Turbulence closure models and their application in RAMS

Turbulence closures are fundamental for modelling the atmospheric diffusion in numerical codes and the resulting eddy diffusivities are key parameters in describing the transport and dispersion in the boundary layer. In this work, four turbulence closure schemes have been applied for reproducing a neutral flow over schematic complex terrain using the meteorological model RAMS. Two of the closures, a one-equation (E-l) and a two-equations (E-) model, have been implemented in RAMS in alternative to the ones originally available. In these cases, an analytical method based on the similarity theory for the atmospheric surface layer and boundary layer is adopted to calculate the empirical constants of the turbulence closures. Some examples of numerical studies performed to simulate the flow and turbulence over a 3-D hill in wind-tunnel experiment in neutral stratification are presented and discussed. An intercomparison of simulations related to different closures is considered by analysing the main features of the flow over the hill and by comparing calculated vertical profiles of turbulent kinetic energy with measured ones.     

A σ-coordinate transport model coupled with rotational boussinesq-type equations

This paper describes a σ-coordinate scalar transport model coupled with a Boussinesq-type hydrodynamic model. The Boussinesq model has the ability to calculate both three-dimensional velocity distributions and the water surface motion. To capture ‘dispersion’ processes in open channel flow, horizontal vorticity effects induced by a bottom shear stress are included in the Boussinesq model. Thus, a reasonable representation of vertical flow structure can be captured in shallow and wavy flow fields. To solve the coupled Boussinesq and scalar transport system, a finite-volume method, based on a Godunov-type scheme with the HLL Riemann solver, is employed. Basic advection and advection–diffusion numerical tests in a non-rectangular domain were carried out and the computed results show good agreement with analytic solutions. With quantitative comparisons of dispersion experiments in an open channel, it is verified that the proposed coupled model is appropriate for both near and far field scalar transport predictions. From numerical simulations in the surf zone, physically reasonable results showing expected vertical variation are obtained.     

Efficient numerical computation and experimental study of temporally long equilibrium scour development around abutment

For the abutment bed scour to reach its equilibrium state, a long flow time is needed. Hence, the employment of usual strategy of simulating such scouring event using the 3D numerical model is very time consuming and less practical. In order to develop an applicable model to consider temporally long abutment scouring process, this study modifies the common approach of 2D shallow water equations (SWEs) model to account for the sediment transport and turbulence, and provides a realistic approach to simulate the long scouring process to reach the full scour equilibrium. Due to the high demand of the 2D SWEs numerical scheme performance to simulate the abutment bed scouring, a recently proposed surface gradient upwind method (SGUM) was also used to improve the simulation of the numerical source terms. The abutment scour experiments of this study were conducted using the facility of Hydraulics Laboratory at Nanyang Technological University, Singapore to compare with the presented 2D SGUM–SWEs model. Fifteen experiments were conducted with their scouring flow durations vary from 46 to 546 h. The comparison shows that the 2D SGUM–SWEs model gives good representation to the experimental results with the practical advantage.     

A Numerical and Field Investigation of Surface Heat Fluxes from Small Wind-Sheltered Waterbodies in Semi-Arid Western Australia

Shelterbelts are used for a variety of purposes in agricultural environments, primarily because of their ability to improve the downwind microclimate. Excessive evaporative losses from small, agricultural water supply reservoirs in semi-arid Western Australia motivated a combined numerical modelling and field investigation into the potential for using shelterbelts to reduce evaporation from these open waterbodies. A numerical model of the disturbed momentum and turbulence fields in the region modified by the wind-shelter was employed and accounted for the presence of a waterbody downwind. The model was coupled with conservation equations for heat and moisture and sensible and latent heat fluxes were estimated from the simulated momentum, temperature and humidity fields. The numerical simulations were tested against four days of field data from two experiments conducted in the agricultural districts of southwest Western Australia that measured boundary-layer evolution over a variety of small waterbodies protected by artifical and natural wind-shelters. The model provided good predictions of windspeed during neutral conditions, but inadequate specification of the upwind boundary during non-neutral stabilities resulted in the model failing to capture any sensitivity to atmospheric stability as seen in the field data. Despite this limitation, the temperature and humidity fields were adequately captured by the model, and evaporative mass flux predictions also agreed well with estimates taken from water-balance measurements. It is concluded that well-designed wind-shelters can reduce evaporation from open waterbodies by 20–30% as a result of reductions in the velocity scales responsible for removing moisture from the water surface. The model can be used to estimate the values of various shelterbelt design parameters (e.g., porosity, height) that could be applied in the field to provide optimum evaporation reductions.     

