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A General Lagrangian Tracking Methodology for Riverine Flow and Transport
Abstract
This paper presents a new public domain tool for generalized Lagrangian particle tracking in rivers. The approach can be applied with a variety of two‐ and three‐dimensional flow solvers. Particle advection by the flow is incorporated using flow fields from the chosen solver assuming particles follow the Reynolds‐averaged flow, although some other simple passive and active particle behaviors are also treated. Turbulence effects are treated using a random walk algorithm with spatial step lengths randomly chosen from Gaussian distributions characterized by the diffusivity from the flow solver. Our work extends this concept to a general framework that is solver and coordinate system independent to allow easy comparisons between differing flow treatments. To better treat problems where detailed information is required in specific regions, the approach includes novel cloning and colligation algorithms which enhance local resolution at modest computational expense. We also provide tools for computing local concentrations and total exposure over a user‐specified time interval. Several examples of predictions are provided to illustrate application of the technique, including examination of the role of curvature‐driven secondary flows, storage in lateral separation eddies, treatment of larval drift, treatment of fuel spill dispersion, river‐floodplain connections, and sedimentation in floodplain ponds by tie channel connections. We also demonstrate that the model can reproduce analytically derived concentration profiles for simple diffusivities. These examples show that the Lagrangian particle tracking approach and the extensions proposed here are broadly applicable and viable for treating difficult river problems with multiple temporal and spatial scales. The examples also illustrate the utility of the cloning/colligation extensions and show how these can decrease the computational effort required on problems where high local resolution is required. Enhancement of the tools and even broader applicability can be achieved through the inclusion of multiple particle populations and particle‐particle interactions.
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In view of the severity of oceanic pollution, based on the finite volume coastal ocean model (FVCOM), a Lagrangian particle-tracking model was used to numerically investigate the coastal pollution transport and water exchange capability in Tangdao Bay, in China. The severe pollution in the bay was numerically simulated by releasing and tracking particles inside it. The simulation results demonstrate that the water exchange
capability in the bay is very low. Once the bay has suffered pollution, a long period will be required before the environment can purify itself. In order to eliminate or at least reduce the pollution level, environmental improvement measures have been proposed to enhance the seawater exchange capability and speed up the water purification inside the bay. The study findings presented in this paper are believed to be instructive and useful for future environmental policy makers and it is also anticipated that the numerical model in this paper can serve as an effective technological tool to study many emerging coastal environment problems.
Predicting the motion of driftwood around hydraulic structures such as bridge piers and spur dikes is important. We propose a numerical model for simulating driftwood motion that is based on coupling an Eulerian-type three-dimensional flow model and a Lagrangian-type two-dimensional driftwood model. Laboratory tests were carried out on the driftwood motion in a curved channel and around obstacles to obtain reference data. The computational results showed that three-dimensional flow features considerably affect the motion of driftwood in a curved channel. We defined the driftwood Richardson number (DRI) to classify the three-dimensional behavior of driftwood around obstacles. The experimental results showed that an increasing DRI indicates more three-dimensional behavior by driftwood and a decreased capture ratio by obstacles. We also developed a two-way model in which the drag force from driftwood on the flow is modeled to simulate the backwater elevation and the flow deceleration behind the stacked driftwood. The computational results showed that the two-way model could reproduce the increase of water level and the decrease of velocity at the upstream region of the obstacles. However, such effects caused by the driftwood jamming were underestimated if the jamming happened in a three-dimensional manner.
The most innovative hydraulic research flows from the needs of applications in diverse, very often complex settings. The aim of this preface is to provide a brief overview on mass transport in complex natural flows, highlighting relevant but often neglected considerations, advances presented in the articles of this Special Issue, and ways forward. Understanding and prediction of how dissolved nutrients and other solutes, suspended sediment and other particulate matter, and thermal pollution are propagated and mixed in natural channels are important for designing effective management and mitigation strategies concerning these scalars.
Complexity stressed in the title of this Special Issue is in fact a philosophical notion, typically not sufficiently well defined. Complex or complexity is a keyword very often used in environmental hydraulics, in most cases intuitively, sometimes as synonyms of the adjective complicated. At the same time, complexity has strong scientific connotation and is treated almost as a separate research domain. In contrast to many other scientific disciplines, in environmental hydraulics, it is not well established when the subject of our investigation can be described as complex.
To develop a better predictive tool for dispersion in rivers over a range of temporal and spatial scales, our group has developed a simple Lagrangian model that is applicable for a wide range of coordinate systems and flow modeling methodologies. The approach allows dispersion computations for a large suite of discretizations, model dimensions (1-, 2-, or 3-dimensional), spatial and temporal discretization, and turbulence closures. As the model is based on a discrete non-interacting particle approach, parallelization is straightforward, such that simulations with large numbers of particles are tractable. Results from the approach are compared to dispersion measurements made with conventional Rhodamine WT dye experiment in which typical at-a-point sensors are employed to determine concentration. The model performs well, but spatial resolution for experiments over large and or complex river flows was inadequate for model testing. To address this issue, we explored the idea of measuring spatial concentrations in river flows using hyperspectral remote sensing. Experiments both for idealized channels and real rivers show that this technique is viable and can provide high levels of spatial detail in concentration measurements with quantitatively accurate concentrations.
