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The installation of free falling jet grade control structures has become a popular choice for river bed stabilization. However, the formation and development of scour downstream of the structure may lead to failure of the structure itself. The current approaches to scour depth prediction are generally based on studies conducted with the absence of upward seepage. In the present study, the effects of upward seepage on the scour depth were investigated. A total of 78 tests without and with the application of upward seepage were carried out using three different sediment sizes, three different tailwater depths, four different flow discharges, and four different upward seepage flow discharge rates. In some tests, the three-dimensional components of the flow velocity within the scour hole were measured for both the cases with and without upward seepage. The scour depth measured for the no-seepage results compared well with the most accurate relationship found in the literature. It was found that generally the upward seepage reduced the downward velocity components near the bed, which led to a decrease in the maximum scour depth. A maximum scour depth reduction of 49% was found for a minimum tailwater depth, small sediment size, and high flow discharge. A decay of the downward velocity vector within the jet impingement was found due to the upward seepage flow velocity. The well known equation of D'Agostino and Ferro was modified to account for the effect of upward seepage, which satisfactorily predicted the experimental scour depth, with a reasonable average error of 10.7%. © 2016 Shafai-Bejestan et al.

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Department of Civil & Infrastructure Engineering

Fulltext

Acta Geophysica

Scour downstream of grade control structures under the influence of upward seepage

Characteristics of turbulent mixing-length, length scales and anisotropy in the wall-wake flow downstream of a sphere placed on a rough wall are studied. The Prandtl's mixing-length in wall-wake flow increases compared to that in upstream flow, while the Taylor microscale and the Kolmogorov length scale decrease. As the downstream distance increases, the defects (difference between upstream and downstream distributions) in vertical distributions of mixing-length and length scales gradually disappear to recover their distributions in undisturbed upstream flow. These distributions of the defects exhibit some degree of similarity, as they are scaled by their individual peak values and the vertical distance is scaled by the height of occurrence of their individual half-peak defects. In anisotropy analysis, the streamwise, spanwise and vertical components of anisotropy in wall-wake flow are less, more and invariant, compared to their individual upstream trends. However, the former two components recover with an increase in downstream distance. © 2015 International Association for Hydro-Environment Engineering and Research.

Journal of Hydraulic Research

Turbulent length scales and anisotropy downstream of a wall mounted sphere

The turbulence anisotropy in flow over noncohesive sediment beds at an entrainment threshold, as compared to that over immobile beds, is studied. The streamwise component of anisotropy tensor in near-bed flow for threshold beds yields more anisotropic stream as compared to that for immobile beds, whereas all other components of anisotropy tensor in near-bed flow for threshold beds yield less anisotropic stream. The anisotropic invariant maps illustrate the anisotropy in near-bed flow layer tending to be a two-component isotropy for both immobile and threshold beds. The data plots for immobile beds with an increase in vertical distance have an affinity to a one-component isotropy, whereas those for mobile beds show a tendency to become a three-dimensional isotropy near the midportion of the flow depth. Invariant function plots show a better two-dimensional isotropy in the inner layer of flow and a quasi-three-dimensional isotropy in the outer layer of flow over threshold beds than those over immobile beds. © 2015 American Society of Civil Engineers.

Journal of Hydraulic Engineering

Turbulence anisotropy in flow at an entrainment threshold of sediment

Is the energy equation for gradually-varied flow the best approximation for the free surface profile computations in river flows? Determination of flood inundation in rivers and natural waterways is based on the hydraulic computation of flow profiles. This is usually done using energy-based gradually-varied flow models, like HEC-RAS, that adopts a vertical division method for discharge prediction in compound channel sections. However, this discharge prediction method is not so accurate in the context of advancements over the last three decades. This paper firstly presents a study of the impact of discharge prediction on the gradually-varied flow computations by comparing thirteen different methods for compound channels, where both energy and momentum equations are applied. The discharge, velocity distribution coefficients, specific energy, momentum and flow profiles are determined. After the study of gradually-varied flow predictions, a new theory is developed to produce higher-order energy and momentum equations for rapidly-varied flow in compound channels. These generalized equations enable to describe the flow profiles with more generality than the gradually-varied flow computations. As an outcome, results of gradually-varied flow provide realistic conclusions for computations of flow in compound channels, showing that momentum-based models are in general more accurate; whereas the new theory developed for rapidly-varied flow opens a new research direction, so far not investigated in flows through compound channels. © 2015 Elsevier B.V.

Journal of Hydrology

Free surface profiles in river flows: Can standard energy-based gradually-varied flow computations be pursued?

