The mode of sediment transport where the sediment particles are surrounded by the fluid over an appreciably long period of time is known as the suspended-load transport[aut]Suspended-load transportdefinition. This chapter introduces basic concepts of sediment suspension and formulations to predict the suspended-load transport rate. The introduction to[aut]Turbulent kinetic energy budget componentsadvection advection–diffusion model made a considerable progress in deriving the distribution of sediment concentration in sediment-laden flows. Diffusion in turbulent flow[aut]Turbulent flow results in an exchange of momentum and suspended sediment particles between the flow layers. When the terminal fall velocity of sediment is slow enough, the sediment particles go in suspension. The suspended-load transport[aut]Suspended-load transportdefinition 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 flow layer to another. 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 KármánVon Kármán, T., constant, and turbulence characteristics are also discussed in details. Further, the findings on the[aut]Effects of suspended loadon turbulence characteristicsresponse of turbulent bursting response of turbulent burst[aut]Burstturbulent burst to sediment suspension are detailed. The turbidity currents are characterized by a rapidly advancing submerged sediment-laden current moving down a slope. The turbidity current formation and its mathematical modeling are discussed. The computation of suspended-load transport[aut]Suspended-load transportdefinition rate is exemplified through worked-out problems.

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[aut]Fluid and suspended sediment mixturefluid–sediment mixture are discussed in details. The additional feature of this chapter is the discussion on terminal fall velocity of particles.

The mode of sediment transport where the sediment particles slide, roll, and/or travel in succession of low jumps close to the bed is known as the bedload transport. In this chapter, theories of bedload and formulations to predict the bedload transport rate are presented. The pioneering attempt to predict the bedload transport rate was due to MP du Boys in 1879, who expressed bedload 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 bedload 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. Besides, the application of the turbulence phenomenological theory provides the origin of the scaling law of the bedload transport. The additional features of this chapter are the discussion on particle saltation, sediment sorting, streambed armoring, and sediment entrainment probability to bedload. The effects of bedload on velocity distribution, length scales of turbulence, and von Kármán constant are also discussed in detail. The methods of computation of bedload transport are illustrated through worked-out examples.

The phenomenon of lowering the riverbed level due to removal of sediment is known as the scour. In general, scour is classified as general scour[aut]Scourgeneral scour, contraction scour[aut]Scourcontraction scour, and local scour[aut]Scourlocal scour. This chapter provides a comprehensive discussion on scour within channel contractions[aut]Scour typeschannel contractions, downstream of structures[aut]Scour typesdownstream of structures, below horizontal pipelines[aut]Scour typeshorizontal pipelines, and 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.

The turbulence in a fluid flow is characterized by irregular and chaotic motion of fluid particles. It is a complex phenomenon. In this chapter, the turbulence characteristics are discussed with reference to the flow over a sediment bed. An application of Reynolds decomposition[aut]Reynolds decomposition and time-averaging to theStokes, G. G., Navier–Stokes equations yields the Reynolds-averaged Navier–Stokes (RANS) equations[aut]Reynolds averaged Navier-Stokes (RANS) equationsRANS equations, containing the terms of Reynolds stresses. The RANS equations along with the time-averaged continuity equation are the main equations to analyze the turbulent flow[aut]Turbulent flow. The classical turbulence theories were proposed by PrandtlPrandtl, L., and von KármánVon Kármán, T.,. PrandtlPrandtl, L., simulated the momentum exchange on a macro-scale to explain the mixing phenomenon in a turbulent flow[aut]Turbulent flow establishing the mixing length[aut]Mixing length theory, while von Kármán’sVon Kármán, T., relationship for the mixing length[aut]Mixing length is based on the similarity hypothesis. The velocity distribution in an open-channel flow follows the linear law[aut]Velocity distributionlinear law in viscous sublayer in viscous sublayer[aut]Flow layersviscous sublayer, the logarithmic law in turbulent wall-shear layer[aut]Flow layersturbulent wall-shear layer, and the wake law in the outer layer. The determination of bed shear stress is always a challenging task. Different methods for the determination of bed shear stress are discussed. Flow in a narrow channel[aut]Dip phenomenonnarrow channel exhibits strong turbulence-induced secondary currents, and as a result, the maximum velocity appears below the free surface, known as the dip phenomenon. Isotropic turbulence theory deals with the turbulent kinetic energy (TKE) transfer from the large-scale motions to smaller scale until attaining an adequately small length scale so that the fluid molecular viscosity can dissipate the TKE into heat. Anisotropy in turbulence is analyzed by mainly the anisotropic invariant mapping (AIM)[aut]Anisotropyanisotropic invariant map (AIM) and by some other methods to quantify the degree of the departure from an isotropic turbulence. Higher-order correlations are given by skewness[aut]Higher-order correlationsskewness and kurtosis of velocity fluctuations, TKE flux[aut]Turbulent kinetic energyTKE flux, and budget. This chapter also includes most of the modern development of turbulent phenomena, such as coherent structures and burst phenomena, and double-averaging of heterogeneous flow over gravel beds.

The flow condition that is just adequate to initiate the motion of sediment particles at the bed surface is called the sediment threshold. Albert Frank Shields carried out his doctoral research study on sediment transport at the Technische Hochschule Berlin, Germany. He is well known for proposing a useful diagram, known as the 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 to in the literature. It has provided an enormous inspiration to initiate a sizable number of researches over last eight decades on the beginning of sediment motion. Since his pioneering work, numerous attempts have so far been made to quantify the required flow condition for the initiation of sediment motion. In this chapter, the important experimental and theoretical studies on sediment threshold under steady stream flow are discussed, highlighting the empirical formulations and semitheoretical analyses. Both deterministic and probabilistic models of sediment threshold are described. The turbulence phenomenological approach provides the origin of the scaling law of the threshold of sediment entrainment. The special feature of this chapter is a discussion on the influence of turbulent burst[aut]Burstturbulent burst on sediment threshold. Latest experimental findings evidenced that the mechanism of sediment entrainment is governed by the sweep event. The concept of sediment threshold is applied to determine the stable-ideal section of a channel, known as the 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.

