Rivers – Physical, Fluvial and Environmental Processes

A “one-and-a-half”-dimensional model of a river is developed. It is actually one-dimensional but allows for horizontal curvature using natural curvilinear co-ordinates. The governing long wave equations can be developed with very few limiting approximations, especially using momentum rather than energy. The curvature is then shown to be rarely important and is subsequently ignored. Wave periods, imposed by boundary conditions, are asserted to be fundamental. Long waves have speeds and propagation properties that depend on period, and there is no such thing as a single long wave speed. Examination of dimensionless equations and solution of linearised equations using wave period shows a novel interpretation of terms in the momentum equation: the “kinematic” approximation and wave are misnomers: the approximation lies not in the neglect of inertial terms but is actually a very long period one. The outstanding problem of river modelling, however, is that of resistance to the flow. A large data set from stream-gauging is considered and it is shown that the state of the bed, namely the arrangement of bed grains by previous flows, is more important than actual grain size. A formula for resistance is proposed which contains a parameter representing bed state. As that state is usually changing with flow, one can not be sure what the resistance actually will be. This uncertainty may have important implications for modelling. The momentum principle is then applied also to obstacles such as bridge piers, and a simple approximation gives greater understanding and a practical method for incorporation in river models. Finally, river junctions are considered, and the momentum approach with the very long period approximation shows that they can be modelled simply.

The study of turbulence has always been a challenge for scientists working on geophysical flows. Turbulent flows are common in nature and have an important role in geophysical disciplines such as river morphology, landscape modeling, atmospheric dynamics and ocean currents. At present, new measurement and observation techniques suitable for fieldwork can be combined with laboratory and theoretical work to advance the understanding of river processes. Nevertheless, despite more than a century of attempts to correctly formalize turbulent flows, much still remains to be done by researchers and engineers working in hydraulics and fluid mechanics. In this contribution we introduce a general framework for the analysis of river turbulence. We revisit some findings and theoretical frameworks and provide a critical analysis of where the study of turbulence is important and how to include detailed information of this in the analysis of fluvial processes. We also provide a perspective of some general aspects that are essential for researchers/practitioners addressing the subject for the first time. Furthermore, we show some results of interest to scientists and engineers working on river flows.

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.

Low-head structures are widely used in river restoration. Their function is to regulate the sediment transport and at the same time they can assure optimal habitat for fish species in the river. They strongly affect river morphology because of the erosive processes occurring downstream of them. Thus, a correct design has to take into account several aspects, i.e. technical, economic, environmental, etc. The present chapter aims to present the most recent achievements in scientific literature regarding the design criteria for low-head structures. In particular, low-environmental impact structures will be analyzed and illustrated. In the last decades, the environmental sensibility has increasingly forced hydraulic engineers to propose design solutions which can conjugate both hydraulic functioning and environmental impact minimization. This chapter proposes a synthesis of criteria to predict scour characteristics of the stilling basin downstream of several low-head structure typologies. Namely, the scour process downstream of block ramps will be discussed and the effect of both stilling basin geometry and ramp configuration will be analyzed, for both clear water and live bed conditions. Furthermore, the erosive process downstream of rock grade control structures and stepped gabion weirs will be illustrated along with relationships to predict the characteristic lengths of the scour hole and dune.

Many environmental flows can be considered as shallow. The effects of shallowness are reflected in a strong influence of bed friction and in horizontal velocity gradients as a result of variations in bathymetry and roughness. The horizontal length scales, being generally larger than the vertical length scales, dominate the flow pattern through horizontal momentum exchange. However, three-dimensional effects do play an important role as non-uniformity of bed roughness gives rise to secondary circulation driven by turbulence anisotropy. This not only results in vertical motion, but also hampers the development of eddies formed in the horizontal shear layers. This chapter addresses a few examples where the flow structure is affected by groynes, and examples where roughness variations are the dominant mechanisms creating horizontal shear layers. In the latter cases, the contribution of secondary circulation to horizontal momentum transfer cannot be neglected, demonstrating the importance of three-dimensional effects in shallow flows.

In this chapter, modeling of the unsteady open channel flow using one-dimensional approach is considered. As this question belongs to the well-known and standard problems of open channel hydraulic engineering, comprehensively presented and described in many books and publications, our attention is focused on some selected aspects only. As far as the numerical solution of the governing equations is considered, one can find out that essentially there are no problems with provided accuracy. Usually, the implementation of the Saint Venant equations (i.e. the full dynamic wave model) for any case study is successful as long as the basic assumptions introduced during their derivation are fulfilled. Otherwise, some computational difficulties can occur. For this reason we would like to draw the readers’ attention only to such situations when special computational tricks or simplification of the governing equations should be applied.