This paper presents the results of an experimental study to quantify the effects of bed slope and relative submergence on incipient motion of sediment under decelerating flows. Experiments were conducted in an experimental tilting-flume of 8 m long 0.4 m wide and 0.6 m deep with glass-walls. Three uniform sediments with median grain sizes of 0.95, 1.8 and 3.8 mm and three bed slopes of 0.0075, 0.0125 and 0.015 were used under decelerating flow. The main conclusion is that the Shields diagram, which is commonly used to evaluate the critical shear stress, is not suitable to predict the critical shear stress under decelerating flows. © 2015 Ramin Bolhassani et al., published by De Gruyter Open.

Journal of Hydrology and Hydromechanics

Effects of relative submergence and bed slope on sediment incipient motion under decelerating flows

This paper presents a hydrodynamic analysis for the fully developed turbidity currents over a plane bed stemming from the classical three-equation model (depth-averaged fluid continuity, sediment continuity, and fluid momentum equations). The streamwise velocity and the concentration distributions preserve self-similarity characteristics and are expressed as single functions of vertical distance over the turbidity current layer. Using the experimental data of turbidity and salinity currents, the undetermined coefficients and exponents are approximated. The proposed relationships for velocity and concentration distributions exhibit self-preserving characteristics for turbidity currents. The depth-averaged velocity, momentum, and energy coefficients are thus obtained using the proposed expression for velocity law. Also, from the expressions for velocity and concentration, the turbulent diffusivity and the Reynolds shear stress distributions are deduced with the aid of the diffusion equation of sediment concentration and the Boussinesq hypothesis. The generalized equation of unsteady nonuniform turbidity current is developed by using the velocity and concentration distributions in the moments of the integral scales over the turbidity current layer. Then, the equation is applied to analyze the gradually varied turbidity currents considering closure relationships for boundary interaction and shear velocity. The streamwise variations of current depth, velocity, concentration, reduced sediment flux, and Richardson number are presented. Further, the self-accelerating and depositional characteristics of turbidity currents including the transitional feature from erosional to depositional modes are addressed. The effects of the streamwise bed slope are also accounted for in the mathematical derivations. The results obtained from the present model are compared with those from the classical model. © 2015. American Geophysical Union. All Rights Reserved.

Journal of Geophysical Research: Earth Surface

Hydrodynamic analysis of fully developed turbidity currents over plane beds based on self-preserving velocity and concentration distributions

An undular hydraulic jump corresponds to the weak transition from super- to subcritical-flow in the form of steady free surface undulations. Previous models on undular hydraulic jumps employed the potential flow theory, i.e., the solitary and cnoidal wave theories. Experimental observations indicate the inadequacy of this theory, which motivated the development of more advanced approximations. Basic flow features including friction effects on the velocity profile, modelling of the bed-shear stress, and Reynolds stresses are considered. However, none of the models currently available include all these aspects. In this study, a general depth-averaged model is developed based on the κ- ε turbulence closure. The general depth-averaged equations are applied to the undular jump problem, introducing a suitable time-averaged velocity distribution based on a composite power-law model, in which both streamline curvature and vorticity are accounted for. The bed-shear stress closure is included by a boundary layer method. Predictions of the depth-averaged Reynolds averaged Navier-Stokes (RANS) model are shown to be close to the 2D RANS solution and to experimental observations. © 2014 International Association for Hydro-Environment Engineering and Research.

Depth-averaged model for undular hydraulic jump

Natural streambed does not exhibit a plane bed surface, but takes various geometrical forms known as bedforms. In this book chapter, the studies dealing with the formation mechanism of bedforms and their stability are discussed. The important feature of this chapter is the presentation of mathematical models proposed by various researchers. © Springer International Publishing Switzerland 2015.

GeoPlanet: Earth and Planetary Sciences

Principles of mechanics of bedforms

Closure to "sediment entrainment probability and threshold of sediment suspension: Exponential-based approach" by Sujit K. Bose and Subhasish Dey

The total amount of sediment transported through a given section of a river for the given flow and sediment bed conditions is called total-load transport. Based on the mode of sediment transport, the total load is the sum of the bed, suspended, and wash load. The total load is also informally called the bed-material load as it contains only those sediment particles that come from the sediment bed excluding the wash load. There are two general approaches to determine the total load. They are indirect approach and direct approach. In indirect approach, bed and suspended loads are estimated separately and then added together to quantify the total load. In direct approach, the total-load function is directly determined without dividing it into bed and suspended loads. The method of computation of total-load transport is illustrated through worked out examples. © 2014, Springer-Verlag Berlin Heidelberg.

Total-load transport

The chapter provides an introduction to the fluvial hydrodynamics, scope and outline of this book. As the subject deals with the interaction between fluid and sediment particles, an understanding of the physical properties of fluid and sediment is an essential prerequisite. In this chapter, the properties of fluid, sediment and fluid–sediment mixture are discussed in details. The additional feature of this chapter is the discussion on terminal fall velocity of particles. © 2014, Springer-Verlag Berlin Heidelberg.

