Power-law index for velocity profiles in open channel flows

Turbulence theory has demonstrated that the log law is one of the established theoretical results for describing velocity profiles, which is in principle applicable for the near-bed overlap region, being less than about 20% of the flow depth. In comparison, the power law that is often presented in an empirical fashion could apply to larger fraction of the flow domain. However, limited information is available for evaluating the power-law exponent or index. This paper attempts to show that the power law can be derived as a first-order approximation to the log law, and its power-law index is computed as a function of the Reynolds number as well as the relative roughness height. The result obtained also coincides with the fact that the one-sixth power included in the Manning equation is of prevalent acceptance, while higher indexes would be required for flows over very rough boundaries.     

Velocity profiles and basal stresses in natural debris flows

The internal deformation within debris flows holds essential information on dynamics and flow resistance of such mass-wasting processes. Systematic measurements of velocity profiles in real-scale debris flows are not yet available. Additionally, data on basal stresses of the solid and the fluid phase are rare. Here, we present and analyse measurements of vertical velocity profiles in two debris flows naturally occurring in the Gadria Creek, Italy. The method is based on cross-correlation of paired conductivity signals from an array of sensors installed on a fin-shaped wall located in the middle of the channel. Additionally, we measure normal stress and pore fluid pressure by two force plates with integrated pressure transducers. We find internal deformation throughout the flows. Only at the very front was some en-bloc movement observed. Velocity profiles varied from front to tail and between flows. For one debris flow, pore fluid pressure close to normal stress was measured, whereas the other flow was less liquefied. The median shear rates were mostly less than 5 s⁻¹ and Savage numbers at the basal layer ranged from 0.01 to 1. Our results highlight the variable nature of debris flows and provide quantitative data on shear rate and basal stress distribution to help guide model development for hazard assessment and landscape evolution. © 2020 The Authors. Earth Surface Processes and Landforms published by 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.     

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.     

Estimation of the mean velocity of particulate flows by counting

Using Smoluchowski's theory of the probability after-effect it is possible to estimate the mean speed or velocity of a particulate flow by counting the number of particles present in a selected region at a sequence of equal time intervals. Apart from a knowledge of the dimensions of the region the only conditions are that the process is, in a wide sense, stationary and that the speeds of individual particles are independent. Subsequent refinements and extensions to the theory by Furth, Ruben, Rothschild and Lindley are incorporated to provide a method of velocity estimation of wide application in geomorphology. Finally, a numerical example on pedestrian speeds is assessed against an independent estimate.     

Velocity and concentration profiles of particle movement in sheet flows

Sheet flows occur widely in natural free-surface flows including rivers in flood, tidal estuaries and coastal waters in storm conditions when bed shear stress becomes sufficiently high. Particle volumetric concentration in sheet flows normally follows a linear distribution with the Rouse [Rouse H. Modern conceptions of the mechanics of fluid turbulence. Trans ASCE, 1937;102:463–543] distribution applicable in the dilute water column above the sheet-flow layer. However, a well-verified formula for determining particle velocity distribution in sheet flows is still lacking. This paper presents formulas to describe the particle velocity profile in steady or oscillatory sheet flows. They compare well with measured data. In particular, the novel formula for determining the particle velocity at the top of bedload–sediment-dominated sublayer in sheet flows is also well verified with measured data.     

Sensitivity of bed shear stress estimated from vertical velocity profiles: the problem of sampling resolution

Bed shear stress in open channel flows is often estimated from the logarithmic vertical velocity profile. However, most measuring devices used in the field do not allow for flow velocity to be measured very close to the bed. The lack of near-bed measurements is a critical loss of information which may affect bed shear stress estimates. Detailed velocity profiles obtained from a field acoustic Doppler velocimeter over three different bed roughnesses clearly show that the inclusion of near-bed points is critical for the estimation of bed shear stress in a shallow river environment. Moreover, the results indicate that using the full flow depth instead of the bottom 20 per cent of the profile generates an underestimation of the shear stress when flow is uniform. © 1998 John Wiley & Sons, Ltd.     

Vertical profiles of fluid velocity and suspended sediment concentration in nearshore

Based on the power function of velocity and the friction velocity,a velocity profile is obtained.By solving the Schmidt’s diffusion equation,an equilibrium suspended sediment concentration profile is further deduced.The profiles of velocity and suspended sediment concentration agree well with the field data,and the profile of suspended sediment concentration avoids the unreasonableness of the classical Rouse profile such as a zero value at the water surface.According to these profiles,an expression which is easy to use for calculating the suspended sediment transport rate is derived.     

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.     