This chapter presents a state of the art review and research challenges in modeling flood propagation and floodplain inundation. The challenges for flood inundation models are directly linked to the representation of flow processes, to the formulation of theoretical physical laws and to practical considerations. First, we review the various structures of coupled spatially distributed hydrological-hydraulic models and the corresponding spatial representation of flow processes. Second, we present the theoretical basis of 1-D and 2-D Saint-Venant “shallow water” equations with overbank flow, the approximation of Saint-Venant models such as the Diffusive Wave and the Kinematic Wave models and then discuss the domains and limits of applications of each type of models. Practical considerations linked to numerical solution schemes, boundary conditions and model parameterization, calibration, validation and uncertainty analysis were also considered. Finally, the discussion addresses the research challenges for guiding the modeler, according to the principle of parsimony, in seeking the simplest modeling strategy capable of (i) a realistic representation of the physical processes, (ii) matching the performances of more complex models and (iii) providing the right answers for the right reasons.

Nowadays, numerical 1-D and 2-D flow simulations represent state-of-the-art solutions in hydraulic engineering. Hence, 1-D and 2-D as well as coupled simulations are enrooted in consulting companies and used as basic tools to answer various questions from flood protection to flow optimization. An exception are 3-D flow simulations. Due to complex boundary conditions and high calculation requirements, 3-D CFD simulations are expert tools for universities and research institutions. Here, detailed simulation models, e.g. for hydraulic structure flow optimization, are built up under massive time consumption. The present chapter deals with the basics of numerical flow simulations in practical applications. Additionally, various example flow simulations are mentioned to give an impression about the development of numerical modeling in practical application for the past decade.

Hydraulic modeling is the classical approach to investigate and describe complex fluid motion. Many empirical formulas in the literature used for the hydraulic design of river training measures and structures have been developed using experimental data from the laboratory. Although computer capacities have increased to a high level which allows to run complex numerical simulations on standard workstation nowadays, non-standard design of structures may still raise the need to perform physical model investigations. These investigations deliver insight into details of flow patterns and the effect of varying boundary conditions. Data from hydraulic model tests may be used for calibration of numerical models as well. As the field of hydraulic modeling is very complex, this chapter intends to give a short overview on capacities and limits of hydraulic modeling in regard to river flows and hydraulic structures only. The reader shall get a first idea of modeling principles and basic considerations. More detailed information can be found in the references.

Experimental research was undertaken to investigate the changes in spatial turbulence intensity, water turbulent kinetic energy, the time and spatial macro-scale, scales of turbulent eddies (macro- and microeddies) in a compound channel. Three tests for two various roughness values were realized. The surface of the main channel bed was smooth and made of concrete, whereas the floodplains and sloping banks were covered by cement mortar composed of terrazzo. Instantaneous velocities were measured with the use of a three-component Acoustic Doppler Velocimeter (ADV). The distributions of relative turbulence intensity (u′/U, v′/U, w′/U) in the main channel and on the floodplains were presented. It was found that the longitudinal (u′/U) and transverse (v′/U) turbulence values decreased from the bottom upwards to the floodplain elevation (z/h = 0.56) in the main channel, but remained constant above the floodplain level. Vertical relative turbulence intensity (w′/U) increased going up from the bottom until z/h = 0.15, decreased until about z/h = 0.7, and then increased again upwards to the water surface. The distributions of relative turbulence intensities were described with regression equations. The distributions of turbulent kinetic energy at different water depths were described by regression equations. Vertical distributions of turbulent kinetic energy on the floodplains and over the banks of the main channel were divided into three zones. Over the bottom of the main channel, four zones were determined, containing the middle zone of the flow field divided into two zones of different trends. Measurements of instantaneous velocities are used to investigations of the longitudinal sizes of the smallest eddies (Kolmogorov’s microscale). Presented analyses were based on the already published results.

Uncertainty analysis is an essential step in river modelling. Knowledge of the uncertainty is crucial for a meaningful interpretation of the model results. In this chapter we describe the whole process of an uncertainty analysis in four steps: identification, prioritization, quantification and propagation. In each step the rationale behind choosing a method is described and illustrated with an example of the design water level computation of the Dutch river Waal with a 2D hydrodynamic model. The sources of uncertainty related to the case study are identified and their (relative) importance is determined using expert opinions combined with a novel uncertainty identification method. Subsequently, the sources with the largest effect on the design water levels are individually quantified and propagated using Monte Carlo analysis to yield the quantified uncertainty in the design water levels. The uncertainty analysis provided information about the reliability of the model results and about further actions to possibly reduce the uncertainty and their benefits in terms of increased accuracy.

