Anti-diffusion and source identification with the ‘RAW’ scheme: A particle-based censored random walk

This paper presents a novel methodology for time reversal in advective-diffusive pollutant transport in groundwater systems and other environmental flow systems (specifically: time reversal of diffusive terms). The method developed in this paper extends previous particle-based approaches like the Reversed Time Particle Tracking Method of Bagtzoglou [6]. The reversal of the ‘diffusive’ and/or ‘macrodispersive’ component of pollutant migration is especially under focus here. The basis of the proposed scheme for anti-diffusion is a continuous time, censored, non-local random walk capable of tracking groundwater solute concentration profiles over time while conserving the (reverse) Fickian properties of the anti-diffusing particle cloud in terms of moments. This scheme is an alternative to the direct solution of the eulerian concentration-based diffusion PDE, which is notoriously unstable in reverse time. Our analysis leads to the conclusion that an adaptive time stepping scheme—with decreasing time step—is necessary in order to maintain a constant amount of anti-diffusion (the reverse form of Fick’s law). Specifically, we study the relations between the following parameters: time step evolution vs. time (or vs. number of steps); variance evolution (decrease rate); total time (or number of steps) required to reach a fully anti-diffused solution. The proposed approach is shown to be quite efficient; typically, for every ten time steps, one to two orders of magnitude reduction of the dispersion width of the plume can be attained. Furthermore, the method is shown to be asymptotically exact for reverse Fickian diffusion. The method is applied with success to several situations involving the diffusive transport of a conservative solute in the following cases: (i) Single source recovery in one-dimensional space with constant diffusion parameters (this example serves as a validation test for the theory); (ii) Single source recovery in two-dimensional space with constant isotropic diffusion (this example also serves as a test for the theory); (iii) Multiple source recovery in two-dimensional space, assuming isotropic diffusion. It is expected that the methodology tested in this paper is applicable more generally to complex environmental pollution problems involving multiple sources, anisotropic hydrodynamic dispersion, and space-time variable advection-diffusion flow systems; the modeling of reverse diffusion/dispersion in such systems is currently under investigation.     

Two-phase flow insights into open-channel flows with suspended particles of different densities

The effect of particle density on the turbulent open-channel flow carrying dilute particle suspensions is investigated using two specific gravities and three concentrations of solid particles. The particles, identical in size and similar in shape, were natural sand and a neutrally buoyant plastic. The particles were fully suspended, and formed no particle streaks on the channel’s bed. Accordingly, the changes in the flow are attributed to the interactions between suspended particles and flow turbulence structures. Measurements were obtained by means of image velocimetry enabling simultaneous, but distinct, measurement of liquid and particle velocities. The experimental results show that, irrespective of particle specific gravity, particle suspension influences bulk velocity of flow and the Kármán coefficient, while friction velocity essentially remains constant. The results also show that particles in suspension modify local water turbulence over the flow depth, but in ways not accurately predicted using the customary parameters for characterizing turbulence modification.     

Solute Transport in Open-Channel Networks in Unsteady Flow Regime

In this paper we propose a robust algorithm to evaluate solute transport in open-channel networks with transient storage under an unsteady flow regime. In the proposed approach, through the integration of junction equations into the model and solving them explicitly, the analysis of solute transport problems in open-channel networks is simplified significantly. Furthermore, when coupled with a transient hydrodynamic open-channel network model for flow simulation, the proposed model can be utilized in the solution of solute transport problems under unsteady flow regimes. In the proposed model, the governing equations are written in a conservative form and are solved using a fractional-step algorithm, which is based on a relaxation and central difference scheme. The proposed algorithm is robust and accurate even for advection dominant cases. A pure advection with discontinuities, a field application and solute transport in an open-channel network in an unsteady flow regime are included, to demonstrate the performance of the proposed algorithm.     

