VELOCITY PROFILES OF SEDIMENT-LADEN FLOW

The time-average velocity profiles of the flows carrying natural sand particles and three kinds of plastic particles as suspension and neutrally buoyant load are measured and analyzed. The velocity profiles of the sediment-laden flow can approximately be divided into two regions - the near-bed region and the far-bed region. Main factors affecting the velocity profiles are viscosity, density gradient, grain shear stress and damping of turbulence due to particles. Based on these physical conceptions, a velocity profile model of sediment-laden flow is developed. It agrees well with the experimental data. The discrepancy is 1.57% for the plastic particle-laden flow and 3.67% for the natural sand-laden flow. In the far-bed region, von Karman constants are smaller than those of the clear water flow.     

LONGITUDINAL DISPERSION IN SEDIMENT-LADEN OPEN CHANNEL FLOWS

Laboratory experiments on longitudinal dispersion in clear-water and sediment-laden open channel flows are reported. Data from these experiments and those available from previous studies indicate that the suspended sediment present in the flow affects the longitudinal dispersion process. The observed velocity distributions over the depth of sediment-laden flows indicate that the velocity deviates from the mean velocity more in sediment-laden flows than in clear-water flows. The velocity distributions over the cross section and secondary flow in the channel are also expected to be altereddue to the presence of suspended sediments in the flow. For these reasons, more dispersion is found in sediment-laden flows than in corresponding clear-water flows. A predictor for the dispersion coefficient in sediment-laden flows is proposed.     

INHERENT DISTRIBUTION LAW OF TURBULENT INTENSITY IN SEDIMENT-LADEN FLOW

LINTRODUCTIONTheturbulenceoftheflowvelocityisresultedfromthecombinationofinnerinstabilityoftheflowandouterdisturbance.Int1Vo-dimensionalsteadyuniformflowasac7eknow.nomattersedimentconcentrationis0ingeneralorveryhigh.TheverticaldistributionofturbulentintensityoflongitudinalvelocityQhasasimilartendenc}'fohasaminimumatthesurface,thenincreasesinpacewiththedecreasingofthedistancefromthebedy,atsomewherenearthebed.Itreachesamaalmtlm(forhyperconcentratedflowwithaflowcoreinwhichvelocitygradientdu…     

Reinvestigation on mixing length in an open channel turbulent flow

The present study proposes a model on vertical distribution of streamwise velocity in an open channel turbulent flow through a newly proposed mixing length, which is derived for both clear water and sediment-laden turbulent flows. The analysis is based on a theoretical consideration which explores the effect of density stratification on the streamwise velocity profile. The derivation of mixing length makes use of the diffusion equation where both the sediment diffusivity and momentum diffusivity are taken as a function of height from the channel bed. The damping factor present in the mixing length of sediment-fluid mixture contains velocity and concentration gradients. This factor is capable of describing the dip-phenomenon of velocity distribution. From the existing experimental data of velocity, the mixing length data are calculated. The pattern shows that mixing length increases from bed to the dip-position, having a larger value at dip-position and then decreases up to the water surface with a zero value thereat. The present model agrees well with these data sets and this behavior cannot be described by any other existing model. Finally, the proposed mixing length model is applied to find the velocity distribution in wide and narrow open channels. The derived velocity distribution is compared with laboratory channel data of velocity, and the comparison shows good agreement.     

Flow resistance equation for rills

In this paper, a new flow resistance equation for rill flow was deduced applying dimensional analysis and self‐similarity theory. At first, the incomplete self‐similarity hypothesis was used for establishing the flow velocity distribution whose integration gives the theoretical expression of the Darcy–Weisbach friction factor. Then the deduced theoretical resistance equation was tested by some measurements of flow velocity, water depth, cross section area, wetted perimeter, and bed slope carried out in 106 reaches of some rills shaped on an experimental plot. A relationship between the velocity profile, the channel slope, and the flow Froude number was also established. The analysis showed that the Darcy–Weisbach friction factor can be accurately estimated by the proposed theoretical approach based on a power–velocity profile.     

