Simulation of dam/levee-break hydrodynamics with a three-dimensional implicit unstructured-mesh finite element model

Dam failures usually cause huge economic and life losses , especially in urban areas where there is a high concentration of inhabitants and economic actors. In order to understand the physical mechanisms of the formation and development of dam-break flooding, lots of efforts have been put into different types of modelling techniques. However, most of existing models are 1D (one-dimensional) or 2D models based on the shallow water equations. In this paper, we present a 3D numerical modelling investigation of dam-break flow hydrodynamics in an open L-shape channel. A newly developed 3D unstructured mesh finite element model is used here. An absorption-like term is introduced to the Navier–Stokes equations in order to control the conditioning of the matrix equation in the numerical solution process and thus improve the stability. A wetting and drying algorithm is used here to allow the free surface height to be treated with a high level of implicitness and stability. The 3D model has been validated by comparing the results with the published experimental data. Good agreement has been achieved at six selected locations. This study shows that the 3D unstructured mesh model is capable of capturing the 3D hydraulic aspects and complicated local flows around structures in simulation of dam-break flows.     

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.     

LE of shallow mixing interfaces: A review

Eddy-resolving techniques have become a powerful tool to investigate shallow flows at both laboratory and field scale. In this paper several examples are given where high-resolution 3D numerical simulation are used to investigate the spatial development of mixing interfaces (MIs) forming in shallow environments like open channels with idealized and natural bathymetry where the bed friction plays a major role in the spatial development of the MI and associated large-scale turbulence. The focus is on the coherent structures forming within the MI and in its vicinity that control the momentum and mass exchange and heat transfer between the two sides of the MI. Examples include: (1) a MI developing in a flat-bed open channel downstream of a splitter wall separating two parallel fully-turbulent streams of different velocities, (2) a MI developing in a flat-bed open channel downstream of a 60 \(^{\circ }\) wedge separating two non-parallel fully turbulent streams of different velocities, (3) a MI developing downstream of a river confluence for cases with a large and, respectively, a small difference between the mean velocities of the two streams. Stratification effects due to unequal densities of the two incoming streams are also discussed, (4) a MI developing between a main rectangular straight channel and a series of shallow embayments present at one of the channel banks. Besides using available experimental data to demonstrate that eddy resolving techniques can accurately predict the structure of the MI and its development, the paper discusses new insights into the physics of these flows obtained based on the simulations. The paper also provides an overview of the main numerical approaches that can be used to simulate the unsteady dynamics of the large scale turbulence in flows containing shallow MIs.     

The effects of groundwater table and flood irrigation strategies on soil water and salt dynamics and reed water use in the Yellow River Delta, China

Vegetation management in shallow groundwater table environments requires an understanding of the interactions between the physical and biological factors that determine root-zone soil salinization and moisture. In this study, the effects of groundwater depth and flood irrigation strategies on water and salt dynamics and reed water use were analyzed in the shallow groundwater region of the Yellow River Delta in China using the HYDRUS-1D model. The results indicated that there is a conflict between water, salt stress, and reed water use with variations in groundwater depth. A water table depth of 3.5 m is the minimum limit to maintain a safe level of soil salinity, but at this depth, the environmental stress on reeds is worsened by the decrease in soil water storage. Maintaining the flood pulses on the wetland, especially during May, may be critical for restoring the reed wetland in the Yellow River Delta.     

