Depth-Averaged Two-Dimensional Numerical Modeling of Unsteady Flow and Nonuniform Sediment Transport in Open Channels

A depth-averaged two-dimensional (2D) numerical model for unsteady flow and nonuniform sediment transport in open channels is established using the finite volume method on a nonstaggered, curvilinear grid. The 2D shallow water equations are solved by the SIMPLE(C) algorithms with the Rhie and Chow’s momentum interpolation technique. The proposed sediment transport model adopts a nonequilibrium approach for nonuniform total-load sediment transport. The bed load and suspended load are calculated separately or jointly according to sediment transport mode. The sediment transport capacity is determined by four formulas which are capable of accounting for the hiding and exposure effects among different size classes. An empirical formula is proposed to consider the effects of the gravity on the sediment transport capacity and the bed-load movement direction in channels with steep slopes. Flow and sediment transport are simulated in a decoupled manner, but the sediment module adopts a coupling procedure for the computations of sediment transport, bed change, and bed material sorting. The model has been tested against several experimental and field cases, showing good agreement between the simulated results and measured data.     

Observation and Simulation of Surface Waves in Two Water Supply Reservoirs

Observations and model predictions of progressive surface waves were made for Cannonsville and Schoharie Reservoirs, located in southeastern New York State. These reservoirs are deep with steep bottom slopes and relatively small fetch. The Donelan/Great Lakes Environmental Research Lab model, a parametric second-generation wave model was applied to these reservoirs assuming deep water throughout the domain. This assumption was based on the relatively small waves and steep bottom slopes, resulting in a very narrow region of wave interaction with the bottom along a lee shore. Previous applications of this model have been for water bodies with larger fetch. Observations of wave characteristics were made near the shoreline at two sites in Cannonsville and one site in Schoharie using submerged pressure sensors, from which the height of larger waves was determined. Model hindcasts were made for the observation periods with model inputs being wind speed and direction and water surface elevation. The model performed well in simulating significant wave height determined from observations. Some implications of the use of wave model simulations to predict sediment resuspension in these and other deep lakes and reservoirs are discussed.     

Application of Three-Dimensional Hydrodynamic Model for Lake Okeechobee

A 3D hydrodynamic and heat transport model was developed for Lake Okeechobee. Continuity, momentum, and temperature transport equations were solved. Dynamically coupled transport equations for turbulent kinetic energy and turbulent scale also were solved. The numerical scheme used spatial finite differencing and a three-time-level, external-internal mode splitting procedure. A 28-day calibration was conducted, using measured bathymetry, rainfall, relative humidity, total solar radiation, wind velocity, inflow, and outflow data. During the calibration period, little rainfall occurred, and lake water levels receded. Water surface elevation, horizontal velocities, and temperature were computed. Agreement between observed and simulated values was based on graphical comparisons, minimizing mean absolute and root-mean-square errors, and spectral analysis. Comparisons showed that the model reproduced general observed trends and short-term fluctuations. The model's heat transport and turbulence closure schemes behaved as expected with regard to water column stratification and mixing. Simulation accuracy may potentially be improved by adding wind-wave and vegetation resistance algorithms to the model.     

Flood Simulation Using a Well-Balanced Shallow Flow Model

This work extends and improves a one-dimensional shallow flow model to two-dimensional (2D) for real-world flood simulations. The model solves a prebalanced formulation of the fully 2D shallow water equations, including friction source terms using a finite volume Godunov-type numerical scheme. A reconstruction method ensuring nonnegative depth is used along with a Harten, Lax, and van Leer approximate Riemann solver with the contact wave restored for calculation of interface fluxes. A local bed modification method is proposed to maintain the well-balanced property of the algorithm for simulations involving wetting and drying. Second-order accurate scheme is achieved by using the slope limited linear reconstruction together with a Runge-Kutta time integration method. The model is applicable to calculate different types of flood wave ranging from slow-varying inundations to extreme and violent floods, propagating over complex domains including natural terrains and dense urban areas. After validating against an analytical case of flow sloshing in a domain with a parabolic bed profile, the model is applied to simulate an inundation event in a 36?km2 floodplain in Thamesmead near London. The numerical predictions are compared with analytical solutions and alternative numerical results.     