Hydrodynamics and contaminant transport on a degraded bed at a 90-degree channel confluence

Channel confluences at which two channels merge have an important effect on momentum exchange and contaminant diffusion in both natural rivers and artificial canals. In this study, a three-dimensional numerical model, which is based on the Reynolds Averaged Navier–Stokes equations and Reynolds Stress Turbulence model, is applied to simulate and compare flow patterns and contaminant transport processes for different bed morphologies. The results clearly show that the distribution of contaminant concentrations is mainly controlled by the shear layer and two counter-rotating helical cells, which in turn are affected by the discharge ratio and the bed morphology. As the discharge ratio increases, the shear flow moves to the outer bank and the counter-clockwise tributary helical cell caused by flow deflection is enlarged, leading the mixing happens near the outer bank and the mixing layer distorted. The bed morphology can induce shrinkage of the separation zone and increase of the clockwise main channel helical cell, which is initiated by the interaction between the tributary helical cell and the main channel flow and strengthened by the deep scour hole. The bed morphology can also affect the distortion direction of the mixing layer. Both a large discharge ratio and the bed morphology could lead to an increase in mixing intensity.     

浅水流动有限体积法/Osher格式的二维水流-水质模拟

应用无结构网格有限体积法 /Osher格式的二维水流 -水质耦合数值模型 ,采用黎曼近似解计算模拟区域水量、动量及污染物输送通量。通过对长江南京八卦洲江段浓度场的模拟计算 ,其结果与遥感卫星图片确定的污染带分布相吻合 ,证实了模型的合理性和模拟能力     

Modeling the buoyant flow of heated water discharged from surface and submerged side outfalls in shallow and deep water with a cross flow

In this study, a three-dimensional model was used to numerically study the buoyant flow, along with its mixing characteristics, of heated water discharged from the surface and submerged side outfalls in shallow and deep water with a cross flow. Hydraulic experimental data were used to evaluate the applicability of the model. The simulation results agree well with the experimental results, particularly, the jet trajectories, the dimensions of the recirculating zone, and the distribution of the dimensionless excess temperature. The level of accuracy of the simulation results of the present study is nearly identical to that of the results conducted by McGuirk and Rodi (1978). If the heated water is discharged into shallow water where the momentum flux ratio and the discharge densimetric Froude number are high, the submerged discharge method is better than the surface discharge method in terms of the scale of the recirculating zone and the minimum dilution. In deep water, where the momentum flux ratio and discharge densimetric Froude number are low, however, the submerged discharge method had few advantages. In shallow water, the discharge jet is deflected by the ambient cross flow, while forcing the ambient flow to bend towards the far bank for the full depth. For a submerged discharge in shallow water, the recirculating zone is the largest in the lowest layer but becomes smaller in the upper layer. As the water depth increases, the ambient flow goes over the jet and diminishes the blocking effect, thereby decreasing the bending of the jet.     

A stochastic Lagrangian micromixing model for the dispersion of reactive scalars in turbulent flows: role of concentration fluctuations and improvements to the conserved scalar theory under non-homogeneous conditions

Several reaction schemes, based on the conserved scalar theory, are implemented within a stochastic Lagrangian micromixing model to simulate the dispersion of reactive scalars in turbulent flows. In particular, the formulation of the reaction-dominated limit (RDL) reaction scheme is here extended to improve the model performance under non-homogeneous conditions (NHRDL scheme). The validation of the stochastic model is obtained by comparison with the available measurements of reactive pollutant concentrations in a grid-generated turbulent flow. This test case describes the dispersion of two atmospheric reactant species (NO and O₃) and their reaction product (NO₂) in an unbounded turbulent flow. Model inter-comparisons are also assessed, by considering the results of state-of-the-art models for pollutant dispersion. The present validation shows that RDL reaction scheme provides a systematic overestimation (relative error of ca. 85% around the centreline) in computing the local reactant consumption/production rate, whereas the NHRDL scheme drastically reduces this gap (relative error lower than 5% around the centreline). In terms of NO₂ production (or reactant consumption), neglecting concentration fluctuations determines overestimations of the product mean of around 100% and a NO₂ local production of one order of magnitude higher than the reference simulation. In terms of standard deviations, the concentration fluctuations of both the passive and reactive scalars are generally of the same order of magnitude or up to 1 or 2 orders of magnitudes higher than the corresponding ensemble mean values, except for the background reactant close to the plume edges. The study highlights the importance of modelling pollutant reactions depending on the instantaneous instead of the mean concentrations of the reactants, thus quantifying the role of the turbulent fluctuations of concentration, in terms of scalar statistics (mean, standard deviation, intensity of fluctuations, skewness and kurtosis of concentration, segregation coefficient, simulated reaction rate). This stochastic particle method represents an efficient numerical technique to solve the convection–diffusion equation for reactive scalars and involves several application fields: micro-scale air quality (urban and street-canyon scales), accidental releases, impact of odours, water quality and fluid flow industrial processes (e.g. combustion).     