Oil spreading in instantaneous and continuous spills on rotating earth

The effect of the Coriolis force on the oil spill spreading in the gravity-viscous regime is examined. A new shallow water model for the transport and spreading of oil slick of arbitrary shape is described in which the Coriolis force is included in the momentum equations and the oil–water friction is parameterized in a frame of the boundary layer theory including the Ekman friction. The numerical Lagrangian method based on smoothed particle dynamics is described. New similarity solutions of the model equations are obtained for unidirectional and axisymmetric spreading in gravity-viscous, gravity-turbulent and gravity-viscous-rotational regimes for instantaneous as well as continuous releases. The numerical simulation extends these results for the case of continuous release in the presence of currents. It was shown that Coriolis term in the momentum equation can be omitted if slick thickness is much less of the laminar Ekman layer thickness. However, the Ekman friction should be retained for slicks of any thickness for larger times. The Ekman friction results in the essential slowdown of the spreading as well as in the deflection of the oil spreading velocity at 45° from the direction of velocity in the non-rotation case. Numerical simulations of large-scale spills showed that after the 2?days the slick area with the Coriolis effect was approximately less than half of that without rotation. Therefore, the earth rotation can be also important in the oil weathering.     

Verification of a 3D CFD model for vertical slot fish-passes

In the present work, we verified a 3D computational fluid dynamics model for vertical slot fish-passes (VSFs) that employs the renormalization-group k-epsilon turbulence model (RNG KE) and the volume of fluid (VOF) method. We compared model calculations with experiments in two pool designs T1 and T2 of an experimental VSF and with 2D calculations using the shallow water equations (SWE) and the standard k-epsilon (2D SKE) model. Calculations of the 3D model showed (1) good agreement with experiments and 2D calculations in predicting mean flow velocities, (2) better performance in the determination of the water surface in the VSF, which is attributed to the accurate VOF method, (3) superior prediction of turbulence characteristics than the 2D model, which is due to the 3D RNG KE model that overcomes the problem of turbulence overestimation of the 2D SKE model, and to the fact that the 3D model takes into account the 3D features of the flow in the fish pass. Moreover, the present 3D calculations showed that the common assumptions in VSFs that (1) the flow is 2D, and (2) the simulation of 4 pools of a VSF is sufficient to obtain satisfactory results, are not always valid. Flow can be considered as 2D only in pool design T2 and for certain geometries and flow characteristics in pool design T1; while, eventually, all the pools of a fish pass need to be modeled to ensure accurate results. Finally, the present work illustrates the need to perform fish experiments simultaneously with flow experiments.     

3D numerical modelling of turbidity currents

During floods, the density of river water usually increases due to a subsequent increase in the concentration of the suspended sediment that the river carries, causing the river to plunge underneath the free surface of a receiving water basin and form a turbidity current that continues to flow along the bottom. The study and understanding of such complex phenomena is of great importance, as they constitute one of the major mechanisms for suspended sediment transport from rivers into oceans, lakes or reservoirs. Unlike most of the previous numerical investigations on turbidity currents, in this paper, a 3D numerical model that simulates the dynamics and flow structure of turbidity currents, through a multiphase flow approach is proposed, using the commercial CFD code FLUENT. A series of numerical simulations that reproduce particular published laboratory flows are presented. The detailed qualitative and quantitative comparison of numerical with laboratory results indicates that apart from the global flow structure, the proposed numerical approach efficiently predicts various important aspects of turbidity current flows, such as the effect of suspended sediment mixture composition in the temporal and spatial evolution of the simulated currents, the interaction of turbidity currents with loose sediment bottom layers and the formation of internal hydraulic jumps. Furthermore, various extreme cases among the numerical runs considered are further analyzed, in order to identify the importance of various controlling flow parameters.     

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.     

Modelling algal blooms in the Dutch coastal waters by integrated numerical and fuzzy cellular automata approaches

In this paper, an integrated numerical and fuzzy cellular automata model was developed to predict possible algal blooms in Dutch coastal waters basing on the irradiance, nutrients and neighbourhood conditions. The numerical module used Delft3D-WAQ to compute the abiotic conditions, and fuzzy cellular automata approach was applied to predict the algal biomass that was indicated by chlorophyll a concentration. The simulated results of year 1995 were compared with that from BLOOM II model, and the advantages, disadvantages as well as future improvement were presented. In general, through this study, it is seen that the integrated modelling deserves more research inputs because: (1) the hydrodynamic processes and nutrients concentrations can be simulated in details by numerical method; (2) the irregular and sparse water quality and biological data, and the empirical knowledge from experts can be explored by the fuzzy logic technique; (3) the spatial heterogeneity, local interactions and the emerge of patchiness could be well captured through the cellular automata paradigm.     