Sediment and Metals Modeling in Shallow River

It is a challenge to apply coupled hydrodynamic, sediment process, and contaminant fate and transport models to the studies of surface water systems. So far, there are few published modeling studies on sediment and metal transport in rivers that simulate storm events on an hourly basis and use comprehensive data sets for model input and model calibration. The United States Environmental Protection Agency (USEPA) in 1997 emphasized the need for credible modeling tools that can be used to quantitatively evaluate the impacts of point sources, nonpoint sources, and internal transport processes in 1D/2D/3D environments. A 1D and time-dependent hydrodynamic, sediment, and toxic model, within the framework of the 3D Environmental Fluid Dynamics Code (EFDC), has been developed and applied to Blackstone River, Mass. The Blackstone River Initiative (USEPA) in 1996, a multiyear and multimillion-dollar project, provided the most comprehensive surveys on water quality, sediment, and heavy metals in the river, and served as the primary data set for this study. The model simulates three storm events successfully. The river flow rates are well calculated both in amplitude and in phase. The sediment transport and resuspension processes are depicted satisfactorily. The concentrations of sediment and five metals (cadmium, chromium, copper, nickel, and lead) during the three storm events are also simulated very well. Numerical analyses are conducted to clarify the impacts of contaminant sources and sediment resuspension processes on the river. While point sources are important to sediment contamination in the river, other sources, including nonpoint sources from watershed and bed resuspension, were found to contribute significantly to the sediment and metals in the river. Point sources alone cannot account for the total metals in the river. The model presented in this paper can be a useful tool for studying sediment and metals transport in shallow rivers and for water resource management.     

Shallow Turbulent Flow Simulation Using Two-Length-Scale Model

Numerical simulations of the planar starting jets were conducted using a two-length-scale turbulence model and a hydraulic code to study the effect of friction on 2D turbulence in shallow open-channel flow. The simulation results were compared with the data of the starting jets obtained in a recent series of laboratory experiments conducted in a large tank of small thickness. Dividing the turbulence energies into large and small scales, and calculating the energies with separate models, the observed friction effects on the 2D large-scale turbulent motion were correctly simulated by a two-length-scale turbulence model. To maintain the large-scale turbulence in the shallow shear flow, the production of turbulence energy by the transverse shear must be greater than the dissipation of the energy by friction. The critical gradient bed-friction number obtained from the simulations of the starting jets was Sc ? 0.08, which is consistent with the experimental observations in other shallow turbulent flows.     

Improved Discharge Configurations for Brine Effluents from Desalination Plants

Sea water desalination plants discharge a concentrated brine effluent into coastal waters. Modern, large capacity plants require submerged discharges, in the form of a negatively buoyant jet, that ensure a high dilution in order to minimize harmful impacts on the marine environment. Existing design practice favors a steep discharge angle of 60° above horizontal, a practice based on limited and outdated laboratory data for dilutions at the level of maximum rise. Examination of more recent laboratory data and the parametric application of a jet integral model suggest that flatter discharge angles of about 30–45° above horizontal may have considerable design advantages. These relate to better dilution levels at the impingement location, especially if bottom slope and port height are taken into account, there is better offshore transport of the mixed effluent during weak ambient current conditions, and there is the ability to locate in more shallow water near shore.     

Distributed Entrainment Sink Approach for Modeling Mixing and Transport in the Intermediate Field

In densely populated coastal cities in Asia, wastewater outfalls are often located not far from sensitive areas such as beaches or shellfisheries. The impact and risk assessment of effluent discharges poses particular technical challenges, as pollutant concentration needs to be accurately predicted both in the near field and intermediate field. The active mixing close to the discharge can be modeled by proven plume models, while the fate and transport far beyond the mixing zone can be well-predicted by three-dimensional (3D) circulation models based on the hydrostatic pressure approximation. These models are usually applied separately with essentially one-way coupling; the action of the plume mixing on the external flow is neglected. Important phenomena such as surface buoyant spread or source-induced changes in ambient stratification cannot be satisfactorily addressed by such an approach. A Distributed Entrainment Sink Approach is proposed to model effluent mixing and transport in the intermediate field by dynamic coupling of a 3D far field shallow water circulation model with a Lagrangian near-field plume model. The action of the plume on the surrounding flow is modeled by a distribution of sinks along the plume trajectory and an equivalent diluted source flow at the predicted terminal height of rise. In this way, a two-way dynamic link can be established at grid cell level between the near and far-field models. The method is demonstrated for a number of complex flows including the interaction of a confined rising plume with ambient stratification, and the mixing of a line plume in cross flow. Numerical predictions are in excellent agreement with basic laboratory data. The general method can be readily incorporated in existing circulation models to yield accurate predictions of mixing and transport in the intermediate/far field.     