River configurations in plan view are highly variable. Under specific environmental and hydraulic conditions, the type of planform geometry of a river is controlled by the sediment transport and its capacity of the river. Alluvial river configurations are in general categorized as straight, meandering, and braided rivers. While long, straight rivers[aut]Straight rivers seldom occur in nature, meandering and braided rivers are common. This chapter focuses on the characteristics of meandering and braided rivers. The turbulence phenomenological approach provides the underlying mechanism of the onset of meandering of a straight river[aut]Straight rivers. Mathematical models of flow in a curved channel, meandering rivers, and their stability analysis are presented.

Natural streambed does not exhibit a flatbed surface but takes various geometrical forms known as the 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 detail. Bedforms in gravel-bed streams are also detailed. 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 at the end of the chapter.

The total amount of sediment transported through a given section of a river for the given flow and sediment bed conditions is called the total-load transport. Based on the mode of sediment transport, the total load is the sum of the bedload, suspended load, 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, bedload and suspended load 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 bedload and suspended load. The methods of computation of total-load transport are illustrated through worked out examples.

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 applications in open-channel flow. The continuity equation ensures the mass conservation. 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, andStokes, G. G., Stokes’ law[aut]Stokes’ law.

Dimensional analysis is a powerful tool in designing, ordering, and analyzing the experiment results and also synthesizing them. The important theorem in dimensional analysis is known as theBuckingham, E., Buckingham Π theorem[aut]Buckingham Π theorem, so called since it involves nondimensional groups[aut]Dimensional analysisBuckingham Π theoremnondimensional group of the products of the quantities. In this chapter, BuckinghamBuckingham, E., 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 the physical models are to replicate a small-scale hydraulic structure or a 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 laboratory model studies 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 similitudes. Two categories of hydraulic models are discussed: immobile-bed model[aut]Similitudemodelimmobile bed model and mobile-bed model. The analysis leads to the definition of model-scale ratios. A number of illustrative examples are presented.

The chapter furnishes solutions to the problems linked with the Buckingham Π theorem, hydraulic similitude, immobile bed model, and mobile bed model.

The chapter provides solutions to the problems related to the properties of fluid, sediment, fluid–sediment mixture, and terminal fall velocity of particles.

The chapter furnishes solutions to the problems linked with the predictors of various bedformsBedforms, mathematical models of bedforms, and resistance to flow due to bedforms.

The chapter furnishes solutions to the problems linked with the bedload transport rateBedload transport rate of uniform and nonuniform sediment, particle saltation, sediment sorting, streambed armoring, sediment entrainment probabilityEntrainment probability to bedload, and effects of bedload on velocity distribution.

The chapter presents solutions to the problems associated with the vertical distribution of suspended sediment concentrationSediment concentration, suspended-load transport rateSuspended-load transport rate, and turbidity currentsTurbidity currents.

The chapter presents solutions to the problems associated with the Navier–Stokes and the Reynolds averaged Navier–Stokes (RANS) equationsRANS equation, mixing length theory, velocity distribution and bed shear stress in an open-channel flow, isotropic turbulence theory, turbulent kinetic energy (TKE) budget, isotropic turbulence theory, phenomenological theory of turbulencePhenomenological theory of turbulence, and turbulence anisotropy.

The chapter provides solutions to the problems related to the total-load transport rateTotal-load transport rate in an open-channel flow.

The chapter provides solutions to the problems related to the scour within channel contractions, scour downstream of structures, scour below horizontal pipelines, scour at bridge piers and abutments, and scour countermeasures.

The chapter presents solutions to the problems associated with the characteristics of meanderingMeandering and braided rivers, onset of meandering of a straight river, flow in a curved channelFlow in a curved channel, mathematical models of meandering rivers, and stability analysis.

The chapter provides solutions to the problems related to the Shields diagram, deterministic and probabilistic models of sediment threshold, turbulence phenomenological approach, and stable-ideal section of a channel.

The chapter furnishes solutions to the problems linked with the hydrodynamic principles that deal with the mechanics of fluid flow, three conservation principles: mass, momentum, and energy, graduallyGradually varied flow (GVF) and rapidly varied flows, boundary layer theory, and hydrodynamic dragDrag and liftLift on a particle.

Due to increasing industrial concern towards the development of computational models of stirred tank reactors, it is necessary to enhance the accuracy of the model predictions. The rotation of the impeller in a reactor vessel is mainly simulated using the pseudo-steady Multiple Reference Frame (MRF) technique. Earlier studies have highlighted the importance of extending the rotating domain defined for the modelling process, while a definite idea regarding the selection of the same has not been specified so far. The present study aims to develop a generalised criterion for selecting the optimal MRF extents for any configuration of the reactor. The radial and axial extents of MRF boundary were systematically varied in a baffled reactor vessel and the optimal extents of the same were determined from the predictions of underlying flow field characteristics. The balance between the Power number (Npt) computed from the torques of rotating and stationary walls which is based on the principle of conservation of angular momentum is determined as the generalised criterion for selecting the optimal extents of the rotating domain.

The 1819 earthquake (M ≥ 7.5), located in the northern part of the Kachchh (Kutch) rift basin in the state of Gujarat, is the largest and one of the most well-documented continental earthquakes prior to seismic instrumentation. Although located in a region that was sparsely populated, it caused severe impact around its source as well as in distant locations like Hyderabad.