Sediment particles transported as bed load undergo alternating periods of motion and rest, particularly at weak flow intensity. Bed-load transport can be investigated by either following the motion of individual particles (Lagrangian approach) or observing the phenomenon at prescribed locations (Eulerian approach). In this paper, the Lagrangian and Eulerian descriptions are merged into a unifying framework that includes definitions for quantities used to describe the kinematics of particle motion, as well as the relationships among these quantities. The alternation of motion and rest is represented by two complementary descriptions: (i) proportion of motion, indicating either the relative time spent in motion by an individual particle or the relative number of moving particles; (ii) persistence of motion, indicating the extent to which the process consists of relatively few long periods of motion or of many short ones. The framework only involves first moments of the key quantities. The conceptual developments are tested against results from an experiment with weak bed-load transport, demonstrating the soundness of the approach. From an operational point of view, a Lagrangian observation is difficult to perform, since the particle motion is usually investigated for finite spatial domains (e.g., a measurement window within a laboratory or natural reach). Strategies to overcome such limitations are described, suggesting the possibility of obtaining unbiased mean values for Lagrangian descriptors. The proposed framework can be used in any study aimed at parameterizing the kinematic properties of bed-load particles as functions of the hydrodynamic conditions.
One of the mechanisms that greatly affect the pollutant transport in rivers, especially in mountain streams, is the effect of transient storage zones. The main effect of these zones is to retain pollutants temporarily and then release them gradually. Transient storage zones indirectly influence all phenomena related to mass transport in rivers. This paper presents the TOASTS (third-order accuracy simulation of transient storage) model to simulate 1-D pollutant transport in rivers with irregular cross-sections under unsteady flow and transient storage zones. The proposed model was verified versus some analytical solutions and a 2-D hydrodynamic model. In addition, in order to demonstrate the model applicability, two hypothetical examples were designed and four sets of well-established frequently cited tracer study data were used. These cases cover different processes governing transport, cross-section types and flow regimes. The results of the TOASTS model, in comparison with two common contaminant transport models, shows better accuracy and numerical stability.
Predicting fish responses to modified flow regimes is becoming central to fisheries management. In this study we present an agent-based model (ABM) to predict the growth and distribution of young-of-the-year (YOY) and one-year-old (1+) Atlantic salmon and brown trout in response to flow change during summer. A field study of a real population during both natural and low flow conditions provided the simulation environment and validation patterns. Virtual fish were realistic both in terms of bioenergetics and feeding. We tested alternative movement rules to replicate observed patterns of body mass, growth rates, stretch distribution and patch occupancy patterns. Notably, there was no calibration of the model. Virtual fish prioritising consumption rates before predator avoidance replicated observed growth and distribution patterns better than a purely maximising consumption rule. Stream conditions of low predation and harsh winters provide ecological justification for the selection of this behaviour during summer months. Overall, the model was able to predict distribution and growth patterns well across both natural and low flow regimes. The model can be used to support management of salmonids by predicting population responses to predicted flow impacts and associated habitat change.
The Chicago Area Waterway System (CAWS) includes the Chicago Sanitary and Ship Canal (CSSC) and the Calumet-Sag Channel (Cal-Sag), the two primary, man-made connections between the Mississippi River Basin and the Great Lakes. The U.S. Geological Survey (USGS) monitors diversion of Great Lakes water at a streamgage just downstream of the confluence of the CSSC and Cal-Sag (known as Sag Junction). Previous studies have explored the complex hydrodynamics in the CAWS near Sag Junction and at the USGS streamgage near Lemont, Illinois. The current study explores the mixing at Sag Junction which can be purely advection-driven or driven by density differences between the two branches. The current study simulates and analyzes two cases: 1) the density of water in CSSC is greater than in the Cal-Sag, 2) the density of the CSSC water is less than in the Cal-Sag. The density difference between the branches was found to play a major role in influencing the mixing process compared with purely advection-driven mixing. Density differences created near-bed gravity currents, some of which intruded upstream into the CSSC or Cal-Sag creating bi-directional flows. The phenomenon of double plunging was observed, along with formation of a recirculation zone between the two plunging fronts. Local mixing at the confluence was enhanced by density differences between the two channels, but mixing downstream from the confluence was impeded due to formation of a stabilizing stratification.
A multilevel grid-type turbulent shallow flow model combined with an equilibrium sediment transport model (KMR-MB: Kinematic Mesh Reconstruction for Movable Bed) is proposed. The KMR method is a kind of multilevel grid model with dynamic refinement that combines grid cells to efficiently capture the unsteady flow phenomena. Saito et al. (2012)1),2) have applied the KMR approach to open channel flows around a bridge pier and have shown the advantage of the model. They used the maximum value of the strain and rotation parameters for the threshold for quadtree and 3×3 grid divisions. We have extended the model for computations of morphological phenomena in rivers by incorporating an equilibrium sediment transport model as well as a bed continuity equation, and used new criteria for grid cell refinement. We used an average curvature of the bed surface as the criteria for refinement and combined quadtree-type grid cells. The present model has been applied to simulate the alternate bar formations. The experimental result by Akahori et al. (2011)3) was used to validate the model. The comparison between numerical and experimental results showed that the present KMR-MB can excellently simulate the phenomena with less CPU time than those computed with the fixed grid.
