Fluvial Hydrodynamics

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.

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.

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 flow over a sediment bed. An application of Reynolds decomposition and time-averaging to the Navier–Stokes equations yields the Reynolds-averaged Navier–Stokes (RANS) equations, containing terms of Reynolds stresses. The RANS equations along with the time-averaged continuity equation are the main equations to analyze turbulent flow. The classical turbulence theories were proposed by Prandtl and von Kármán. Prandtl simulated the momentum exchange on a macro-scale to explain the mixing phenomenon in a turbulent flow establishing the mixing length theory, while von Kármán’s relationship for the mixing length is based on the similarity hypothesis. The velocity distribution in open-channel flow follows the linear law in viscous sublayer, the logarithmic law in turbulent 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 exhibits strong turbulence-induced secondary currents, and as a result, the maximum velocity appears below the free surface, known as dip phenomenon. Isotropic turbulence theory deals with the turbulent kinetic energy (TKE) transfer from the large-scale motions to smaller-scale motions 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 the anisotropic invariant mapping (AIM) and the anisotropy invariant function to quantify the degree of the departure from isotropy. Higher-order correlations are given by skewness and kurtosis of velocity fluctuations, TKE 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 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.

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.

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.

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.

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.

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 seldom occur in nature; meandering and braided rivers are common. This chapter focuses on the characteristics of meandering and braided rivers. Mathematical models of meandering rivers are presented.

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.

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.