A non-negative and high-resolution finite volume method for the depth-integrated solute transport equation using an unstructured triangular mesh

This paper proposes a new high-resolution finite volume method for solving the two-dimensional (2D) solute transport equation using an unstructured mesh. A new simple r-factor algorithm is introduced into the Total Variation Diminishing flux limiter to achieve a more efficient yet accurate high-resolution scheme for solving the advection term. To avoid the physically-meaningless negative solutions resulted from using the Green–Gauss theorem, a nonlinear two-point flux approximation scheme is adopted to deal with the anisotropic diffusion term. The developed method can be readily coupled with a two-dimensional finite-volume-based flow models under unstructured triangular mesh. By integrating with the ELCIRC flow model, the proposed method was verified using three idealized benchmark cases (i.e., advection of a circle-shaped solute field, advection in a cyclogenesis flow field and transport of a initially square-shaped solute plume), and further applied to simulate the non-reactive solute transport process driven by irregular tides in the Deep Bay, eastern Pearl River Estuary of China. These cases are also simulated by models using other existing methods, including different r-factor for advection term and the Green–Gauss theorem for diffusion term. The comparison between the results from the new method and those from other existing methods demonstrated the new method could describe advection induced concentration shock and discontinuities, and anisotropic diffusion at high resolution without providing spurious oscillations and negative values.     

Numerical Investigation of Boundary-Layer Evolution and Nocturnal Low-Level Jets: Local versus Non-Local PBL Schemes

Numerical simulations of the evolution of the planetary boundary layer (PBL) and nocturnal low-level jets (LLJ) have been carried out using MM5 (version 3.3) with four-dimensional data assimilation (FDDA) for a high pollution episode in the northeastern United States during July 15–20, 1999. In this paper, we assess the impact of different parameterizations on the PBL evolution with two schemes: the Blackadar PBL, a hybrid local (stable regime) and non-local (convective regime) mixing scheme; and the Gayno–Seaman PBL, a turbulent kinetic energy (TKE)-based eddy diffusion scheme. No FDDA was applied within the PBL to evaluate the ability of the two schemes to reproduce the PBL structure and its temporal variation. The restriction of the application of FDDA to the atmosphere above the PBL or the lowest 8 model levels, whichever is higher, has significantly improved the predicted strength and timing of the LLJ during the night. A systematic analysis of the PBL evolution has been performed for the primary meteorological fields (temperature, specific humidity, horizontal winds) and for the derived parameters such as the PBL height, virtual potential temperature, relative humidity, and cloud cover fraction. There are substantial differences between the PBL structures and evolutions simulated by these two different schemes. The model results were compared with independent observations (that were not used in FDDA) measured by aircraft, RASS and wind profiler, lidar, and tethered balloon platforms during the summer of 1999 as part of the NorthEast Oxidant and Particle Study (NE-OPS). The observations tend to support the non-local mixing mechanism better than the layer-to-layer eddy diffusion in the convective PBL.     

Suspended particulate matter dynamics in a particle framework

Suspended particulate matter (SPM) dynamics in ocean models are usually treated with an advection–diffusion equation for one or more sediment size classes coupled to the hydrodynamical part of the model. Numerical solution of these additional partial differential equations unavoidably introduces numerical diffusion, i.e. in the case of sharp gradients the possible occurrence of artificial oscillations and non-positivity. A Lagrangian particle-tracking model has been developed to simulate short-term SPM dynamics. Modelling individual sediment particles allows a straightforward physical interpretation of the processes. The tracking of large numbers of individual and independent particles (up to 25 million in total in a single sediment class) can be achieved on high performance computer clusters, due to efficient parallelisation of particle tracking. The movement of the particles is described by a stochastic differential equation, which is consistent with the advection–diffusion equation. Here, the concentration profile is represented by a set of independent moving particles, which are advected according to the 3D velocity field, while the diffusive displacements of the particles are sampled from a random distribution, which is related to the eddy diffusivity field. To account for erosion a new parameterisation is proposed. Three numerical particle tracking schemes (EULER, MILSTEIN and HEUN) are presented and validated in idealised test cases. Finally, the particle tracking algorithms are applied to a realistic scenario, a severe winter storm in the East Frisian Wadden Sea (southern North Sea). The comparison with observations and an Eulerian SPM transport model seems to indicate a somewhat better fidelity of the Lagrangian approach.     