It is observed, during flood events, that bedforms initially grow in height and make the river bed rougher. But later, under high discharge, the bedforms grow longer with the opposite effect of making the river bed smoother. After the discharge drops to a lower value, new bedforms regenerate on top of the elongated bedforms. This mechanism leads to a significant variation in the bed roughness and the water stage, and hence determines the behaviour of floods and the risk of flood disasters. This work presents detailed modelling of bedforms under discharge hydrographs and simulates the conditions under which the bed is flattened out in the upper plane-bed regime. The flow was simulated by large-eddy simulation, and the sediments were considered as rigid spheres and modelled in a Lagrangian framework. The bed morphodynamics were the result of entrainment and deposition of sediment particles. We examined several discharge hydrographs. In the first case, we increased the discharge linearly and then kept it constant after reaching the upper-plane bed condition. The dunes were generated and grew during the rising stage of discharge. When the flow conditions reached the upper plane-bed regime, high-frequency ripples were generated and helped to flatten the bed. The results also showed that, in contrast with mechanisms in the dune regime, the flattening of the bed was associated with a distinct pattern of sediment transport which deposited sediment mainly in the lee side of the dunes and led to flattening of the bed. After flattening, the sediments were mainly transported in suspension mode. As long as flow conditions stayed in the upper plane-bed regime, the bed remained flat with small high-frequency ripples. We also examined two other scenarios: one with an immediate falling stage of discharge after the rising stage and the other with a period of constant discharge between the rising and falling stages. Dunes were regenerated during the falling stage of discharge for both cases. In the first case, the dunes were regenerated before the bed was flattened because of a time lag between the flow and the bed deformation. Bed flattening was followed by dune regeneration in the second case. Moreover, a significant reduction in the form drag coefficient was observed after the flattening in the second case. The reduction in form drag led to a reduction in the flood intensity. The model showed its ability to reproduce the key phenomena of the development of subaqueous dunes under conditions of a passing flood wave.
One-dimensional (1-D) numerical models of solute transport in streams rely on the advection–dispersion equation, in which the longitudinal dispersion coefficient is an unknown parameter to be calibrated. In this work we investigate the extent to which existing empirical formulations of longitudinal dispersion coefficient can be used in 1-D numerical modelling tools of solute transport under steady and unsteady flow conditions. The 1-D numerical model used here is the open source Mascaret tool. Its relevance is illustrated by simulating theoretical cases with known analytical solutions. Ten empirical formulas of longitudinal dispersion coefficient are then tested by simulating eight laboratory experimental cases under steady flow condition and the solute transport in the Middle Loire River (350 km long) under highly variable flow condition (from July 1st 1999 to December 31st 1999). Comparisons between computed and measured breakthrough curves show that Elder (1959), Fischer (1975) and Iwasa and Aya (1991) formulas rank as the best predictors for the experimental cases. For the field case, Seo and Cheong’s (1998) formula yields the best model-data agreement, followed by Iwasa and Aya’s (1991) formula. The latter formula is, therefore, recommended for the entire range of conditions studied here.
Flows with large scale vortices are often observed in many natural, geophysical as well as anthropogenic activities. In this study, the Stuart vortices having both the singular points (the vortex and saddle points) are considered to study the basic turbulent properties. Using a realizable non-linear κ-ε A model, the approximate solutions are derived and numerical simulations are carried out. Using the approximate solution, the values of model constants are tuned considering the predictability of turbulent structures at the vortex center. The numerical results prove the effectiveness of the approximate approach, and reveals that the model with the estimated constants is applicable to simulate large scale vortices. The spatial changes in the topological structures of turbulent energy and turbulent stresses are found compatible with the previous experimental results.
We present a 3-D physics-based high-resolution modeling approach to the
dynamics of underwater ripples and dunes. The flow is modeled by large
eddy simulation on a Cartesian grid with local refinements. The sediment
transport is modeled by computing pickup, transport over the bed,
transport in the water column, and deposition of rigid spherical
particles in a Lagrangian framework. The morphological development of
the bed is modeled by a sediment balance equation in which the pickup
and deposition from the sediment motion submodels appear as source and
sink terms. The model realistically replicated the formation and
migration of dunes. Model results showed a good agreement with data from
five flume experiments. We subsequently applied the model to investigate
the effect of sediment grain size on ripples. Finer sediments were found
to yield more superimposed ripples than coarser sediments. Moreover,
under the same hydrodynamic conditions, the finer sediments yielded
two-dimensional bed forms, whereas for coarser sediment irregularities
increased. We extended the tests to pronounced 3-D morphologies by
simulating the development of local scour at a pier. The results agreed
well with experimental data. The model contributes to unraveling the
complex problem of small-scale morphodynamics and may be used in a wide
range of applications, for instance, to develop more reliable
parameterizations of small-scale processes for application in
large-scale morphodynamic models.
The paper describes a numerical model for simulating sediment transport
with eddy-resolving 3-D models. This sediment model consists of four
submodels: pickup, transport over the bed, transport in the water column
and deposition, all based on a turbulent flow model using large-eddy
simulation. The sediment is considered as uniform rigid spherical
particles. This is usually a valid assumption for sand-bed rivers where
underwater dune formation is most prominent. Under certain shear stress
conditions, these particles are picked up from the bed due to an
imbalance of gravity and flow forces. They either roll and slide on the
bed in a sheet of sediment or separate from the bed and get suspended in
the flow. Sooner or later, the suspended particles settle on the bed
again. Each of these steps is modeled separately, yielding a
physics-based process model for sediment transport, suitable for the
simulation of bed morphodynamics. The sediment model is validated with
theoretical findings such as the Rouse profile as well as with empirical
relations of sediment bed load and suspended load transport. The current
model shows good agreement with these theoretical and empirical
relations. Moreover, the saltation mechanism is simulated, and the
average saltation length, height, and velocity are found to be in good
agreement with experimental results.
We present a three-dimensional high-resolution hydrodynamic model for
unsteady incompressible flow over an evolving bed topography. This is
achieved by using a multilevel Cartesian grid technique that allows the
grid to be refined in high-gradient regions and in the vicinity of the
river bed. The grid can be locally refined and adapted to the bed
geometry, managing the Cartesian grid cells and faces using a
hierarchical tree data approach. A ghost-cell immersed-boundary
technique is applied to cells intersecting the bed topography. The
governing equations have been discretized using a finite-volume method
on a staggered grid, conserving second-order accuracy in time and space.
The solution advances in time using the fractional step approach.
Large-eddy simulation is used as turbulence closure. We validate the
model against several experiments and other results from literature.