Influence of flow speed on the functional response of a passive suspension feeder,the spionid polychaete <Emphasis Type="Italic">Polydora cornuta</Emphasis>

Passive suspension feeders rely on surrounding flow to deliver food particles to them. Therefore, the classic conception of functional response (feeding rate vs. food concentration) may require modification to account for flow speed as a second independent variable. I compared the functional response of Polydora cornuta at different velocities and determined whether food capture was proportional to particle flux (concentration × velocity). To understand feeding responses at a mechanistic level, I measured the functional responses in terms of contact and capture rates and determined particle retention efficiency. Experiments were run separately with two sizes of food particles, and with juvenile or adult worms. For both worm sizes and both particle sizes, capture rate in weak flow was directly related to concentration, but in strong flow it was constant. Worms were therefore unable to benefit from abundant food when in strong flow. The critical velocity at which the capture rate became constant was lower for adult worms than for juvenile worms, and it was lower for small particles than for large particles. Retention efficiency was constant among all treatments, and the results for contact rate were essentially the same as for capture rate. Therefore, the mechanics of particle contact must explain the effects of velocity on the functional response. Contact rate was not a constant proportion of particle flux; treatments with similar fluxes yielded different contact rates depending on the strength of flow. The results appeared to be caused by a velocity-induced behavioral change in appendage posture that affects contact rates: in moderate flow, worms form their feeding palps into helical coils, which they tighten as the velocity increases. I suggest this behavior constrains suspension feeding rates and the mechanical selection between particle sizes when worms are in strong flow, and that the effect changes with ontogeny. Because the results are consistent with patterns in measured growth rates of P. cornuta, I hypothesize that this influence of velocity on the functional response can constrain growth and population dynamics in this species.     

Study on the concentration distribution in a trapezoidal open-channel flow with a side discharge

The number and distribution of pollutant concentration in a trapezoidal open channel flow with a side discharge is calculated and effects of the bank gradient are investigated in this paper. A sigma-coordinate water quality numerical model is used to simulate the process of both water and pollutant transportation in the trapezoidal channel open flow. The diffusion coefficient used in the prediction is determined by two methods including constant coefficient and the depth-averaged k-epsilon turbulence closure model. The change of the concentration with the bank gradient is acquired based on the simulation of cases with different bank gradients. An analytical formula is derived by using the mirror image method and related diffusion theories, ignoring the discharge momentum and the influence of the opposite bank. The formula can predict the number and distribution of pollutant concentration with some acceptable errors. The results demonstrate that the bank gradient has great influence on the concentration distribution which will decrease with the increase of the bank gradient approximately following a hyperbolic law.     

A mathematical model for type II profile of concentration distribution in turbulent flows

This paper presents a mathematical model to investigate type II profile of suspension concentration distribution (i.e., the concentration profile where the maximum concentration appears at some distance above the bed surface) in a steady, uniform turbulent flow through open-channels. Starting from the mass and momentum conservation equations of two-phase flow, a theoretical model has been derived. The distribution equation is derived considering the effects of fluid lift force, drag force, particle inertia, particle–particle interactions, particle velocity fluctuations and drift diffusion. The equation is solved numerically and is compared with available experimental data as well as with other models existing in the literature. Good agreement between the observed value and computed result, and minimum error in comparison to other models indicate that the present model can be applied in predicting particle concentration distribution for type II profile for a wide range of flow conditions. The proposed model is also able to show the transition from type I profile to type II profile.     