3D Numerical Modeling of Flow and Sediment Transport in Open Channels

A 3D numerical model for calculating flow and sediment transport in open channels is presented. The flow is calculated by solving the full Reynolds-averaged Navier-Stokes equations with the k ? ε turbulence model. Special free-surface and roughness treatments are introduced for open-channel flow; in particular the water level is determined from a 2D Poisson equation derived from 2D depth-averaged momentum equations. Suspended-load transport is simulated through the general convection-diffusion equation with an empirical settling-velocity term. This equation and the flow equations are solved numerically with a finite-volume method on an adaptive, nonstaggered grid. Bed-load transport is simulated with a nonequilibrium method and the bed deformation is obtained from an overall mass-balance equation. The suspended-load model is tested for channel flow situations with net entrainment from a loose bed and with net deposition, and the full 3D total-load model is validated by calculating the flow and sediment transport in a 180° channel bend with movable bed. In all cases, the agreement with measurements is generally good.     

Solute Transport Modeling in Overland Flow Applied to Fertigation

A model of solute transport in overland flow is developed and applied to the simulation of surface fertigation. Water flow is simulated using the depth-averaged, 1D shallow water equations. Solute flow is represented by an advection-diffusion model. The resulting set of three partial differential equations is sequentially solved at each time step. First, water flow is computed using the explicit two-step McCormack method. Based on the obtained velocity field, solute transport is explicitly determined from the advection-diffusion equation using the operator split technique. Four field experiments involving fertigation events on an impervious free-draining border were performed to validate the proposed model and to obtain estimates of Kx, the longitudinal dispersion coefficient. A value of Kx = 0.075 m2 s?1 satisfactorily reproduces the field experiments. The model is also applied to the simulation of a fertigation event on a pervious border. A sensitivity analysis is performed to assess the dependence of fertilizer distribution uniformity on the value of Kx. Finally, the proposed model is compared with a previous model based on pure advection.     

Investigations on Flow Pattern and Pressure inside SEN below Stopper Rod

In continuous casting of steel, the casting rate is often controlled by a stopper rod placed in the tundish outlet where the submerged entry nozzle (SEN) tube begins. The flow pattern inside the SEN plays an important role for the bubble formation at the argon injection nozzle at the stopper rod tip. High flow velocities are reached in the small gap between stopper rod and the surrounding SEN walls, and a flow separation has to be expected after the gap due to the fast expansion of the cross section. According to theoretical considerations and to the simulations, the absolute pressure in the gap becomes very low for liquid steel, which can cause cavitation‐like effects. PIV‐flow measurements in a 1:1 scaled water model of the caster show a highly oscillating and asymmetric flow pattern with rapidly changing separation regions. The low pressure effects expected in liquid steel cannot be investigated on the water‐model due to the lower density of water. In numerical simulations of the water‐model, the choice of the turbulence model and the usage or the non‐usage of geometrical symmetries for the bound of the computational domain have a great impact on the resulting flow pattern and the accuracy of the predicted pressure drop. The results of various turbulence models are compared with results from measurements on a water‐model. It turns out that only a 3D model using advanced turbulence models (SST k‐ω or Large Eddy) produce acceptable results, while 2D simulations completely fail and the standard turbulence models (e.g. k‐ε) significantly underestimate the pressure drop even in a 3D simulation.     

Modeling of Evaporation Reduction in Drip Irrigation System

Surface drip irrigation is an efficient system for delivering water to crops; however, conditions at the soil surface affect evaporation rate and efficiency. A method is proposed, sand tube irrigation (STI), to increase the efficiency of drip irrigation systems. This method is specific to permanent tree crops where soil is not tilled or turned. The STI method consists of removing a soil core beneath the emitter and filling the void with coarse sand. The SWMS??2D model, implemented in a 3D axisymmetric form, was used to simulate infiltration, water redistribution, evaporation from the soil surface, and rise of water inside the sand tube. Model simulations were compared with laboratory measurements determined from a weighing lysimeter. The simulated values of water height inside the sand tube and temporal position of the wetting front in both lateral and upward directions closely matched the experimental measurements. The advancement of the wetting front in the downward direction and evaporation estimates was predicted with less accuracy. Experiments showed that relative to surface drip irrigation, the STI method reduced evaporation by approximately 26% over a 4-day period.     