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).     

One-dimensional numerical modelling of dam-break waves over movable beds: application to experimental and field cases

This paper reports a numerical study on dam-break waves over movable beds. A one-dimensional (1-D) model is built upon the Saint-Venant equations for shallow water waves, the Exner equation of sediment mass conservation and a spatial lag equation for non-equilibrium sediment transport. The set of governing equations is solved using an explicit finite difference scheme. The model is tested in various idealized experimental cases, with fairly good agreement between the numerical predictions and measurements. Discrepancies are observed at the earlier stage of the dam-break wave and around the dam location due to no vertical velocity component being taken into account. Sensitivity tests confirm that the friction coefficient is an important parameter for the evaluation of sediment transport processes operating during a dam-break wave. The influence of the non-equilibrium adaptation length (or the lag distance) is negligible on the wavefront celerity and weak on the free surface and bed profiles, which indicates that one may ignore the spatial lag effect in dam-break wave studies. Finally, the simulation of the Lake Ha!Ha! dyke-break flood event shows that the model can provide relevant results if a convenient formula for computing the sediment transport capacity and an appropriate median grain diameter of riverbed material are selected.     

浏河引排水对城厢镇水质影响的数值计算

城厢镇地表水水源的污染特点在很大程度上取决于浏河闸的运行启闭情况,对通过引排水方案来改善滞流期恶劣的水质状况.文中首先用一维Saint—Venant方程组及CBOD—NBOD—DO联偶反应方程组分别建立水量及水质模式,通过有限差分法数值求解.利用1990年11月5日开闸排水期间水量与水质同步监测资料进行验证,结果表明,模式能够满足水质规划的要求.本文对水质的动态变化规律进行评价,认为只要合理组合引排方案,就能达到改善城厢镇地表水源水质的目的.     

A numerical model of wave- and current-driven nutrient uptake by coral reef communities

We developed a numerical model capable of simulating the spatial zonation of nutrient uptake in coral reef systems driven by hydrodynamic forcing (both from waves and currents). Relationships between nutrient uptake and bed stress derived from flume and field studies were added to a four-component biogeochemical model embedded within a three-dimensional (3-D) hydrodynamic ocean model coupled to a numerical wave model. The performance of the resulting coupled physical-biogeochemical model was first evaluated in an idealized one-dimensional (1-D) channel for both a pure current and a combined wave-current flow. Waves in the channel were represented by an oscillatory flow with constant amplitude and frequency. The simulated nutrient concentrations were in good agreement with the analytical solution for nutrient depletion along a uniform channel, as well as with existing observations of phosphate uptake across a real reef flat. We then applied this integrated model to investigate more complex two-dimensional (2-D) nutrient dynamics, firstly to an idealized coral reef-lagoon morphology, and secondly to a realistic section of Ningaloo Reef in Western Australia, where nutrients were advected into the domain via alongshore coastal currents. Both the idealized reef and Ningaloo Reef simulations showed similar patterns of maximum uptake rates on the shallow forereef and reef crest, and with nutrient concentration decreasing as water flowed over the reef flat. As a result of the cumulative outflow of nutrient-depleted water exiting the reef channels and then being advected down the coast by alongshore currents, both reef simulations exhibited substantial alongshore variation in nutrient concentrations. The coupled models successfully reproduced the observed spatial-variability in nitrate concentration across the Ningaloo Reef system.     

Sensitivity of a coupled physical–biological model to turbulence: high-frequency simulations in a northern Adriatic station