Model results for Stokes flow around a cylinder in the vicinity of a
moving wall agree well with Wannier's analytical solution. At higher
Reynolds numbers, computed trailing bubble length, separation angle, and
drag coefficient compare favorably with experimental and previous
computational results. Results for the flow over two- and
three-dimensional dunes agree well with published data, including a fair
reproduction of recirculation zones, horse-shoe structures, and boiling
effects. This shows that the model is suitable for being used as a
hydrodynamic submodel in the high-resolution modeling of sediment
transport and formation and evolution of subaqueous ripples and dunes.
A 3D Lagrangian model of the saltation of solid spherical particles on the bed of an open channel flow, accounting for turbulence-induced mechanisms, is proposed and employed as the key tool of the study. The differences between conventional 2D models and a proposed 3D saltation model are discussed and the advantages of the 3D model are highlighted. Particularly, the 3D model includes a special procedure allowing generation of 3D flow velocity fields. This procedure is based on the assumption that the spectra of streamwise, vertical and transverse velocity components are known at any distance from the bed. The 3D model was used to identify and quantify effects of turbulence on particle entrainment and saltation. The analysis of particle trajectories focused on their diffusive nature, clarifying: (i) the effect of particle mobility parameter; (ii) the effect of bed topography; and (iii) the effect of turbulence. Specifically, the results of numerical simulations describing the abovementioned effects on the change in time of the variance are presented. In addition, the change in time of the skewness and kurtosis, which are likely to reflect the turbulence influence on the spread of particles, are also shown. Two different diffusion regimes (local and intermediate) for each of the investigated flow conditions are confidently identified.
As outfalls from various water reclamation plants, pumping stations, and combined sewer overflow outfalls discharge into the Chicago Area Waterway System (CAWS), an enhanced understanding of the final fate of crucial water quality state variables is of utmost importance. This paper reports the development and application of a 3D water quality model for a modified CAWS combined with the hydrodynamic kernel of Environmental Fluid Dynamics Code (EFDC). The modified CAWS is used to demonstrate the usefulness of the model while eliminating complications beyond the scope of this initial effort. The water quality model developed and presented in this research is a simplistic dissolved oxygen (DO)—biochemical oxygen demand model with the facility to account for the interaction between the water column and the bed. The aforementioned model is applied for the month of May 2009. The results from the hydrodynamic (EFDC) and water quality model is validated with the help of the observed data obtained from United States Geological Survey gaging stations and Metropolitan Water Reclamation District of Greater Chicago monitoring stations present inside the modeled domain. The 3D modeling captured the hydrodynamic and water-quality processes in CAWS in a satisfactory manner. Furthermore, modeling results showed and proved the interdependence of water quality characteristics in Bubbly Creek and CAWS with the effluent concentration from Racine Avenue Pumping Station situated at the head of Bubbly Creek, South Fork of South Branch of Chicago River.
The physical characteristics of mountain streams differ from the uniform
and conceptually well- defined open channels for which the analysis of
solute transport has been oriented in the past and is now well
understood. These physical conditions significantly influence solute
transport behavior, as demonstrated by a transient storage model
simulation of solute transport in a very small (0.0125
m3s-1) mountain pool-and-riffle stream. The
application is to a carefully controlled and intensively monitored
chloride injection experiment. The data from the experiment are not
explained by the standard convection-dispersion mechanisms alone. A
transient storage model, which couples dead zones with the
one-dimensional convection-dispersion equation, simulates the general
characteristics of the solute transport behavior and a set of simulation
parameters were determined that yield an adequate fit to the data.
However, considerable uncertainty remains in determining physically
realistic values of these parameters. The values of the simulation
parameters used are compared to values used by other authors for other
streams. The comparison supports, at least qualitatively, the determined
parameter values.
Station Helgoland Roads in the south-eastern North Sea (German Bight) hosts one of the richest long-term time series of marine
observations. Hydrodynamic transport simulations can help understand variability in the local data brought about by intermittent
changes of water masses. The objective of our study is to estimate to which extent the outcome of such transport simulations
depends on the choice of a specific hydrodynamic model. Our basic experiment consists of 3,377 Lagrangian simulations in time-reversed
mode initialized every 7 h within the period Feb 2002–Oct 2004. Fifty-day backward simulations were performed based on hourly
current fields from four different hydrodynamic models that are all well established but differ with regard to spatial resolution,
dimensionality (2D or 3D), the origin of atmospheric forcing data, treatment of boundary conditions, presence or absence of
baroclinic terms, and the numerical scheme. The particle-tracking algorithm is 2D; fields from 3D models were averaged vertically.
Drift simulations were evaluated quantitatively in terms of the fraction of released particles that crossed each cell of a
network of receptor regions centred at the island of Helgoland. We found substantial systematic differences between drift
simulations based on each of the four hydrodynamic models. Sensitivity studies with regard to spatial resolution and the effects
of baroclinic processes suggest that differences in model output cannot unambiguously be assigned to certain model properties
or restrictions. Therefore, multi-model simulations are needed for a proper identification of uncertainties in long-term Lagrangian
drift simulations.