River morphology and morphodynamics are subject to governing conditions that include the volume and timing of water flows, the volume and calibre of sediment introduced into the river, the nature of bed and bank materials and vegetation, and the geologic and topographic setting of the river, including landscape gradient, climate and human interference. Water flows set the scale of the channel and the sediment regime lends distinctive character to river morphology. Consequently, rivers can usefully be classified on the basis of scale, sediment calibre and gradient, leading to the distinction of steep, intermediate and low gradient channels that generally correspond to channels of high, intermediate and low boundary roughness. Channel changes associated with the downstream passage of sediment constitute the morphodynamics of rivers. Primary morphodynamical effects include channel deformation, channel division, and channel gradation. A fundamental lesson is that rivers transporting a significant charge of bed material sediment necessarily have a lateral style of instability: lateral displacement of the channel is a normal part of their equilibrium function. Hence the required channel zone is larger than the presently active channel. Implications of this circumstance are considered in the context of channel management and river restoration.

This text addresses the particular case of motion and causes of motion of granular material as bedload in the fluvial domain. The aim is to perform and overview of key concepts, main achievements and recent advances on the description of the processes involved in erosion, deposition and transport of sediment in open-channels. The theoretical functional relations describing both the initiation of motion and the sediment transport are introduced. The classical problem of the initiation of motion of particles is treated at grain and at reach scales, accounting for the stochastic nature of flow. Concepts of granular kinematics and methods for quantifying the sediment transport rate in rivers are presented. The latter results from the interactions between the flow and the particles on the bed surface. The sediment transport rate, which has been shown to have a stochastic behaviour, is converted to a lumped statistic distribution. Finally, some field and laboratory techniques for measuring sediment transport, accounting for its inherent fluctuations, are introduced.

This paper presents a review of the present understanding of the kinematics of meandering flow, and its relationship to bed deformation as well as downstream migration and lateral expansion of meander loops. Taking into account the conditions prevailing in natural, low-land alluvial meandering rivers, the paper focuses primarily on the behaviour of streams having “large” values of width-to-depth ratio. The present review is preceded by a brief description of meandering defining geometric characteristics, as these are invoked throughout this manuscript. The paper is also used as an opportunity to outline future directions for research. These involve matters related to the topics under consideration that remain obscure and which, in the writer’s view, constitute subjects particularly worthwhile as future research topics for their scientific as well as practical significance. More specifically, these concern the nature and analytical formulation of meander wavelength; the value of width-to-depth ratio beyond which the effect of cross-circulation becomes of secondary importance where the meandering bed deformation is concerned; and, finally, the unification of present methods of determination of meandering planimetric evolution with the principle of self-formation of alluvial streams as expressed by regime theory.

Braided rivers are characterized by an unstable network of multiple channels and very active channel processes. They can be found in different climate regions (e.g. from glacial areas to arid regions) and physiographic settings (e.g. from steep mountain areas to low coastal plains). This chapter aims to summarize the present knowledge about braided rivers and to point out some gaps that still require further research. The first part of the chapter focuses on channel processes while the second part deals with channel changes through time. As for the first part, the following processes are illustrated: bar formation and development; processes at bifurcations and confluences; lateral mobility; bedload transport; role of vegetation on river morphodynamics. The second part deals with the evolution of braided rivers, mainly in response to human alteration of fluvial systems, over some decades up to some centuries. The historical perspective is crucial to understand present morphology and processes, as well as to assess future channel evolution. Understanding about braided river morphology and processes has significantly increased over the last three decades or so, through physical modeling, field observations, and, to a lesser extent, numerical modeling. On the other hand, several open questions still remain and future research should address aspects such as metrics used to characterized braided rivers, measurements of flow and sediment transport, and prediction of future channel evolution.

One hundred years of research on the saltation in rivers, both experimental and numerical, has allowed for a fairly good improvement of our knowledge of the physics of the saltation process. Lagrangian modelling has played a huge role in this field and has made it possible to apply the knowledge obtained in the analysis of processes associated with the movement of sediment particles. The present paper briefly reviews the current state-of-the-art of the Lagrangian modelling of saltating grains in open channels and highlights recent findings in three areas in which employment of the Lagrangian models of saltation improve our understanding of sediment transport in rivers, namely: initial motion of saltating grains, diffusion of particles and calculation of the bedload transport rate. The particular challenges in all of these research areas are discussed and future ways forward are presented.