塔里木盆地中原探区速度场研究方法

利用自行编程设计的速度场算法,建立了塔里木盆地中原探区的速度场模型,并应用于油气勘探生产之中．在塔中地区,影响平均速度的主要因素是地层埋深和火成岩的岩性．在巴楚地区,影响平均速度变化的主要因素是大的构造运动形成的多角度不整合界面和断距较大的断层．总结出了一套适合地质复杂地区速度场建立的方法;利用该速度场进行变速成图,能够提高成图精度、排除假构造、发现新的圈闭、减小勘探风险,落实发现了一批圈闭,提供探井多口,实现了油气勘探的突破。     

The effect of roughness configuration on velocity profiles in an artificial channel

In order to determine the effect of bed roughness on velocity distribution, we used seven different configurations of bed roughness, with 16 test runs of varying discharge and slope for each configuration. For each run, one-dimensional velocity profiles were measured at 1 cm vertical increments over the crest of the roughness element, and at intervals of 4·25 cm downstream. Results indicate that velocity profile shape remains fairly constant for a given slope and roughness configuration as discharge increases. As slope increases, the profiles become less linear, with a much larger near-bed velocity gradient and a more pronounced velocity peak close to 0·6 flow depth at the measurement point immediately downstream from the roughness element. The zone of large near-bed velocity gradients increases in both length and depth as roughness concentration decreases, up to a length/height ratio of about 9, at which point maximum flow resistance occurs. Longitudinal roughness elements do not create nearly as much flow resistance as do transverse elements. Rates of velocity increase suggest that roughness elements spaced at a length/height ratio of about 9 are most effective at creating flow resistance over a range of discharges in channels with steeper slopes. © 1998 John Wiley & Sons, Ltd.     

Visualization of the turbulent flow structure in a gravel-bed river

A novel technique for visualizing turbulent flow data from a gravel-bed river is presented. The time development of flow velocity and shear stress at three heights is displayed using a computer program. This can be used to observe how the fluctuations of velocity and shear stress interact both spatially and temporally. We highlight examples of flow events which are important for the understanding of flow dynamics. The visualization suggests that the turbulent flow-field is characterized not only by coherence over time at a point, but also by spatial interdependence between points. We suggest that this new visualization approach will assist further interpretation of statistical analyses of turbulent signals, as well as focusing future measurement strategies by providing a clearer spatio-temporal picture of the flow structure.     

Characterisation of shear wave velocity profiles of non-uniform bi-layer soil deposits: Analytical evaluation and experimental validation

A crucial aspect of physical geotechnical model tests (under both 1-g and n-g conditions) is the evaluation of the initial (low-strain) stiffness of the soil layers of the sample test deposit, especially in the case of coarse materials. While for uniform soil deposits this issue can be addressed in a straightforward manner, e.g. by determining the fundamental frequency through the transfer function of an applied white-noise excitation, the problem becomes cumbersome for multi-layered deposits. After reviewing a number of available theoretical solutions, this paper illustrates a simplified yet reliable analytical procedure for determining the shear wave velocity profile (V_s) in a single or bi-layer deposit, taking into account the inhomogeneity of the individual soil layers, under the hypothesis of vanishing shear modulus at ground surface. The fundamental natural frequency of the inhomogeneous bi-layer deposit is analysed using the Rayleigh quotient procedure. The associated shape function is evaluated by considering the equilibrium of the soil column under a pseudo-static lateral inertial excitation imposed at its base, accounting for both layering and inhomogeneity. A validation of the proposed method is provided by comparing numerical results obtained from both time- and frequency- domain analyses against experimental data on Leighton Buzzard sand, from a recently-completed research project conducted on the shaking table facility at BLADE Laboratory, University of Bristol (UK).     

P‐wave velocity distribution in basalt flows of the Enni Formation in the Faroe Islands from refraction seismic analysis

The main objective of this work is to establish the applicability of shallow surface‐seismic traveltime tomography in basalt‐covered areas. A densely sampled ～1300‐m long surface seismic profile, acquired as part of the SeiFaBa project in 2003 ( Japsen et al. 2006 ) at Glyvursnes in the Faroe Islands, served as the basis to evaluate the performance of the tomographic method in basalt‐covered areas. The profile is centred at a ～700‐m deep well. V_P, V_S and density logs, a zero‐offset VSP, downhole‐geophone recordings and geological mapping in the area provided good means of control. The inversion was performed with facilities of the Wide Angle Reflection/Refraction Profiling program package ( Ditmar et al. 1999 ). We tested many inversion sequences while varying the inversion parameters. Modelled traveltimes were verified by full‐waveform modelling. Typically an inversion sequence consists in several iterations that proceed until a satisfactory solution is reached. However, in the present case with high velocity contrasts in the subsurface we obtained the best result with two iterations: first obtaining a smooth starting model with small traveltime residuals by inverting with a high smoothing constraint and then inverting with the lowest possible smoothing constraint to allow the inversion to have the full benefit of the traveltime residuals. The tomogram gives usable velocity information for the near‐surface geology in the area but fails to reproduce the expected velocity distribution of the layered basalt flows. Based on the analysis of the tomogram and geological mapping in the area, a model was defined that correctly models first arrivals from both surface seismic data and downhole‐geophone data.     