Considerable technical developments over the past half century have enabled widespread application of electronic tags to the study of animals in the wild, including in freshwater environments. We review the constraints associated with freshwater telemetry and biologging and the technical developments relevant to their use. Technical constraints for tracking animals are often influenced by the characteristics of the animals being studied and the environment they inhabit. Collectively, they influence which and how technologies can be used and their relative effectiveness. Although radio telemetry has historically been the most commonly used technology in freshwater, passive integrated transponder (PIT) technology, acoustic telemetry and biologgers are becoming more popular. Most telemetry studies have focused on fish, although an increasing number have focused on other taxa, such as turtles, crustaceans and molluscs. Key technical developments for freshwater systems include: miniaturization of tags for tracking small-size life stages and species, fixed stations and coded tags for tracking large samples of animals over long distances and large temporal scales, inexpensive PIT systems that enable mass tagging to yield population-and community-level relevant sample sizes, incorporation of sensors into electronic tags, validation of tag attachment procedures with a focus on maintaining animal welfare, incorporation of different techniques (for example, genetics, stable isotopes) and peripheral technologies (for example, geographic information systems, hydroacoustics), development of novel analytical techniques, and extensive international collaboration. Innovations are still needed in tag miniaturization, data analysis and visualization, and in tracking animals over larger spatial scales (for example, pelagic areas of lakes) and in challenging environments (for example, large dynamic floodplain systems, under ice). There seems to be a particular need for adapting various global positioning system and satellite tagging approaches to freshwater. Electronic tagging provides a mechanism to collect detailed information from imperilled animals and species that have no direct economic value. Current and future advances will continue to improve our knowledge of the natural history of aquatic animals and ecological processes in freshwater ecosystems while facilitating evidence-based resource management and conservation.
A random walk model to describe the dispersion of pollutants in shallow water is developed. By deriving the Fokker-Planck equation, the model is shown to be consistent with the two-dimensional advection-diffusion equation with space-varying dispersion coefficient and water depth. To improve the behaviour of the model shortly after the deployment of the pollutant, a random flight model is developed too. It is shown that over long simulation periods, this model is again consistent with the advection-diffusion equation. The various numerical aspects of the implementation of the stochastic models are discussed and finally a realistic application to predict the dispersion of a pollutant in the Eastern Scheldt estuary is described.
In articles published in 2009 and 2010, Suk and Yeh reported the development of an accurate and efficient particle tracking algorithm for simulating a path line under complicated unsteady flow conditions, using a range of elements within finite elements in multidimensions. Here two examples, an aquifer storage and recovery (ASR) example and a landfill leachate migration example, are examined to enhance the practical implementation of the proposed particle tracking method, known as Suk's method, to a real field of groundwater flow and transport. Results obtained by Suk's method are compared with those obtained by Pollock's method. Suk's method produces superior tracking accuracy, which suggests that Suk's method can describe more accurately various advection-dominated transport problems in a real field than existing popular particle tracking methods, such as Pollock's method. To illustrate the wide and practical applicability of Suk's method to random-walk particle tracking (RWPT), the original RWPT has been modified to incorporate Suk's method. Performance of the modified RWPT using Suk's method is compared with the original RWPT scheme by examining the concentration distributions obtained by the modified RWPT and the original RWPT under complicated transient flow systems.
This paper describes the unsteady Reynolds-averaged Navier-Stokes (URANS) computations of a quasi-two-dimensional (2D) grid turbulence in shallow open-channel flows, generated downstream of multiple piers aligned at regular intervals over the channel width. In shallow open-channel flows, the vertical confinement of the flow generally suppresses the three dimensionality and attains two-dimensional features with up-cascading of turbulent kinetic energy from small-scale toward large-scale structures. In this study, 2D depth averaged and 3D Reynolds-averaged equations with linear and nonlinear URANS turbulence models are applied to a shallow open-channel flow downstream of multiple piers and numerical results are discussed through a comparison with the experimental results performed by Uijttewaal and Jirka in 2003. We employed 0-equation models and k-ε models for the 2D and 3D computations, respectively. In 2D computations, vortices downstream of the grid occurred synchronously in the computation with both the linear and nonlinear 0-equation models. In the 3D computations, vortex merging and up-cascading of the kinetic energy were captured when artificial disturbance is added at the inlet. The measured decay of the turbulent kinetic energy in the streamwise direction, with a slope of -1.3, was well captured by computation with the 3D models with inlet disturbance. The flow sensitivity on the inlet disturbance was rather small in the wide range of the disturbance ratios.
The migration of larval fish from spawning to rearing habitat in rivers is not well understood. This paper describes a methodology to predict larval drift using a Lagrangian particle-tracking (LPT) model with passive and active behavioural components loosely coupled to a quasi-three-dimensional hydraulic model. In the absence of measured larval drift, a heuristic approach is presented for the larval drift of two species of interest, white sturgeon (Acipenser transmontanus) and burbot (Lota lota), in the Kootenai River, Idaho. Previous studies found that many fish species prefer certain vertical zones within the water column; sturgeon tend to be found near the bottom and burbot close to the water surface. Limiting the vertical movement of larvae is incorporated into the active component of the LPT model. The results illustrate a pattern of drift where secondary flow in meander bends and other zones of flow curvature redistributes particles toward the outside of the bend for surface drifters and toward the inside of the bend for bottom drifters. This pattern periodically reinforces the intersection of drifting larvae with channel margins in meander bends. In the absence of measured larval drift data, the model provides a tool for hypothesis testing and a guide to both field and laboratory experiments to further define the role of active behaviour in drifting larvae.
It is important to predict driftwood motions around hydraulic structures. We proposed a numerical model to simulate driftwood motions based on the coupling of a Euler type three-dimensional flow model and a Lagrangian type two-dimensional driftwood model. Laboratory tests on the driftwood motions in a curved channel and around obstacles are also carried out for obtaining the reference data. The computational results showed that three-dimensional flow features consierabley affect the motion of driftwood in a curved channel. We defined the driftwood Richardson number to consider the three-dimensional behavior of driftwood. The experimental results showed that if the driftwood Richardson number increases, the driftwood shows more three-diemensional behavior and the captureing rate by the obstacle decreases. In addition, we developed a two-way model to consider the drag force from the driftwood toward the flow to simulate the change of flow structures around stacked driftwood.