In many parts of the world, forest fires are very common. Fires burn more or less severely the vegetation and even the most organic parts of the forest soil. Fire can modify the physical properties of soil; due to the combustion of vegetation and organic matter, some chemical substances appear and ashes are deposited in the soil surface in various quantities. During the combustion, there is a production of gases, which go to the atmosphere but some of them go deep into the soil and condensate around the soil particles. Due to these important changes resulting from fires, the rainfall arrives at the soil surface in a different way, the infiltration capacity changes due to hydrophobicity, the runoff generation can increase and also the movement of fine and coarse soil particles takes place. All these changes are important for the water and sediment production at the slopes and the consequences can remain during months or years at a basin scale.

Ecological thresholds and resilience are powerful heuristics for understanding how lotic ecosystems change. Ecosystems may exist in self-organized states based on their taxonomic composition or the range of ecosystem functions, which are influenced by environmental drivers such as thermal or hydrologic regimes, channel morphology, and availability of nutrients. Changes in these underlying drivers may exceed an ecosystem’s ability to maintain its characteristic attributes and shift the system into alternative states of organization, which are often regarded as degraded or undesired. The boundaries where transitions occur are known as ecological thresholds and often show a rapid ecosystem response across a relatively small change in the environmental driver. Resilient ecosystems have the capacity to retain attributes in the face of disturbances. However, at some disturbance magnitude an ecosystem may become altered, and the magnitude necessary for a regime shift decreases as resilience declines. While ecological resilience remains largely metaphorical in lotic ecosystems, we describe some approaches for identification and assessment.

This chapter focuses on how flow and associated geomorphic processes influence river and stream invertebrates. It stresses the importance of flows and fluvial dynamics across a range of scales, discussing how they influence individual organisms, populations and whole communities. It considers not just benthic larvae, but how flow and sedimentological conditions influence other life stages. Consideration is also given to how organisms influence habitat—so called ‘habitat engineering’. The chapter argues that a detailed understanding of species’ ecologies is needed if we are to understand precisely why they are affected by flow conditions and to allow us to manage rivers sustainably.

Within scientific hydrological, geomorphological and also engineering literature the two discharges that very often demand attention of hydrologists as well as ecologists and river engineers and water catchment managers are, respectively, the dominant and bankfull discharges. What are they? Do we really need them and why? The present paper explains the main ways of the dominant and bankfull discharges determinations and calculations. As far as the dominant discharge is concerned, the most important methods to find its value are: the Rzanicyn, the Debski, the Lambor, the Marlette and Walker, the Wolman and Miller, and the Makkavieiev methods. When considering bankfull discharge, the most important concepts and definitions as well as methods of its determination are: the Williams, the Wolman, the Schumm and Brown, the Riley, the Woodyer as well as the Radecki-Pawlik and Skalski methods. All those concepts and methods are described. Additionally, examples of bankfull calculations are given from one of the Carpathians rivers to show the difference obtained in bankfull values using different methods. Both morphometric and biological methods are used to determine bankfull. Special attention is given to biological approaches of bankfull methods since the Water Framework Directive gives priority to biological measures and findings along river and stream reaches.

Hydrodynamics of vegetated channels and streams is a rapidly developing research area, and this chapter summarizes the current knowledge considering both aquatic and riparian zones. The benefit of an advanced parameterization of plant morphology and biomechanical properties is highlighted. For this purpose, the response of flexible and foliated plants and plant communities to the flow is illustrated, and advanced models for the determination of drag forces of flexible plants are described. Hydrodynamic processes governing flow patterns in vegetated flows are presented for submerged and emergent conditions considering spatial scales ranging from the leaf to the vegetated reach scale.