MODELING UNSTEADY TURBIDITY CURRENTS IN A STEEP NARROW RESERVOIR

1.IN~DUCTIONTurbiditycurrentisoneclassofflowsnameddensitycurrentorgravitycurrent(therHunterRouse(Yih(1980)),whichdePictstheintmsionofheaVyfluidintoalighterone.Usually,thedensitydifferencebetWeentWonuidisrelativelysmallandmixingacrosstheimerfaceoccurs.ThedrivingforceofdensitycurrentsisnotdensitydifferenceitselfbutthedifferenceinspeCmcweights.Turbiditycurrentisnamedwhenthedensitydifferenceisespeciallycausedbysuspendedfinesedimentparticles.Sincesediment-ladenflowcaninteraCtwiththelowerbou…     

Numerical prediction of turbidity currents on unsteady sediment-supply

A three-dimensional(3D) numerical model of unstable turbidity currents is developed based on the mechanism of sediment transport and turbulence theory.In this model,numerical simulation of turbidity currents without subsequent supply of muddy water was conducted using the same parameters as were used in the flume experiments.The evolution process of turbidity currents of completely losing supplies observed in the experiment was simulated by the model;validation of the numerical model and the algorithm was conducted.If momentarily interrupted process is regarded as a special case of the gradually interrupted,based on the preceding numerical simulation validity,it is feasible to simulate the motion law of turbidity currents under losing gradually supplies.By this method in this article,the characteristic of sediment-laden flow of losing gradually supplies was obtained,as well as its relationship between front velocity and sediment concentration.     

Testing a theoretical resistance law for overland flow on a stony hillslope

Overland flow, sediments, and nutrients transported in runoff are important processes involved in soil erosion and water pollution. Modelling transport of sediments and chemicals requires accurate estimates of hydraulic resistance, which is one of the key variables characterizing runoff water depth and velocity. In this paper, a new theoretical power–velocity profile, originally deduced neglecting the impact effect of rainfall, was initially modified for taking into account the effect of rainfall intensity. Then a theoretical flow resistance law was obtained by integration of the new flow velocity distribution. This flow resistance law was tested using field measurements by Nearing for the condition of overland flow under simulated rainfall. Measurements of the Darcy–Weisbach friction factor, corresponding to flow Reynolds number ranging from 48 to 194, were obtained for simulated rainfall with two different rainfall intensity values (59 and 178 mm hr⁻¹). The database, including measurements of flow velocity, water depth, cross-sectional area, wetted perimeter, and bed slope, allowed for calibration of the relationship between the velocity profile parameter Γ, the slope steepness s, and the flow Froude number F, taking also into account the influence of rainfall intensity i. Results yielded the following conclusions: (a) The proposed theoretical flow resistance equation accurately estimated the Darcy–Weisbach friction factor for overland flow under simulated rainfall, (b) the flow resistance increased with rainfall intensity for laminar overland flow, and (c) the mean flow velocity was quasi-independent of the slope gradient.     

EFFECT OF TIDAL FLOW ON ESTUARINE SEDIMENTATION

1. INTRODUCTIONIn the regulation of an estuary and the maintenance of a tidal channel for navigation, it is highlyimportant to investigate the interplay between tide and river flow and to anticipate its effects on sedimentation. In this paper. sediment--laden flow in an estuary is treated as a case of two--phase flow. resulting in a set of four governing equations. A theoretical solution is then derived for a simplified casefor qualitative assessment. Numerical computations are also carri…     

Rill flow resistance law under equilibrium bed‐load transport conditions

In this paper, a recently deduced flow resistance equation for open channel flow was tested under equilibrium bed‐load transport conditions in a rill. First, the flow resistance equation was deduced applying dimensional analysis and the incomplete self‐similarity condition for the flow velocity distribution. Then, the following steps were carried out for developing the analysis: (a) a relationship (Equation  13 ) between the Γ function of the velocity profile, the rill slope, and the Froude number was calibrated by the available measurements by Jiang et al.; (b) a relationship (Equation  17 ) between the Γ function, the rill slope, the Shields number, and the Froude number was calibrated by the same measurements; and (c) the Darcy–Weisbach friction factor values measured by Jiang et al. were compared with those calculated by the rill flow resistance equation with Γ estimated by Equations  13 and 17 . This last comparison demonstrated that the rill flow resistance equation, in which slope and Shields number, representative of sediment transport effects, are introduced, is characterized by the lowest values of the estimate errors.     