On the role of physical modelling in atmospheric and oceanic forecast

We discuss how physical modelling can be used to reproduce atmospheric or oceanic flows in the laboratory. The similarity conditions for the effects of density stratification and Earth rotation are first presented. Then examples of results obtained on the large ‘Coriolis’ platform in Grenoble are described. These include topographic wakes in a stratified fluid and gravity currents. Physical modelling is not used to get direct results of practical relevance, but rather to test numerical models on specific processes of environmental flows. Therefore it must be performed in close relationship with theory and numerical modelling, using advanced measurement and data assimilation techniques.     

Fourier analysis of the roll-up and merging of coherent structures in shallow mixing layers

The current study investigates the role of nonlinearity in the development of two-dimensional coherent structures (2DCS) in shallow mixing layers. A nonlinear numerical model based on the depth-averaged shallow water equations is used to investigate temporal shallow mixing layers, where the mapping from temporal to spatial results is made using the velocity at the center of the mixing layer. The flow is periodic in the stream-wise direction and the transmissive boundary conditions are used in the cross-stream boundaries to prevent reflections. The numerical results are examined with the aid of Fourier decomposition. Results show that the previous success in applying local linear theory to shallow mixing layers does not imply that the flow is truly linear. Linear stability theory is confirmed to be only valid within a short distance from the inflow boundary. Downstream of this linear region, nonlinearity becomes important for the roll-up and merging of 2DCS. While the energy required for the merging of 2DCS is still largely provided by the velocity shear, the merging mechanism is one where nonlinear mode interaction changes the velocity field of the subharmonic mode and the gradient of the along-stream velocity profile which, in turn, changes the magnitude of the energy production of the subharmonic mode by the velocity shear implicitly. The nonlinear mode interaction is associated with energy up-scaling and is consistent with the inverse energy cascade which is expected to occur in shallow shear flows. Current results also show that such implicit nonlinear interaction is sensitive to the phase angle difference between the most unstable mode and its subharmonic. The bed friction effect on the 2DCS is relatively small initially and grows in tandem with the size of the 2DCS. The bed friction also causes a decrease in the velocity gradient as the flow develops downstream. The transition from unstable to stable flow occurs when the bed friction balances the energy production. Beyond this point, the bed friction is more dominant and the 2DCS are progressively damped and eventually get annihilated. The energy production by the velocity shear plays an important role from the upstream end all the way to the point of transition to stable flow. The fact that linear stability theory is valid only for a short distance from the inflow boundary suggests that some elements of nonlinearity is incorporated in the mean velocity profile in experiments by the averaging process. The implicit nature of nonlinear interaction in shallow mixing layers and the sensitivity of the nonlinear interaction to phase angle difference between the most unstable mode and its subharmonic allows local linear theory to be successful in reproducing features of the instability such as the dominant mode of the 2DCS and its amplitude.     

Shallow flows: 2D or not 2D?

It is commonly assumed that shallow flows are in good approximation two-dimensional (2D) or quasi-2D. We will provide evidence that this is not always the case, and that the simple scaling argument based on the continuity equation does not always apply. Laboratory experiments on vortex flows in shallow fluid layers have revealed that locally significant three-dimensional (3D) effects and substantial vertical motions may occur, clearly destroying the assumed 2D character of the flow. For example, in the case of a dipolar vortex structure, an oscillatory vertical motion is observed in the vortex cores, while a spanwise circulation roll is present in front of the travelling dipole. These laboratory observations are confirmed by 3D numerical flow simulations. Attention will be given to a correct scaling analysis, in which both the aspect ratio of the fluid depth and a typical horizontal scale and the Reynolds number play a role.     