An important application of environmental hydraulics is the prediction of the fate and transport of dissolved oxygen within fluvial systems. For rivers this requires knowledge of the principle hydrological processes such as advection and dispersion and the physico-chemical process of re-aeration. Currently, in the absence of appropriate field measurements quantifying the mixing or aeration processes in a river, we rely on semi-empirical predictive equations that attempt to relate these processes to global flow and channel parameters. Although there is some theoretical justification for the form of these equations, they are not particularly successful even for channels of simple shape. As more complex channel shapes (e.g. two-stage flood relief channels) are tackled the equations become increasingly inappropriate. To help address this concern, the chapter proposes a theoretical approach for evaluating both the longitudinal dispersion coefficient and the re-aeration coefficient in channels of arbitrary shape that is based on integral formulations and which uses theoretical predictions of the transverse flow structure that are based on Shiono and Knight’s (J Fluid Mech 222:617–646, 1991) momentum balance equation. The results for a simple channel (trapezoidal) are consistent with current knowledge, but they reveal unexpected patterns for a complex channel (two-stage, trapezoidal with active floodplains) that contains zones of distinctly different velocity and depth. The results also explore the role of the transverse turbulent transfer of momentum. For the simple channel, the dispersion coefficient was very small (being in the range 0–1 m²/s for flow rates between 0 and 35 m³/s and channel widths of approximately 15 m), and increased approximately linearly with flow rate. The influence of the transverse turbulent momentum exchange was relatively significant. For the complex channel, the dispersion coefficient was very large (being in the range 27,000–500 m²/s for flow rates between 35 and 175 m³/s and widths of approximately 55 m), and decreased with flow rate according to a power law with an exponent of about −4.7. The influence of the transverse turbulent momentum exchange was less than for the simple channel case. The predictions for both flow conditions are consistent with observed trends reported in Rutherford (River mixing. Wiley, Chichester, 1994). The very large dispersion coefficients found in the complex channel case could not be predicted using the existing semi-empirical equations proposed by Liu (J Environ Eng Div, Am Soc Civil Eng 103(EE1):59–69, 1977) and Deng et al. (J Hydraul Eng, Am Soc Civil Eng 127(11):919–927, 2001); neither could the rapid decrease with increasing flow rate. This is not surprising because the equations cannot represent the extremely strong transverse velocity shear that exists in these flows that contain zones of quite different velocity and depth. For the re-aeration coefficient in the simple channel we identified a power law decrease (exponent of about −0.5) with flow rate from about 40 to 10 per day up to the bank full condition. Once flows went over-bank the re-aeration coefficient jumped considerably (to about 100 per day) due to the small depths on the floodplains. It then reduced as a power law as flow rate increased (exponent of about −0.9). The influence of the transverse turbulent momentum exchange was not very significant for either channel case. Results from a semi-empirical equation proposed by Bennett and Rathbun (Reaeration in open-channel flow. United Sates Geological Survey, Washington, 74 pp, 1972) mirrored the computational results, but under-predicted the coefficient by about 50 % for both the simple and complex channel cases. Clearly, existing semi-empirical equations for the dispersion coefficient and the re-aeration coefficient should not be used for predicting non-conservative chemical transport for the over-bank case of a complex channel. A sensitivity analysis for the case of a steady oxygen demanding waste water discharge showed that the maximum dissolved oxygen sag and its location were insensitive to dispersion but were significantly sensitive to re-aeration for both channel cases. Hence, for this waste water scenario future work should focus on improving the prediction of re-aeration coefficients in both types of channel.

The fate of solute and pollutants is controlled by a broad number of different transport and storage mechanisms, ranging from simple processes (i.e. molecular diffusion, advection etc.) to more complex phenomena (i.e. evapotranspiration, groundwater flows, etc.). Different mathematical models, accounting for different exchange processes, have been developed and applied to specific experimental studies to assess transport and storage parameters. Experimental research focused on transport and retention processes induced by the transient storage in the dead zones, by the river bed topography and vegetation, by evapotranspiration. The analysis of these physical processes is generally conducted observing the behavior of solutes in field environments or in scaled laboratory models, using artificial or environmental tracers to track the fate of transported substances and assess transport and retention parameters. To improve the knowledge of pollutant exchange mechanism between a river and the surrounding environment, new experimental techniques focusing on long timescale retention and investigating the link between river biology and hydrodynamics are required. The development of new protocols for tracer tests design and the use of new specific tracers will open future research perspectives.

Modeling framework for stream temperature, especially after introducing substantial amount of heat pollution, is presented in this chapter. An overview of the mathematics and solution techniques suited for heat transfer quantification is given and the models presented range from 3D aimed at short distances towards 1D approach allowing for modeling of heat transfer over long distances. A special attention has been paid to the depth averaged two-dimensional models which are particularly useful when the fate of heat pollution such as the heat discharged from a steam power station is considered. The processes of exchange between the river water and river surrounding are also discussed. Examples of computational solutions are provided and discussed as well.