Characteristics of energy dissipation in hyperconcentrated flows

An equilibrium equation for the turbulence energy in of solid-liquid two-phase flow theory. The equation sediment-laden flows was derived on the basis was simplified for two-dimensional, uniform, steady and fully developed turbulent hyperconcentrated flows. An energy efficiency coefficient of suspended-load motion was obtained from the turbulence energy equation, which is defined as the ratio of the sediment suspension energy to the turbulence energy of the sediment-laden flows. Laboratory experiments were conducted to investigate the characteristics of energy dissipation in hyperconcentrated flows. A total of 115 experimental runs were carried out, comprising 70 runs with natural sediments and 45 runs with cinder powder. Effects of sediment concentration on sediment suspension energy and flow resistance were analyzed and the relation between the energy efficiency coefficient of suspended-load motion and sediment concentration was established on the basis of experimental data. Furthermore, the characteristics of energy dissipation in hyperconcentrated flows were identified and described. It was found that the high sediment concentration does not increase the energy dissipation; on the contrary, it decreases flow resistance.     

FLUVIAL PROCESSES AND SEDIMENT SCOUR RATE OF THE YELLOW RIVER UNDER ACTION OF UNSTEADY FLOWS

1 wrsoooCTIoxThe Yeuow mver crtes a huge amoun of sedimcht and the noods often cause raPid and severeerosinn and dePOsihon. The channl bed of the YelOw mver often exPeriences degIadation in the mainchannel during fioods. In some cases vigorous erosion uP to l0 meters takes place in a shOrt Period oftiIn. Such phenomenon usually occurs in the ndddie reaChs of the Yelow mver and its tributaries suchas the Wdse mVer the Beiluohe mver etc. For examPle, th6 hyPenconcentraed nood in July l…     

SEDIMENT TRANSPORT CAPACITY -AN IMPROVED BAGNOLD FORMULA

This paper re-examines Bagnold’s theorem of sediment transport. Different from the stream power defined by Bagnold, i.e., τoV, this study shows that the total load of sediment-laden flow, gt, is related to near bed energy dissipation rate, i.e., τou*’. An attempt is made to explain the empirical relation. The ratio (=k) of measured total load, gt, to the product of near bed velocity, u*’, and energy dissipation rate, τou*’, is analyzed. It is found that k is independent of the Rouse number, Z, if Z is greater than 2.6, but the coefficient k decreases with the increase of Z when Z < 2.6. An empirical relation between k and Z is developed. A systematic and thorough analysis of 1,458 sets of data collected from 16 rivers and canals confirms that the proposed formula can be used to compute the total load with accuracy.     

Effect of saltating sediment on flow resistance and bed roughness in overland flow

The acceleration of saltating grains by overland flow causes momentum to be transferred from the flow to the grains, thereby increasing flow resistance and bed roughness. To assess the impact of saltating sediment on overland flow hydraulics, velocity profiles in transitional and turbulent flows on a fixed sand-covered bed were measured using hot-film anemometry. Five discharges were studied. At each discharge, three flows were measured: one free of sediment, one with a relatively low sediment load, and one with a relatively high sediment load. In these flows from 83 to 90 per cent of the sediment was travelling by saltation. As a result, in the sediment-laden flows the near-bed velocities were smaller and the velocity profiles steeper than those in the equivalent sediment-free flows. Sediment loads ranged up to 87·0 per cent of transport capacity and accounted for as much as 20·8 per cent of flow resistance (measured by the friction factor) and 89·7 per cent of bed roughness (measured by the ratio of the roughness length to median grain diameter). It is concluded that saltating sediment has a considerable impact on overland flow hydraulics, at least on fixed granular beds. Saltation is likely to have a relatively smaller effect on overland flow on natural hillslopes and agricultural fields where form and wave resistance dominate. Still, saltation is generally of greater significance in overland flow than in river flow, and for this reason its effect on overland flow hydraulics is deserving of further study. © 1998 John Wiley & Sons, Ltd.     