Estimation of total sediment load concentration obtained by experimental study using artificial neural networks

Estimation of sediment concentration in rivers is very important for water resources projects planning and managements. The sediment concentration is generally determined from the direct measurement of sediment concentration of river or from sediment transport equations. Direct measurement is very expensive and cannot be conducted for all river gauge stations. However, sediment transport equations do not agree with each other and require many detailed data on the flow and sediment characteristics. The main purpose of the study is to establish an effective model which includes nonlinear relations between dependent (total sediment load concentration) and independent (bed slope, flow discharge, and sediment particle size) variables. In the present study, by performing 60 experiments for various independent data, dependent variables were obtained, because of the complexity of the phenomena, as a soft computing method artificial neural networks (ANNs) which is the powerful tool for input–output mapping is used. However, ANN model was compared with total sediment transport equations. The results show that ANN model is found to be significantly superior to total sediment transport equations.     

漓江上游纳污最适总量及水质变化规律研究

为确保 2 0 0 0 - 2 0 10年桂林漓江上游进入城区水质能保持国家II类水质标准进行纳污总量控制及其水质变化规律研究。采用系数法对 2 0 0 0 - 2 0 10年陆源排污总量进行科学预测 ,按河流功能区划要求 ,首次利用动态数学模型计算河流在不同流量、不同纳污总量条件下保持II类水质的最适纳污值 ,探讨了漓江水质变化规律。为环境管理打下基础     

排水管道内不同粒径沉积颗粒物冲刷率的分析与计算

为探究和量化在水流冲刷下,排水管道中不同粒径颗粒物冲刷沉积的过程,本文模拟排水管道内沉积颗粒的冲刷过程.冲刷过程中,粒径较小的悬移质颗粒(小于0.1 mm),在管道沿线取样测得水流中悬浮固体质量浓度(SS);粒径较大的推移质颗粒(0.1—2 mm),测得管道沿线不同位置沉积的颗粒质量.并建立两个数学模型分别计算排水管道内两类颗粒物的冲刷率.研究发现,悬移质颗粒,以水流中SS为依据,可计算出输送通量和冲刷率;推移质颗粒,以管道不同位置沉积下来的颗粒质量为依据,拟合出了管道中的沉积分布函数,是以e为底数的指数函数,可计算出冲刷量和冲刷率.模型计算出的冲刷率呈现出规律性:悬移质颗粒被冲刷成悬浮状态,随水流迁移过程中部分会再次沉积,使得悬移质颗粒的冲刷率从管道前段至中后段逐步降低,如初始沉积质量为100 g的0.045 mm悬移质颗粒,在0.30 m·s^-1的冲刷流速下,计算出管道前段冲刷率为78.94%,最终在管道后段降至13.89%;对于两类颗粒而言,颗粒物粒径越小,冲刷流速越大,初始沉积质量越小,冲刷率越高.     

Clustering of aerosols in atmospheric turbulent flow

A mechanism of formation of small-scale inhomogeneities in spatial distributions of aerosols and droplets associated with clustering instability in the atmospheric turbulent flow is discussed. The particle clustering is a consequence of a spontaneous breakdown of their homogeneous space distribution due to the clustering instability, and is caused by a combined effect of the particle inertia and a finite correlation time of the turbulent velocity field. In this paper a theoretical approach proposed in Elperin et al. (2002) Phys Rev E 66:036302 is further developed and applied to investigate the mechanisms of formation of small-scale aerosol inhomogeneities in the atmospheric turbulent flow. The theory of the particle clustering instability is extended to the case when the particle Stokes time is larger than the Kolmogorov time scale, but is much smaller than the correlation time at the integral scale of turbulence. We determined the criterion of the clustering instability for the Stokes number larger than 1. We discussed applications of the analyzed effects to the dynamics of aerosols and droplets in the atmospheric turbulent flow.     