Introduction

Safety of a bridge depends on the depth and volume of local scour around the pier. Therefore scour protection measures are most sought after to increase the stability of the bridge foundation. Scour protection measures broadly divided into bed armouring countermeasures and flow-altering countermeasures. Extensive research studies are available on bed armouring counter measures which were proved satisfactory, however flow altering countermeasures are gaining momentum at present. In this research, effect of placing a pier upstream of a bridge pier as a protective measure to decrease the local scour at the bridge pier was studied. Pier placed upstream of a bridge pier modifies the flow field, thereby reducing the eroding power of flow, and hence it reduces depth of the scour hole at the bridge pier. It works perfectly if the wake region formed by the upstream pier has lower velocity as compared to the velocity without the upstream pier. In this process, considerable scour was expected at the upstream pier. The present study attempts to quantify the effect of the mutual interference of front pier and bridge pier on local scour at the bridge pier. The mutual interference of the piers on local scour depends on the shape of the piers, spacing of the piers, flow velocity, flow depth, relative diameters of the piers, sediment size, and oblique distance between the piers and flow oblique angle. These studies were accomplished by measuring equilibrium scour depths in clear water scour in carefully designed and controlled experiments in the laboratory. Two identical piers with series and offset arrangement with several pier diameters of spacing between them were studied. It was observed in on-going experiments that equilibrium scour depth at rear pier increases as the distance between rear and upstream piers increases. However, equilibrium scour depth at upstream pier was independent of streamwise spacing between the piers. In offset arrangement the equilibrium scour depth at rear pier increases as the offset distance increases between them. © 2014 Taylor & Francis Group, London.

Proceedings of the International Conference on Fluvial Hydraulics, RIVER FLOW 2014

Studies on the effect of an upstream pier as a scour protection measure of a downstream bridge pier

The hydrodynamic principles that deal with the mechanics of fluid flow and the derivations are based on three conservation principles: Mass, momentum and energy. In this chapter, these are initially discussed from the viewpoint of classical hydrodynamics and then with reference to their application in open channel flow. The continuity equation ensures the conservation of mass. The specific force equation is based on the momentum principle and calls for force balance. The specific energy equation is based on the energy principle and calls for energy balance. These important principles related to open channel flow are discussed and applications are explained. The additional features of this chapter are the introduction to the boundary layer theory, flow in a curved channel, hydrodynamic drag and lift on a particle and Stokes law. © 2014, Springer-Verlag Berlin Heidelberg.

Hydrodynamic principles

Natural streambed does not exhibit a flat bed surface but takes various geometrical forms known as bedforms. In this chapter, the experimental and theoretical studies dealing with the formation, geometry, and stability of bedforms are furnished. The predictors of various bedforms are discussed in details. Bedforms in gravel-bed streams are given. The important feature of this chapter is the presentation of mathematical models proposed by various researchers. Further, the resistance to flow due to bedforms is of paramount importance to river engineers. This issue is also discussed. Numerical examples on bedforms are given in the end of the chapter. © 2014, Springer-Verlag Berlin Heidelberg.

Bedforms

The phenomenon of lowering the riverbed level due to removal of sediment is known as scour. In general, scour is classified as general scour, contraction scour, and local scour. This chapter provides a comprehensive discussion on scour within channel contractions, downstream of structures, below horizontal pipelines, at bridge piers, and abutments. Further, scour countermeasures are of paramount importance to river engineers. This issue is also discussed. Numerical examples on prediction of scour depths are worked out. © 2014, Springer-Verlag Berlin Heidelberg.

Scour

The mode of sediment transport where the sediment particles are surrounded by the fluid over an appreciably long period of time is known as suspended-load transport. This chapter introduces basic concepts of sediment suspension and formulations to predict the suspended-load transport rate. The introduction of advection–diffusion model made a considerable progress in deriving the distribution of sediment concentration in sediment-laden flows. Diffusion in turbulent flow results in exchange of momentum and suspended sediment particles between layers of the flow. When the terminal fall velocity of sediment is slow enough, the sediment particles go in suspension. The suspended-load transport rate is readily computed from the known vertical distributions of sediment concentration and flow velocity. Also, based on the energy concept, gravitational theory was developed to determine the distribution of suspended sediment particles. The work done per unit time of a unit volume of fluid and suspended sediment mixture is to transfer from a layer to another layer of the flow. The conservation of energy is preserved separately in the fluid and sediment phases by balancing the energy supplied and the energy dissipated. The effects of suspended load on velocity distribution, von Kármán constant, turbulence characteristics are also discussed in details. Further, the findings on the response of turbulent bursting to sediment suspension are detailed. The computation of suspended-load transport is exemplified through worked out problems. © 2014, Springer-Verlag Berlin Heidelberg.