Limitations of Depth-Averaged Modeling for Shallow Wakes

Large-scale horizontal vortical structures are generic features of shallow flows which are often modeled using the two-dimensional (2D) depth-averaged equations. Such modeling is investigated for the well-defined case of shallow wakes of a conical island of small side slope for which a three-dimensional (3D) boundary-layer (3DBL) model has previously been validated through comparison with experiment. The 3DBL model used a 3D, two-mixing-length, eddy-viscosity turbulence model with a vertical mixing length of classical Prandtl form and a horizontal mixing length some multiple of this. A multiple of six gave good predictions. This mixing length approach is reduced to depth-averaged form, giving a horizontal mixing length of about half the water depth. The shallow wakes may be vortex shedding or steady/stable and are conventionally defined by a stability parameter. The critical value above which a stable wake is formed is considerably overestimated by the depth-averaged model (for a range of mixing lengths) and the length of stable wake bubble is considerably underestimated. It seems likely that this is because the amplification of friction coefficient due to horizontal strain rates is not represented. However, when vortex shedding is prominent the 2D and 3DBL wake structures are quite similar. These results show, for example, the limitations of depth-averaged models for the prediction of solute dispersion.     

Hydrodynamic Tracking of the Massive Spring 1998 Red Tide in Hong Kong

In subtropical coastal waters around Hong Kong, algal blooms and red tides have been frequently observed over the past two decades. In particular, in March–April 1998, a massive red tide invaded the northeastern and southern coastal waters of Hong Kong. The devastating red tide resulted in the worst fish kill in Hong Kong’s history, the most significant impacts being at the Lo Tik Wan and Sok Kwu Wan fish culture zones on Lamma Island. This work reports the first scientific investigation of the cause of this massive red tide. A calibrated three-dimensional (3D) hydrodynamic model for the Pearl River Estuary, Delft3D, is applied to study the advective transport of red tides. Based on the tidal boundary conditions and the measured wind data for a typical spring season, the 3D flow field is computed and extensive surface drogue tracking performed for releases in different parts of the coastal waters and for different tidal and wind conditions. The results show that a bloom initiated in Mirs Bay (Nan Au or Tap Mun) in the northeastern water would likely be transported to the southern coastal waters under the combined action of tidal current and wind. The computed bloom tracking patterns are generally supported by observations and are consistent with the temporal and spatial patterns of individual fish kill events in the 1998 red tide. We conclude that the major cause of the bloom being transported into the southern waters and East Lamma Channel (and causing the massive fish kill) is the generally strong wind in March–April 1998 and the change in wind direction in early April under almost diurnal tidal conditions. Further, it is most probable that the red tide originated in Mirs Bay rather than from outside Hong Kong. The findings provide a firm basis for environmental and fisheries management.     

Predicting the structure of apolipoprotein A-I in reconstituted high-density lipoprotein disks

In reconstituted high-density lipoproteins, apolipoprotein A-I and phosphatidylcholines combine to form disks in which the amphipathic alpha-helices of apolipoprotein A-1 bind to the edge of a lipid bilayer core, shielding the hydrophic lipid tails from the aqueous environment. We have employed experimental data, sequence analysis, and molecular modeling to construct an atomic model of such a reconstituted high-density lipoprotein disk consisting of two apolipoprotein A-I proteins and 160 palmitoyloleoylphosphatidylcholine lipids. The initial globular domain (1-47) of apolipoprotein A-I was excluded from the model, which was hydrated with an 8-A shell of water molecules. Molecular dynamics and simulated annealing were used to test the stability of the model. Both head-to-tail and head-to-head forms of a reconstituted high-density lipoprotein were simulated. In our simulations the protein contained and adhered to the lipid bilayer while providing good coverage of the lipid tails.     

