended sediment of fine particles more easily deposited than in the P. malaianus canopy.     

Macroturbulent coherent structures in an ice‐covered river flow using a pulse‐coherent acoustic Doppler profiler

The aim of this work is to compare macroturbulent coherent structures (MCS) geometry and organization between ice covered and open channel flow conditions. Velocity profiles were obtained using a Pulse‐Coherent Acoustic Doppler Profiler in both open channel and ice‐covered conditions. The friction imposed by the ice cover results in parabolic shaped velocity profiles. Reynolds stresses in the streamwise (u) and vertical (v) components of the flow show positive values near the channel bed and negative values near the ice cover, with two distinctive boundary layers with specific turbulent signatures. Vertically aligned stripes of coherent flow motions were revealed from statistics applied to space‐time matrices of flow velocities. In open channel conditions, the macroturbulent structures extended over the entire depth of the flow whereas they were discontinued and nested close to the boundary walls in ice‐covered conditions. The size of MCS is consequently reduced in scale under an ice cover. The average streamwise length scale is reduced from 2.5 to 0.4Y (u) and from 1.5 to 0.4Y (v) where Y is the flow depth. In open channel conditions, the vertical extent of MCS covers the entire flow depth, whereas the vertical extent was in the range 0.58Y–1Y (u) and 0.81Y–1Y (v) in ice‐covered conditions. Under an ice cover, each boundary wall generates its own set of MCS that compete with each other in the outer region of the flow, enhancing mixing and promoting the dissipation of coherent structures. Copyright © 2012 John Wiley & Sons, Ltd.     

Hydrological characteristics of vegetated river flows: a laboratory flume study

Abstract

Laboratory flume experiments were undertaken to measure the vertical profiles of mean flow velocity for three different flow discharges and four different stem densities of Hydrilla verticillata. The data were used to calculate three parameters, namely Manning's roughness coefficient, the Reynolds number and the Froude number. In addition, empirical equations were obtained for the vertical distribution of measured flow velocity within the transitional zone and above the plant canopy. The results show that: (a) the vertical distribution of measured flow velocity exhibits three zone profiles; (b) Manning's roughness coefficient decreases with increasing depth-averaged flow velocity; (c) the relationship between Manning's roughness coefficient and the depth-averaged flow velocity is within the smooth left inverse curve; (d) Manning's roughness coefficient significantly changes with increasing density of Hydrilla; (e) the Froude number is independent of the density of Hydrilla; and (f) both the Reynolds number and the Froude number increase with increasing depth-averaged flow velocity.

Citation Shi, J.Z., Li, Y.-H., Hughes, J.M.R., and Zhao, M., 2013. Hydrological characteristics of vegetated river flows: a laboratory flume study. Hydrological Sciences Journal, 58 (5), 1047–1058.

Editor Z.W. Kundzewicz     

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