To classify a book as 'experimental' rather than 'theoretical' or as 'pure' rather than 'applied' is liable to imply umeal distinctions. Nevertheless, some Classification is necessary to teIl the potential reader whether the book is for him. In this spirit, this book may be said to treat fluid dynamies as a branch of physics, rather than as a branch of applied mathematics or of engineering. I have often heard expressions of the need for such a book, and certainly I have feIt it in my own teaching. I have written it primariIy for students of physics and of physics-based applied science, aIthough I hope others may find it useful. The book differs from existing 'fundamental' books in placing much greater emphasis on what we know through laboratory experiments and their physical interpretation and less on the mathe matieal formalism. It differs from existing 'applied' books in that the choice of topics has been made for the insight they give into the behaviour of fluids in motion rather than for their practical importance. There are differences also from many existing books on fluid dynamics in the branches treated, reflecting to some extent shifts of interest in reeent years. In particular, geophysical and astrophysical applications have prompted important fundamental developments in topics such as conveetion, stratified flow, and the dynamics of rotating fluids. These developments have hitherto been reflected in the contents of textbooks only to a limited extent.
This chapter presents an overview of techniques for predicting flow, sediment transport and bed evolution, emphasizing the physical processes that are captured by various approaches. It first explains the flow conservation laws, such as the conservation of mass and momentum, and the Reynolds stresses. Then, the chapter discusses the sediment-transport relations for bedload transport and suspended load transport. A one-dimensional flow model solves for the cross-sectionally averaged velocity, flow rate or discharge at each model cross-section, but the flow model is generally of limited value for the prediction of morphodynamics. If the flow field of interest includes steering of the flow around islands or bars or if there is significant cross-stream variability in the flow, at least a two-dimensional model should be applied. The chapter also describes bank evolution models and bedform models, before presenting a note on the practical considerations in order to select an appropriate model.
In most streams, pollutants are mixed vertically before mixed transversely because depths of the streams are typically smaller than widths. Thus, in this model, 2-D depth-averaged advection-dispersion equation of water temperature was formulated by finite element model. RAMS-GUI and RAM2 are adopted for water temperature model. Using RAMS-GUI which is the computing module of software RAMS, the finite element mesh of application site was generated. Developed water temperature model using FE method is verified in rectangular channel by 1-dimensional analytical solution. The developed model in the real problem was applied in Han River from Paldang-dam to Jamsil bridge.
Abstract This paper describes a new, public-domain interface for modeling flow, sediment transport and morphodynamics in rivers and other geophysical flows. The interface is named after the International River Interface Cooperative (iRIC), the group that constructed the interface and many of the current solvers included in iRIC. The interface is entirely free to any user and currently houses thirteen models ranging from simple one-dimensional models through three-dimensional large-eddy simulation models. Solvers are only loosely coupled to the interface so it is straightforward to modify existing solvers or to introduce other solvers into the system. Six of the most widely-used solvers are described in detail including example calculations to serve as an aid for users choosing what approach might be most appropriate for their own applications. The example calculations range from practical computations of bed evolution in natural rivers to highly detailed predictions of the development of small-scale bedforms on an initially flat bed. The remaining solvers are also briefly described. Although the focus of most solvers is coupled flow and morphodynamics, several of the solvers are also specifically aimed at providing flood inundation predictions over large spatial domains. Potential users can download the application, solvers, manuals, and educational materials including detailed tutorials at www.-i-ric.org. The iRIC development group encourages scientists and engineers to use the tool and to consider adding their own methods to the iRIC suite of tools.
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.
The CGNS system consists of a collection of conventions, and confonning software, for the storage and retrieval of Computational Fluid Dynamics (CFD) data It facilitates the exchange of data between sites and applications, and helps stabilize the archiving of aerodynamic data The data are stored in a compact, binary format and are accessible through a complete and extensible library of functions. This API (Application Program Interface) is platform independent and can be easily implemented in C, C++, Fortran and Fortran90 applications. The CGNS system supports structured, unstructured and mixed topology, where multi-block connectivity may be either one-to-one abutting, mismatched abutting or overset It defines standards for the storage of grid coordinates, flow solutions, boundary conditions, convergence history, reference state and geometry data. Dimensional units and nondimensionalization information may be associated with each type of data. Additionally, it provides conventions for archiving the governing equations including the gas, viscosity, thermal conductivity, turbulence and diffusion models. The CGNS system can be extended to other types of engineering analysis data, and serve multi-disciplinary applications. It is offered to the CFD community for the purpose of establishing a standard for aerodynamic data storage. This paper presents the different components of the CGNS system, from the essence of its constituents to its supporting data structures and software capacity. It demonstrates the facility to implement the CGNS system through a series of short examples, followed by a review of its incorporation into both research and commercial CFD applications.
A three-dimensional Reynolds-averaged Navier–Stokes computational fluid dynamics (CFD) model is developed for simulating initial mixing in the near field of thermal discharges at real-life geometrical configurations. The domain decomposition method with multilevel embedded overset grids is employed to handle the complexity of real-life diffusers as well as to efficiently account for the large disparity in length scales arising from the relative size of the ambient river reach and the typical diffuser diameter. An algebraic mixing length model with a Richardson-number correction for buoyancy effects is used for the turbulence closure. The governing equations are solved with a second-order-accurate, finite-volume, artificial compressibility method. The model is validated by applying it to simulate thermally stratified shear flows and negatively buoyant wall jet flows and the computed results are shown to be in good overall agreement with the experimental measurements. To demonstrate the potential of the numerical model as a powerful engineering simulation tool we apply it to simulate turbulent initial mixing of thermal discharges loaded from both single-port and multiport diffusers in a prismatic channel and a natural river. Comparisons of the CFD model results with those obtained by applying two widely used empirical mixing zone models show that the results are very similar in terms of both the rate of dilution and overall shape of the plumes. The CFD model further resolves the complex three-dimensional features of such flows, including the complex interplay of the ambient flow and thermal discharges as well as the interaction between each of discharges loaded from multiple ports, which are obviously not accessible by the simpler empirical models.