This paper investigates the impacts of different turbulence models on the biological state at an ocean station in the northern Adriatic sea, named S3, comparing them with other uncertainties inherent to coupled physical–biological simulations. The numerical tool is a 1-D model resulting from the coupling of two advanced numerical models. The hydrodynamic part is modelled using the General Ocean Turbulence Model (www.gotm.net), in a version adopting state-of-the-art second-moment Turbulence Closure Models (TCMs). Marine biogeochemistry is parameterized with the Biogeochemical Flux Model (http://www.bo.ingv.it/bfm), which is a direct descendant of ERSEM (European Regional Sea Ecosystem Model). Results, obtained by forcing the model with hourly wind and solar radiation data and assimilating salinity casts, are compared against monthly observations made at the station during 2000–2001. Provided that modern second-moment TCMs are employed, the comparisons indicate that both the physical and the biological dynamics are relatively insensitive to the choice of the particular scheme adopted, suggesting that TCMs have finally ‘converged’ in recent years. As a further example, the choice of the nutrient boundary conditions has an impact on the system evolution that is more significant than the choice of the specific TCM, therefore representing a possible limitation of the 1-D model applied to stations located in a Region of Freshwater Influence. The 1-D model simulates the onset and intensity of the spring–summer bloom quite well, although the duration of the bloom is not as prolonged as in the data. Since local dynamics appears unable to sustain the bloom conditions well into summer, phytoplankton at the station was most likely influenced by river input or advection processes, an aspect that was not found when the S3 behaviour was adequately modelled using climatological forcings. When the focus is in predicting high-frequency dynamics, it is more likely that lateral advection cannot be neglected. While the physical state can be satisfactorily estimated at these short time scales, the accurate estimation of the biological state in coastal regions still appears as rather elusive.     

Sensitivity of air quality model prediction to parameterization of vertical eddy diffusivity

This paper investigates the effects of vertical eddy diffusivities derived from the 3 different planetary boundary layer (PBL) schemes on predictions of chemical components in the troposphere of East Asia. Three PBL schemes were incorporated into a regional air quality model (RAQM) to represent vertical mixing process and sensitivity simulations were conducted with the three schemes while other options are identical. At altitudes <2km, all schemes exhibit similar skill for predicting SO₂ and O₃, but more difference in the predicted NO_x concentration. The Gayno–Seaman scheme produces the smallest vertical eddy diffusivity (Kz) among all schemes, leading to higher SO₂ and NO_x concentrations near the surface than that from the other 2 schemes. However, the effect of vertical mixing on O₃ concentration is complex and varies spatially due to chemistry. The Gayno–Seaman scheme predicts lower O₃ concentrations than the other two schemes in the parts of northern China (generally VOC-limited) and higher ones in most parts of southern China (NO_x-limited). The Byun and Dennis scheme produces the largest mixing depth in the daytime, which bring more NO_x into upper levels, and the mixing depth predicted by the Gayno–Seaman scheme is the smallest, leading to higher NO_x and lower O₃ concentrations near the surface over intensive emission regions.     

Solution of fully-coupled shallow water equations and contaminant transport using a primitive-variable Riemann method

A Riemann-solver scheme, using primitive variables rather than conserved variables, is configured and tuned for the solution of the fully-coupled two-dimensional shallow water and contaminant transport equations. This scheme is based on the unstructured finite volume discretization using primitive-variable Roe-flux approximation with an entropy fix. The primitive-variable flux associated with the exact source-term balancing is well-behaved and well-balanced for both still-water and dry regions with arbitrary bed topography. Second-order accuracy is used in space and time. The present study uses a nonlinear implicit scheme based on Newton-iterative algorithm for the time integration. In order to show the accuracy of the scheme, numerical results are verified by different test cases for contaminant advection and diffusion. A scenario of contaminant transport in a complex geometry with wet and dry elements is also simulated to demonstrate that the present work can be implemented on practical applications involving flooding and contaminant transport.     

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.     

Two-phase SPH modelling of advective diffusion processes

This paper deals with a two-dimensional numerical model based on the smoothed particle hydrodynamics (SPH) technique for the evaluation of the concentration field of pollutants in water. A SPH model is formulated to solve the fickian diffusion equation applied to pollutants with the same density as the water. A lagrangian SPH formalism of the advective diffusion equation is also developed for pollutant-water, taking into account the effects of molecular diffusion and natural advection induced by differences between the fluid densities. These equations are coupled with the fluid mechanics equations. Attention is paid to the numerical aspects involved in the solution procedure and to the optimization of the model parameters. Environmental engineering problems concerning diffusion and natural advection phenomena occur in the presence of a pollutant in still water. Numerical tests referring to a strip and a bubble of contaminant in a water tank with different initial concentration laws have been carried out. The results obtained by the proposed SPH models are compared with other available SPH formulations, showing an overall better agreement with standard analytical solutions in terms of spatial evolution of the concentration values. Capabilities and limits of the proposed SPH models to simulate advective diffusion phenomena for a wide range of density ratios are discussed.     