基于GPS速度场变化结果研究汶川地震前后南北地震带地壳运动动态特征

本文针对制约多期GPS速度场动态演化特征分析的关键问题,提出速度场稳定基准选取中顾及基准偏移的影响,给出了改进拟准检定(QUAD)初选指标的方法,有效解决多期速度场的基准偏移对粗差剔除的影响.并在此基础上通过对1999—2013年南北地震带地区多期GPS速度场做以华南地块为统一参考基准的处理、最小二乘配置统一协方差参数估算,获取了南北带地区多期GPS速度场的网格化结果.结果显示: (1) 汶川地震影响在震后迅速衰减;震前2004—2007年及2007—2009年相对于1999—2004年南北地震带地区中北部地区存在大范围的北东向运动增强.(2) 2007—2009年相对于2004—2007年的速度场差值变化图像显示,这期间汶川地震的调整影响范围较大,鲜水河左旋剪切有所减弱,龙门山南段应变积累增强.(3) 川滇块体南东向的挤出滑移在2011—2013年相对2009—2011年有所增强.     

Listen to the sound of moving sediment in a small gravel-bed river

In order to assess the dynamics of rivers, a reliable characterization of bedload transport particularly during unsteady flow regimes is required. In contrast to highly energetic cases in hillslope areas, we aim to answer the question whether the usage of acoustic measurements can improve the characterization of bedload in small rivers draining low land mountains with comparatively low water discharge and bedload. In addition to the investigation of natural flood events, controlled floods were generated by releasing water from a reservoir into a small gravel-bed stream. The controlled releases allow for an evaluation of bedload solely from channel storage or bank erosion. For acoustical in-situ characterization of bedload transport, hydrophones were mounted onto the bottom side of steel plates, thus recording the impacts of sediments via the acoustic vibrations on the surface of the plates while at the same time minimizing the disturbing noise resulting from water turbulence. Corresponding bedload traps are removable boxes with open lids fixed in the riverbed so that bedload material registered by the hydrophone is trapped. The acoustic signals correlate well with the quantity of the transported material. During summer flood events the highest transport rates occur at the beginning of the rising limb fea-turing clockwise hysteresis. This is due to the rising transport energy of the flow and the presence of loose, unconsolidated material. During typical winter flood events bedload shows anticlockwise loops. The intensification of bedload conveyance after the runoff peak can be explained by a decreasing stability of the bed material from the beginning to the end of a transport event. Anticlockwise behavior also results from a combination of bedload exhaustion in the vicinity of the monitoring station with a delayed arrival of new material from distal sources later in the hydrograph.     

Roughness effect on the correction factor of surface velocity for rill flows

Flow velocity is one of the most important hydrodynamic variables for both channelized (rill and gullies) and interrill erosive phenomena. The dye tracer technique to measure surface flow velocity V_s is based on the measurement of the travel time of a tracer needed to cover a known distance. The measured V_s must be corrected to obtain the mean flow velocity V using a factor α_v = V/V_s which is generally empirically deduced. The V_s measurement can be influenced by the method applied to time the travel of the dye-tracer and α_v can vary in different flow conditions. Experiments were performed by a fixed bed small flume simulating a rill channel for two roughness conditions (sieved soil, gravel). The comparison between a chronometer-based (CB) and video-based (VB) technique to measure V_s was carried out. For each slope-discharge combination, 20 measurements of V_s, characterized by a sample mean V_m, were carried out. For both techniques, the frequency distributions of V_s/V_m resulted independent of slope and discharge. For a given technique, all measurements resulted normally distributed, with a mean equal to one, and featured by a low variability. Therefore, V_m was considered representative of surface flow velocity. Regardless of roughness, the V_m values obtained by the two techniques were very close and characterized by a good measurement precision. The developed analysis on α_v highlighted that it is not correlated with Reynolds number for turbulent flow regime. Moreover, α_v is correlated neither with the Froude number nor with channel slope. However, the analysis of the empirical frequency distributions of the correction factor demonstrated a slope effect. For each technique (CB, VB)-roughness (soil, gravel) combination, a constant correction factor was statistically representative even if resulted in less accurate V estimations compared to those yielded by the slope-specific correction factor.     

An appraisal of the velocity-reversal hypothesis for stable pool-riffle sequences in the river severn,England

The ‘velocity-reversal hypothesis’ is the linchpin for a number of recent conceptual models pertaining to sediment sorting and the maintenance of pool-riffle sequences in gravel-bedded streams. The literature in support of the hypothesis together with published adverse criticism is reviewed. It is concluded that convincing evidence for the ubiquitous occurrence of such a reversal in a range of channel geometries is currently unavailable. Continuity considerations indicate that riffles need to be considerably wider than pools for a reversal in the mean velocity to occur under conditions of subcritical flow, high stage, and stable morphology. These observations are substantiated by a detailed study of the hydraulic geometry of stable pool-riffle sequences in the River Severn, England. Neither the sectionally-averaged velocity nor the near-bed shear velocity is sensibly greater in the pools than over the riffles during bankfull or near bankfull flow. Instead a tendency towards equalization of the values of average hydraulic variables is noted as discharge increases. A detailed investigation of the three-dimensional character of the flow is required to demonstrate whether the entrainment forces within pools can locally exceed those over neighbouring riffles. Unusual behaviour of the energy gradient over riffles during moderate discharges is related to backwater effects as mediated by the spacing of the riffles. The hydraulic data are used to comment on the stability of the test reaches in the context of the development of the River Severn in the vicinity of Shrewsbury.     

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.