The Chemical Composition and Flow of the River Lea, Spain

Weekly measurements of chemical composition were made at four sampling sites on the Lea River (Spain) between July 1985 and August 1986. at two stations there were gauging-weirs for stream discharge monitoring. Conductivity, pH, alkalinity, silicon, calcium, magnesium, sodium, potassium, ammonia, nitrate, sulphate, chloride, reactive phosphate, and total phosphate, were recorded in each site.

Results were analysed using multiple regression techniques to study the relationship between flow and chemical components.

Conductivity, alkalinity, calcium, magnesium and sulphate were strongly related to flow, decreasing in concentration with increased flow. Ammonia, potassium, reactive phosphate and total phosphate varied most widely, with peaks at times of heavy rainfall. Nitrate increased at times of high discharge, with little variation between sampling points. Silicon decreased in summer and autumn in the lower catchment area whilst chloride and sodium were higher in the lower catchment of the River Lea.     

Numerical modelling of horizontal sediment-laden jets

Sediment-laden turbulent flows are commonly encountered in natural and engineered environments. It is well known that turbulence generates fluctuations to the particle motion, resulting in modulation of the particle settling velocity. A novel stochastic particle tracking model is developed to predict the particle settling out and deposition from a sediment-laden jet. Particle velocity fluctuations in the jet flow are modelled from a Lagrangian velocity autocorrelation function that incorporates the physical mechanism leading to a reduction of settling velocity. The model is first applied to study the settling velocity modulation in a homogeneous turbulence field. Consistent with basic experiments using grid-generated turbulence and computational fluid dynamics (CFD) calculations, the model predicts that the apparent settling velocity can be reduced by as much as 30 % of the stillwater settling velocity. Using analytical solution for the jet mean flow and semi-empirical RMS turbulent velocity fluctuation and dissipation rate profiles derived from CFD predictions, model predictions of the sediment deposition and cross-sectional concentration profiles of horizontal sediment-laden jets are in excellent agreement with data. Unlike CFD calculations of sediment fall out and deposition from a jet flow, the present method does not require any a priori adjustment of particle settling velocity.     

Stability and Mixing of a Vertical Axisymmetric Buoyant Jet in Shallow Water

The stability, mixing and effect of downstream control on axisymmetric turbulent buoyant jets discharging vertically into shallow stagnant water is studied using 3D Reynolds-averaged Navier–Stokes equations (RANS) combined with a buoyancy-extended k –ε model. The steady axisymmetric turbulent flow, temperature (or tracer concentration) and turbulence fields are computed using the finite volume method on a high resolution grid. The numerical predictions demonstrate two generic flow patterns for different turbulent heated jet discharges and environmental parameters (i) a stable buoyant discharge with the mixed fluid leaving the vertical jet region in a surface warm water layer; and (ii) an unstable buoyant discharge with flow recirculation and re-entrainment of heated water. A stratified counterflow region always appears in the far-field for both stable and unstable buoyant discharges. Provided that the domain radius L exceeds about 6H, the near field interaction and hence discharge stability is governed chiefly by the jet momentum length scale to depth ratio l_M/H, regardless of downstream control. The near field jet stability criterion is determined to be l_M/H = 3.5. A radial internal hydraulic jump always exists beyond the surface impingement region, with a 3- to 6-fold increase in dilution across the jump compared with vertical buoyant jet mixing. The predicted stability category, velocity and temperature/concentration fields are well-supported by experiments of all previous investigators.     