A model of sand transport in water is produced by combining a turbulence-resolving large eddy simulation (LES) with a discrete element model (DEM) prescribing the motion of individual grains of medium sand. The momentum effect of each particle on the fluid is calculated at the LES cell containing the particle, and the fluid velocity and pressure, interpolated to each particle center, is used to derive fluid force on each particle in the DEM. Eleven numerical experiments are conducted of an initially flat bed of particles. The experiments span a range of motion, from essentially no motion to vigorous suspension. Hydraulic roughness is found to increase abruptly at the transition from bedload to suspended load transport. Suspended sediment extracts momentum from the flow and decreases the rate of shear. Whereas, slightly higher in the flow, vertical drag by suspended grains damps turbulence and increases the rate of shear. Vertical sediment diffusivity and effective particle settling velocity are much smaller than is commonly assumed in suspended sediment models. The bedload experiments suggest that saltation by itself is a poor model of bedload sand transport. In contrast to expectations from saltation models, the peak bedload flux occurs at essentially the same level as the bed, and grains move slowly in frequent contact with other grains. Higher and faster moving bedload grains that can be considered to be in saltation represent a smaller portion of the total flux. Entrainmentof bedload grains occurs in response to fluid penetration of the bed by high-vorticity turbulence structures embedded within broader high speed fluid regions referred to as a sweeps or high-speed wedges.
Simulations of tracer experiments conducted with a three-dimensional primitive-equation hydrodynamic and transport model are used to understand the processes controlling the rate of mixing between two rivers (Ebro and Segre), with distinct physical and chemical properties, at their confluence, upstream of a meandering reservoir (Ribarroja reservoir). Mixing rates downstream of the confluence are subject to hourly scale oscillations, driven partly by changes in inflow densities and also as a result of turbulent eddies that develop within the shear layer between the confluent rivers and near a dead zone located downstream of the confluence. Even though density contrasts are low − at most O(10-1) kgm-3 difference among sources−, and almost negligible from a dynamic point of view − compared with inertial forces −, they are important for mixing. Mixing rates between the confluent streams under weakly buoyant conditions can be of up to 40% larger than those occurring under neutrally buoyant conditions. The buoyancy effects on mixing rates are interpreted as the result of changes in the contact area available for mixing (distortion of the mixing layer). For strong density contrasts, though, when the contact area between the streams become nearly horizontal, larger density differences between streams will lead to weaker mixing rates, as a result of the stabilizing effect of vertical density gradients.
The velocity, flux, and concentration distribution of solid particles in a turbulent boundary layer of a horizontal water flume were investigated experimentally by means of LDA and visualization techniques. The particles were of polystyrene (specific density ∼1.05). Results show that coherent wall structures are responsible for most of the characteristics of particle behavior throughout the boundary layer. Particles are often concentrated in regions of low velocity, associated with wall structures, and as a result the average particle velocity is lower than the fluid’s. This was also noted previously by Rashidi et al., but not explained. The actual relative velocity between the particles and the surrounding fluid is often small. In addition, the data suggest that as the shear rate increases, the particle flux profiles asymptotically approach a shape where a strong gradient of particle flux exists in the lower part of the boundary layer (y+≤250), while it is relatively constant at higher elevations. This phenomenon may also be attributable to interactions with the wall structures.
Seasonal circulation of the Bohai Sea (BS) in 1992 was investigated using Lagrangian particle tracking method. The hydrography of the BS was simulated based on an unstructured grid, finite-volume, three-dimensional primitive equation ocean model. With the use of the unstructured triangular grid, the model can easily fit the irregular coastal boundary of the BS. The simulated tides, tidal current, and thermohaline field agreed well with the observations. The transport of particles has three-dimensional structure in the BS. Compared with central Bohai and Bohai Strait, the differences of particles’ transportation between surface and bottom layer in three bays are small. The circulation in the summer is stronger than that in the winter, with the average residual velocity in the surface layer being about 3.7 cm/s during the summer while only 1.8 cm/s during the winter. Using the same model, several well-designed numerical experiments were performed to investigate the effect of oceanic tide, river discharge, wind stress, and thermal stratification on the circulation. It is shown that winds play an important role in the circulation of the BS during both the winter and the summer. Density circulation is important during the summer; however, it is negligible during the winter. River runoff only affects the area around the river mouth. Compared with wind and thermohaline effect, the contribution of tides is small during the summer, and the circulation under only M2 tidal constituent could not reflect the actual circulation of the BS.
Random-walk particle tracking models have been advantageously applied to the simulation of transport by groundwater. This paper presents the development and analysis of a depth-averaged random-walk particle tracking model for simulating transport in vertically well-mixed estuaries and coastal waters. The model is tested by comparing simulated concentrations and residence times with corresponding analytical solutions for a one-dimensional estuary. Excellent agreement is obtained.