Generation of Three-Dimensional Fully Nonlinear Water Waves by a Submerged Moving Object

This paper describes a numerical investigation on the generation of three-dimensional (3D) fully nonlinear water waves by a submerged object moving at speeds varied from subcritical to supercritical conditions in an unbounded fluid domain. Considering a semispheroid as the moving object, simulations of the time evolutions of 3D free-surface elevation and flow field are performed. The present 3D model results are found to agree reasonably well with other published vertical two-dimensional (2D) and quasi-3D numerical solutions using Boussinesq-type models. Different from the 2D cases with near critical moving speeds, the 3D long-term wave pattern suggests that in addition to the circularly expanded upstream advancing solitonlike waves, a sequence of divergent and transverse waves are also developed behind the moving object. The velocity distributions and associated fluid-particle trajectories at the free-surface and middle layers are presented to show the 3D feature of the motion. The results under various vertical positions (referred as gap) of a moving object are also compared. It is found the gap has shown a substantial influence on the generated waves, especially in the wake region, when an object moves at a near critical or subcritical speed. However, the results under the case with a high supercritical moving speed indicate the gap has a negligible effect on the generated upstream and downstream waves.     

BIEM Modeling of 3D Circulation and Transport in Stratified Estuaries

Here the boundary integral equation method (BIEM) is used for 3D modeling of hydrodynamics and pollutant transport in stratified estuaries. The flow computations are made using a newly developed BIEM solution. The transport modeling has been done using an Eulerian-Lagrangian BIEM (ELBIEM) model. In ELBIEM, the advection part in the transport equation is treated by the concept of the Eulerian-Lagrangian scheme, which overcomes the limitation of traditional BIEM to deal with an arbitrary velocity field. The coupling of the 3D shallow water BIEM model and advection-diffusion ELBIEM model enables one to effectively deal with fluctuation of free surface and density stratification in an estuary. The main advantages of the BIEM model include reduction in computational dimensions, ease in discretization and data preparation, accurate free surface simulation, less numerical diffusion and dispersion problems, and direct flux solution at boundaries. The numerical simulation results are compared with other model results and found to be satisfactory. The illustrated case study shows the effectiveness of the model in the simulation of mass, momentum, and heat transfer due to air-water interaction in stratified estuary problems.     

Numerical Modeling of Bed Deformation in Laboratory Channels

A depth-average model using a finite-volume method with boundary-fitted grids has been developed to calculate bed deformation in alluvial channels. The model system consists of an unsteady hydrodynamic module, a sediment transport module and a bed-deformation module. The hydrodynamic module is based on the two-dimensional shallow water equations. The sediment transport module is comprised of semiempirical models of suspended load and nonequilibrium bedload. The bed-deformation module is based on the mass balance for sediment. The secondary flow transport effects are taken into account by adjusting the dimensionless diffusivity coefficient in the depth-average version of the k–ε turbulence model. A quasi-three-dimensional flow approach is used to simulate the effect of secondary flows due to channel curvature on bed-load transport. The effects of bed slope on the rate and direction of bed-load transport are also taken into account. The developed model has been validated by computing the scour hole and the deposition dune produced by a jet discharged into a shallow pool with movable bed. Two further applications of the model are presented in which the bed deformation is calculated in curved alluvial channels under steady- and unsteady-flow conditions. The predictions are compared with data from laboratory measurements. Generally good agreement is obtained.     

Simulation of Flow and Mass Dispersion in Meandering Channels

This paper reports the development of an enhanced two-dimensional (2D) numerical model for the simulation of flow hydrodynamics and mass transport in meandering channels. The hydrodynamic model is based on the solution of the depth-averaged flow continuity and momentum equations where the density of flow varies with the concentration of transported mass. The governing equation for mass transport model is the depth-averaged convection and diffusion equation. The dispersion terms arisen from the integration of the product of the discrepancy between the mean and the actual vertical velocity distribution were included in the momentum equations to take into account the effect of secondary current. Two laboratory experimental cases, flow in mildly and sharply curved channels, were selected to test the hydrodynamic model. The comparison of the simulated velocity and water surface elevation with the measurements indicated that the inclusion of the dispersion terms has improved the simulation results. A laboratory experiment study of dye spreading in a sine-generated channel, in which dye was released at the inner bank, centerline, and outer bank, respectively, was chosen to verify the mass transport model. The simulated concentration field indicated that the Schmidt number can be used as a calibration parameter when dispersion is computed using a 2D approach with a simplified turbulence model.