Application of a multi-step computation scheme to an intratidal estuarine water quality model

A computation scheme, which involves multi-step computation of the decoupled mass-balance equations in water quality models, was proposed by Park and Kuo (1996. Water Res. 30, 2255–2264). Using a simple hypothetical model, they explained the concept and demonstrated the accuracy and computational efficiency of the multi-step scheme. This paper describes the concept and the implementation of the multi-step computation scheme in a more generalized format for both intratidal and intertidal estuarine water quality models. The scheme is applied to a prototype estuary using a laterally-integrated two-dimensional intratidal model. The computational efficiency of the scheme is demonstrated by comparing the model results using the multi-step scheme with those using the traditional single-step explicit numerical solution of the kinetic processes.     

Nested numerical scheme in a polar coordinate shallow water model for the coast of Bangladesh

This study is concerned with the development of storm surge model to predict water level accurately due to surge associated with a cyclone along the coast of Bangladesh. Considering the funnel shape of the Bay of Bengal, coastal bending and the existence of off-shore islands, a vertically integrated model in cylindrical polar coordinate system is developed using nested numerical scheme. A fine mesh scheme capable of incorporating coastal bending and offshore islands properly in the numerical scheme is nested into a coarse mesh scheme covering up to 15° N latitude of the Bay of Bengal. The developed model is used to estimate water levels at different coastal and island stations associated with a few storms that hit the coast of Bangladesh. The computed surge levels compared well with observed ones and predicted surge levels investigated with different approaches.     

Numerical simulation of particle-driven gravity currents

Particle-driven gravity currents frequently occur in nature, for instance as turbidity currents in reservoirs. They are produced by the buoyant forces between fluids of different density and can introduce sediments and pollutants into water bodies. In this study, the propagation dynamics of gravity currents is investigated using the FLOW-3D computational fluid dynamics code. The performance of the numerical model using two different turbulence closure schemes namely the renormalization group (RNG) ${k-\epsilon}$ scheme in a Reynold-averaged Navier-Stokes framework (RANS) and the large-eddy simulation (LES) technique using the Smagorinsky scheme, were compared with laboratory experiments. The numerical simulations focus on two different types of density flows from laboratory experiments namely: Intrusive Gravity Currents (IGC) and Particle-Driven Gravity Currents (PDGC). The simulated evolution profiles and propagation speeds are compared with laboratory experiments and analytical solutions. The numerical model shows good quantitative agreement for predicting the temporal and spatial evolution of intrusive gravity currents. In particular, the simulated propagation speeds are in excellent agreement with experimental results. The simulation results do not show any considerable discrepancies between RNG ${k-\epsilon}$ and LES closure schemes. The FLOW-3D model coupled with a particle dynamics algorithm successfully captured the decreasing propagation speeds of PDGC due to settling of sediment particles. The simulation results show that the ratio of transported to initial concentration C _o /C _i by the gravity current varies as a function of the particle diameter d _s . We classify the transport pattern by PDGC into three regimes: (1) a suspended regime (d _s is less than about 16 μm) where the effect of particle deposition rate on the propagation dynamics of gravity currents is negligible i.e. such flows behave like homogeneous fluids (IGC); (2) a mixed regime (16 μm < d _s <40 μm) where deposition rates significantly change the flow dynamics; and (3) a deposition regime (d _s ?> 40 μm) where the PDGC rapidly loses its forward momentum due to fast deposition. The present work highlights the potential of the RANS simulation technique using the RNG ${k-\epsilon}$ turbulence closure scheme for field scale investigation of particle-driven gravity currents.     

地下水中VOC挥发因子模型的研究

建立了一个计算地下水中挥发性有机物（VOC）挥发因子的模型.选用半挥发性的1,2,4-三氯苯和挥发性的四氯乙烯为VOC的代表,分别计算了非饱和区土壤为砂土和粘土时的挥发因子.结果表明：蒸发使VOC的挥发因子增大,而下渗则使VOC的挥发因子减小;不论VOC的挥发性强弱,蒸发（下渗）对挥发因子的影响均比较明显;蒸发情况下,非饱和区土壤性质对挥发因子的影响不明显,而下渗情况下,非饱和区土壤性质对挥发因子的影响则趋于明显;此外,当非饱和区土壤为粘土时,VOC的挥发因子受蒸发（下渗）的影响更明显.