Testing slope effect on flow resistance equation for mobile bed rills

In this paper, a recently theoretically deduced rill flow resistance equation, based on a power‐velocity profile, is tested experimentally on plots of varying slopes in which mobile bed rills are incised. Initially, measurements of flow velocity, water depth, cross‐sectional area, wetted perimeter and bed slope conducted in 106 reaches of rills incised on an experimental plot having a slope of 14% were used to calibrate the flow resistance equation. Then, the relationship between the velocity profile parameter Γ, the channel slope, and the flow Froude number, which was calibrated using the 106 rill reach data, was tested using measurements carried out in plots having slopes of 22% and 9%. The measurements carried out in the latter slope conditions confirmed that (a) the Darcy–Weisbach friction factor can be accurately estimated using the proposed theoretical approach, and (b) the data were supportive of the slope independence hypothesis of rill velocity stated by Govers.     

Time-averaged sub-layer concentration profiles in oscillatory sheet flows

Although thin on the order of several to tens of millimeters, sheet flows normally comprise a lower pick-up sub-layer and an upper contact-load sub-layer, separated at the bed level (z = 0). The time-averaged concentration profile in the pick-up sub-layer shows a ‘convex upward’ curvature, but ‘concave upward’ shape characterizes the time-averaged concentration profile in the contact-load sub-layer. The time-dependent concentration in the contact-load sub-layer is approximately in-phase with the free stream flow velocity, whereas it is nearly in anti-phase with the free stream flow velocity in the pick-up sub-layer. Two distinct analytical expressions of the time-averaged concentration profiles for the respective sub-layers are proposed. The expressions are validated with detailed observation datasets collected in the Groβer Wellenkanal (GWK) prototype wave flume in Hannover, Germany. The agreement between the predicted and the measured values is excellent. Interparticle collisions in the pick-up sub-layer and convective lifting processes associated with vortex shedding in the contact-load sub-layer are considered responsible for the opposite curvatures and in-phase/anti-phase concentration variations. Both transitional boundary and reference concentration are also elaborated.     

Analytical model for fully three‐dimensional radial dispersion in a finite‐thickness aquifer

Analytical solutions for contaminant transport in a non‐uniform flow filed are very difficult and relatively rare in subsurface hydrology. The difficulty is because of the fact that velocity vector in the non‐uniform flow field is space‐dependent rather than constant. In this study, an analytical model is presented for describing the three‐dimensional contaminant transport from an area source in a radial flow field which is a simplest case of the non‐uniform flow. The development of the analytical model is achieved by coupling the power series technique, the Laplace transform and the two finite Fourier cosine transform. The developed analytical model is examined by comparing with the Laplace transform finite difference (LTFD) solution. Excellent agreements between the developed analytical model and the numerical model certificate the accuracy of the developed model. The developed model can evaluate solution for Peclet number up to 100. Moreover, the mathematical behaviours of the developed solution are also studied. More specifically, a hypothetical convergent flow tracer test is considered as an illustrative example to demonstrate the three‐dimensional concentration distribution in a radial flow field. The developed model can serve as benchmark to check the more comprehensive three‐dimensional numerical solutions describing non‐uniform flow contaminant transport. Copyright © 2009 John Wiley & Sons, Ltd.     

Application of Hausdorff fractal derivative to the determination of the vertical sediment concentration distribution

The Rouse formula and its variants have been widely used to calculate the steady-state vertical concentration distribution for suspended sediment in steady sediment-laden flows, where the diffusive flux is assumed to be Fickian. Turbulent flow, however, exhibits fractal properties, leading to non-Fickian diffusive flux for sediment particles. To characterize non-Fickian dynamics of suspended sediment, the current study proposes a Hausdorff fractal derivative based advection-dispersion equation(H...     

Derivation of different suspension equations in sediment-laden flow from Shannon entropy

In this study the well-known Rouse equation and Barenblatt equation for suspension concentration distribution in a sediment-laden flow is derived using Shannon entropy. Considering dimensionless suspended sediment concentration as a random variable and using principle of maximum entropy, probability density function of suspension concentration is obtained. A new and general cumulative distribution function for the flow domain is proposed which can describe specific previous forms reported in the literature. The cumulative distribution function is tested with a variety sets of experimental data and also compared with previous models. The test results ensure the superiority of the new cumulative distribution function. Further a modified form of the cumulative distribution function is discussed and used to derive the suspension model of Greimann et al. The model parameters are expressed in terms of the Rouse number to show the effectiveness of this study using entropy based approach. Finally a non-linear equation in the Rouse number has been suggested to compute it from the experimental data.