In natural flows, bed sediment particles are entrained and moved by the fluctuating forces, such as lift and drag, exerted by the overlying flow on the particles. To develop a better understanding of these forces and the relation of the forces to the local flow, the downstream and vertical components of force on near-bed fixed particles and of fluid velocity above or in front of them were measured synchronously at turbulence-resolving frequencies (200 or 500 Hz) in a laboratory flume. Measurements were made for a spherical test particle fixed at various heights above a smooth bed, above a smooth bed downstream of a downstream-facing step, and in a gravel bed of similarly sized particles as well as for a cubical test particle and 7 natural particles above a smooth bed. Horizontal force was well correlated with downstream velocity and not correlated with vertical velocity or vertical momentum flux. The standard drag formula worked well to predict the horizontal force, but the required value of the drag coefficient was significantly higher than generally used to model bed load motion. For the spheres, cubes, and natural particles, average drag coefficients were found to be 0.76, 1.36, and 0.91, respectively. For comparison, the drag coefficient for a sphere settling in still water at similar particle Reynolds numbers is only about 0.4. The variability of the horizontal force relative to its mean was strongly increased by the presence of the step and the gravel bed. Peak deviations were about 30% of the mean force for the sphere over the smooth bed, about twice the mean with the step, and 4 times it for the sphere protruding roughly half its diameter above the gravel bed. Vertical force correlated poorly with downstream velocity, vertical velocity, and vertical momentum flux whether measured over or ahead of the test particle. Typical formulas for shear-induced lift based on Bernoulli's principle poorly predict the vertical forces on near-bed particles. The measurements suggest that particle-scale pressure variations associated with turbulence are significant in the particle momentum balance.
A series of experiments were performed in a mixing box in order: (1) to investigate the applicability of phase Doppler anemometry (PDA) to discriminate fluid and sediment particle sizes and velocities in sediment-laden turbulent flows; and (2) to relate the size and amount of sediment in suspension to the grid-generated turbulence. Natural impurities within the water provide excellent 'seeding' to represent the fluid and can be easily discriminated from spherical glass beads (75-355 μm) used as sediment. Slight asphericity in the glass beads results in larger grain size ranges determined by PDA compared to the nominal sieved sizes. The mean, root-mean-square and skewness of the vertical fluid velocities increase at higher grid oscillation frequencies but decrease with distance from the grid. Similarly, the size and amount of suspended sediment increase with grid oscillation frequency and decrease with distance from the grid. The suspension of sediment is shown to be dependent on the magnitude and anisotropy of the fluctuating vertical component of velocity. Phase Doppler anemometry offers a unique methodology to investigate the complex links between the transport of sediment and the turbulent flow field.
The possibility of a contaminant being accidentally or intentionally spilled in a river is a constant concern to those using the water. Methods are developed to estimate: (1) the velocity of a contaminant in a river; (2) the rate of attenuation of the peak concentration of a conservative contaminant; and (3) the time required for a contaminant plume to pass a point. The methods are based on data collected by the U.S. Geological Survey in almost a hundred different rivers representing a wide range of sizes, slopes, and geomorphic types. Although the accuracy of the predictions can be greatly increased by performing time-of-travel studies, the emphasis of this paper is on providing methods for making estimates where few data are available. It is shown that the unit-peak concentration is well correlated with travel time and that the travel time of the leading edge averages 89% of the travel time of the peak concentration.
The forces on a small rigid sphere in a nonuniform flow are considered from first principles in order to resolve the errors in Tchen's equation and the subsequent modified versions that have since appeared. Forces from the undisturbed flow and the disturbance flow created by the presence of the sphere are treated separately. Proper account is taken of the effect of spatial variations of the undisturbed flow on both forces. In particular the appropriate Faxen correction for unsteady Stokes flow is derived and included as part of the consistent approximiation for the equation of motion.
The CFD General Notation System (CGNS) standard has grown significantly since its first public release in May 1998. The Standard Interface Data Structures (SIDS) and corresponding Application Programming Interface (API) have been extended to support unstructured analysis data and geometry-to-mesh association. Several other extensions are currently under review: rigid grid motion, deforming grid, time-accurate and iterative data, chemistry, multigrid, rotating coordinate systems, periodic boundary conditions, wall functions, 2D axisymmetry and Cartesian data. In parallel with the growth of the CGNS standard, the CGNS governing body has evolved into an independent entity and established its own charter. Efforts have also been undertaken to promote CGNS as the ISO standard for the recording of aerodynamic data. This paper reviews the progress made by CGNS over the past eighteen months. It first describes the technical advances in the CGNS database standard, followed by an overview of the new CGNS organization. Then the status of the CGNS in the ISO standardization process is presented, as well as a review of implementation and dissemination of CGNS.
A major assumption of the Empirical Transport Model (ETM), widely adopted by both electric utilities and regulatory agencies
for estimating the effects of entrainment mortality on fish populations in estuaries, is that the fraction of ichthyoplankton
entrained varies only in response to changes in water withdrawals, not to changes in freshwater flow. We evaluated this assumption
using a particle-tracking model to estimmate the probability of entrainment at power plants on the Hudson River during low
and high freshwater flow periods and comparing those probabilities with estimates calculated from the ETM. We found that freshwater
flow had a profound effect on the probability of entrainment. Both the number of river regions from which particles were entrained
and the probabilities of entrainment for particles in those river regions differed between low-flow and high-flow periods.
During high flow, particles spent less time in the grid box next to the intakes, reducing the probability of entrainment for
particles released in the river region of each power plant and the average probability of entrainment across all regions at
three power plants. The reduced probability of entrainment for particles released in the river regions of two power plants
was offset by higher entrainment for particles upriver of these power plants. Although the average probabilities of entrainment
across all river regions estimated with the particle-tracking model and the ETM were relatively similar for some power plants
at high flow, low flow, or both, the probabilities for each river region differed considerably between the models. The number
of river regions from which particles were entrained using the ETM was consistently undersestimated, resulting in probabilities
for regions where entrainment occurred that were biased high compared with the particle-tracking model.
Analysis of dispersion by the random walk method
- Heemink A.W.
Modern conceptions of the mechanics of turbulence: American Society of Civil Engineers
- Rouse H.
User Guide for MODPATH Version 6-A Particle-Tracking Model for MODFLOW: U.S. Geological Survey Techniques and Methods 6-A41 p
- D W Pollock