The economic implications of recycling exhaustible natural resources: The case for crude oil

Regardless of whether the bulk of decision-making in an economy is done by a central unit or by decentralized smaller units, the government can act to propose guidelines to individual agents. This is of particular importance when the activities of the latter cause aggregative or social problems which are not directly acted upon by the smaller agents. The purpose of this paper is to set up a model by which a central authority can make choices in the presence of two pressing social problems, namely, a diminishing domestic supply of an exhaustible resource and the contamination of the environment through discharged waste materials.The model itself takes the form of an integer-linear programming problem which runs through discrete time to a finite horizon. Besides the traditional modes of “virgin” exploration and production and/or importation from abroad, society is also given the choice of recycling. Society will choose combinations of the above three to minimize the costs of satisfying fixed (projected) oil product demands in the future. The costs include those for increasing exploration for virgin refineries; for collection, refining and transportation for refineries and for the cost to society of discharges of waste-oil into the environment. The constraints include process flow restrictions, import quotas, capacity limits and discharge restrictions as well as fixed demands.An effort was made to keep the model as general as possible. Although no numerical solution is obtained in this paper, we feel that the policy implications of some presumed solution (possible through the use of a well-known algorithm for mixed variable problems) are worth examining. They revolve around the model itself, citing the potential attractiveness of recycling as the other two alternatives become increasingly expensive, and as development of alternatives to oil progresses at an alarmingly slow rate. Also mentioned are problems relating to the potential demands for recycled versus virgin oil products, balance-of-trade problems, and the mutability of social and economic institutions in the crisis of economic adjustment that much of the world is now facing.     

Part I : <Emphasis Type="Italic">a priori</Emphasis> study of erosion and deposition with large eddy simulation of turbulent flow over multiple 2D sandy Gaussian hills

The micro-scale prediction of sand trapping or take-off over hilly terrains is a crucial issue in semi-arid regions for soil depletion. In this context, large eddy simulations around one or several hills are performed in order to provide statistical parameters to characterize the flow at micro-scales and provide data for mesoscale modelling. We focus on the determination of recirculation zones since they play an important role in solid particle erosion or entrapment. A new wall modeling adapted from Huang et al. (J Turbul 17:1–24, 2016) for rough boundary layers is found to improve the prediction of the recirculation zone length downstream of an isolated hill and is used for all the numerical cases presented here. A geometrical parameterization of the recirculation zones is proposed. When the recirculation region is assumed to have an ellipsoidal shape, the total surface of the recirculation can be obtained from this new parameterization and easily extrapolated to more general dune configurations. Numerical results are compared with experiments performed in our laboratory (Simoëns et al. in Procedia IUTAM 17:110–118, 2015) and good agreement is achieved. We explore general aerodynamic cases deduced from the urban canopy scheme of Oke (Energy Build 11:103–113, 1988). In this scheme the momentum and mass exchange between the upper layer and the space between hills is sorted according to the streamwise hill spacing within three basic cases of skimming, wake or isolated flow. The study of the recirculation zones, the mean velocity and Reynolds stress profiles around an isolated or two consecutive hills with different distances shows that the double hill configuration with 3H separation behaves as much as a whole to the upcoming flow. The vortex formed between the crests does not strongly affect the overall evolution of the outer flow. By an a priori prediction of the preferential zones of erosion and accumulation of fictive particles, it is shown that isolated dunes present more deposition and less erosion than two-hill configurations. The results presented in this study will be discussed in the presence of Lagrangian transport of sand particles above 2D Gaussian hills in future work.     

Laboratory studies defining flow regimes for negatively buoyant surface discharges into crossflow

Surface discharges of negatively buoyant jets into moving ambient water create a range of complex flow patterns. These complexities arise through the interplay between the discharge’s initial fluxes and the motion of the ambient current. In this study a series of laboratory experiments were conducted for negatively buoyant surface discharges into crossflow to investigate flow patterns under different discharge and ambient conditions. The results compared with simulations of the CORMIX model, an expert system for ocean outfall design. In CORMIX, the simulation module DHYDRO for dense discharges has been used. Finally the flow different patterns were arranged in a dimensionless diagram to propose a modified flow classification system with new criteria.