Suspended-load transport

The mode of sediment transport where the sediment particles slide, roll, or travel in succession of low jumps close to the bed is known as bed-load transport. In this chapter, theories of bed-load and formulations to predict the bed-load transport rate are presented. The pioneering attempt to predict the bed-load transport rate was due to MP du Boys in 1879, who expressed bed-load transport rate as a function of excess bed shear stress, that is the bed shear stress exceeding the threshold bed shear stress. Thereafter, number of researchers suggested du Boys type equations making use of the excess bed shear stress in different forms and coefficients. Other concepts to predict the bed-load transport rate are the discharge concept (Schoklitsch type), the velocity concept, the bedform concept, the probabilistic concept (Einstein type), the deterministic concept (Bagnold type), and the equal mobility concept. The additional features of this chapter are the discussion on particle saltation, sediment sorting, streambed armoring, and sediment entrainment probability to bed load. The effects of bed load on velocity distribution, length scales of turbulence, and von Kármán constant are also discussed in details. The method of computation of bed-load transport is illustrated through worked out examples. © 2014, Springer-Verlag Berlin Heidelberg.

Bed-load transport

Gravity waves propagating over free-surface flows with shallow depth are well-known phenomena. The small-amplitude sinusoidal wave and Korteweg-de Vries (KdV) equations are based on potential-flow theory being widely used to describe water-wave propagation. The KdV equation leads to two basic flow patterns, as follows: (1) cnoidal waves, and (2) solitary waves. However, in case of a real Newtonian fluid, the bed resistance and the rapid motion of fluid generate turbulence (eddies) in the medium. The effects of turbulence are taken into account in this paper by using the equations for the surface elevation η and depth-averaged flow velocity U developed previously. These equations are based on the Reynolds-averaged Navier-Stokes (RANS) equations for turbulent flow in open channels. The wave profile can be approximated by a form a cos kξ̂/(1 -b cos kξ̂), where a and b are constant amplitudes; k = wave number; ξ̂ = dimensionless horizontal distance given by (x-ct)/h; x = horizontal distance; c = wave velocity; t = time; and h = undisturbed flow depth. Such a profile has the characteristic that the peaks are narrower but higher compared to wider but shallower troughs. The effects of streamflow on wave propagations are also considered. If the waves travel in the direction of the streamflow, there is a lengthening effect on the peaks and troughs, whereas if the waves travel against the direction of streamflow, they become shorter. © 2014 American Society of Civil Engineers.

Gravity waves on turbulent shear flow: Reynolds averaged approach

Dimensional analysis is a powerful tool in designing, ordering, and analyzing the experiment results and also synthesizing them. One of the important theorems in dimensional analysis is known as the Buckingham Π theorem, so called since it involves non-dimensional groups of the products of the quantities. In this chapter, Buckingham Π theorem and its uses are thoroughly discussed. Physical models for hydraulic structures or river courses are usually built to carry out experimental studies under controlled laboratory conditions. The main purposes of physical models are to replicate a small-scale hydraulic structure or flow phenomenon in a river and to investigate the model performance under different flow and sediment conditions. The concept of similitude is commonly used so that the measurements made in a laboratory model study can be used to describe the characteristics of similar systems in the practical field situations. This chapter describes hydraulic similitude in terms of geometric, kinematic, and dynamic similitude. Two categories of hydraulic models are discussed: Immobile bed models and mobile bed models. The analysis leads to the definition of model-scale ratios. A number of illustrative examples are presented. © 2014, Springer-Verlag Berlin Heidelberg.

Dimensional analysis and similitude

The flow condition that is just adequate to initiate the motion of sediment particles at the bed surface is called sediment threshold. Albert Frank Shields carried out his doctoral research study on sediment transport at the Technischen Hochschule Berlin, Germany. He is well known for proposing a useful diagram, known as Shields diagram. This diagram provides the criterion for the sediment threshold, which is an essential requirement for the determination of sediment motion in a loose boundary stream. His diagram becomes famous and is most frequently referred in the literature. It has provided an enormous inspiration to initiate a sizable number of researches over last seven decades. Since his pioneering work, numerous attempts have so far been made to quantify the required flow condition for the beginning of sediment motion. In this chapter, the important experimental and theoretical studies on sediment threshold under steady stream flow are furnished, highlighting the empirical formulations and semitheoretical analyses. Both deterministic and probabilistic models of sediment threshold are discussed. The special feature of this chapter is a discussion on the influence of turbulent bursting on threshold of sediment entrainment. Latest experimental findings evidenced that the mechanism of sediment entrainment is governed by the sweep events. The concept of sediment threshold is applied to determine the stable-ideal section of a channel, known as threshold channel. It has a bank profile for which the sediment particles along the wetted perimeter are in a state of incipient motion. The design of threshold channel is demonstrated through numerical examples. © 2014, Springer-Verlag Berlin Heidelberg.