Alternating skimming flow over a stepped spillway

The study of stepped spillways in laboratory scales has been essentially focused on two separated sub-regimes within skimming flow. In this paper we investigate the appearance of an unclassified alternating skimming flow regime in a 0.5 m wide stepped spillway which does not fit on these earlier definitions, and which does not occur in a 0.3 m wide spillway. Our aim is to explain the genesis of this unclassified flow which is visualised in the physical stepped spillway, by using 3D numerical modelling. Flow depths and velocities are measured using an ultrasonic sensor and Bubble Image Velocimetry in the wider flume (0.5 m). The numerical model is validated with the experimental data from the 0.5 m wide spillway. After validation, the channel width of the same numerical model is reduced to 0.3 m wide spillway in order to characterise (compare) the case without (with) alternating skimming flow. Both cases are solved using Reynolds-Averaged Navier–Stokes equations together with the Volume-of-Fluid technique and SST k-\(\omega\) turbulence model. The experimental results reveal that the alternating skimming flow regime is characterised by an evident seesaw pattern of flow properties over consecutive steps. In turn, the numerical modelling clarified that this seesaw pattern is due to the presence of a complex system of cross waves along the spillway. These cross waves are also responsible for a mass and momentum exchange in the transversal direction and for the formation of the alternating skimming flow in the spillway.     

Simulation of water quality in a flood detention area using models of different spatial discretization

Detention areas provide a means to lower peak discharges in rivers by temporarily storing excess water. In the case of extreme flood events, the storage effect reduces the risk of dike failures or extensive inundations for downstream reaches and near the site of abstraction. Due to the large amount of organic matter contained in the river water and the inundation of terrestrial vegetation in the detention area, a deterioration of water quality may occur. In particular, decay processes can cause a severe depletion of dissolved oxygen (DO) in the temporary water body. In this paper, we studied the potential of a water quality model to simulate the DO dynamics in a large but shallow detention area to be built at the Elbe River (Germany). Our focus was on examining the impact of spatial discretization on the model’s performance and usability. Therefore, we used a zero-dimensional (0D) and a two-dimensional (2D) modeling approach in parallel. The two approaches solely differ in their spatial discretization, while conversion processes, parameters, and boundary conditions were kept identical. The dynamics of DO simulated by the two models are similar in the initial flooding period but diverge when the system starts to drain. The deviation can be attributed to the different spatial discretization of the two models, leading to different estimates of flow velocities and water depths. Only the 2D model can account for the impact of spatial variability on the evolution of state variables. However, its application requires high efforts for pre- and post-processing and significantly longer computation times. The 2D model is, therefore, not suitable for investigating various flood scenarios or for analyzing the impact of parameter uncertainty. For practical applications, we recommend to firstly set up a fast-running model of reduced spatial discretization, e.g. a 0D model. Using this tool, the reliability of the simulation results should be checked by analyzing the parameter uncertainty of the water quality model. A particular focus may be on those parameters that are spatially variable and, therefore, believed to be better represented in a 2D approach. The benefit from the application of the more costly 2D model should be assessed, based on the analyses carried out with the 0D model. A 2D model appears to be preferable only if the simulated detention area has a complex topography, flow velocities are highly variable in space, and the parameters of the water quality model are well known.     

Design of a Domain Specific Language for modelling processes in landscapes

The modelling of processes that occur in landscapes is often confronted to issues related to the representation of space and the difficulty of properly handling time and multiple scales. In order to investigate these issues, a flexible modelling environment is required. We propose to develop such a tool based on a Domain Specific Language (DSL) that capitalises on the service-oriented architecture (SOA) paradigm. The modelling framework around the DSL is composed of a model building environment, a code generator and compiler, and a program execution platform. The DSL introduces five language elements (entity, service, relation, scenario and datafacer) that can be combined to offer a wide range of possibilities for modelling in space and time at different scales. When developing a model, model parts are either built using the DSL or taken from libraries of previously built ones, and adapted to the specific model. The practical usage of the DSL is illustrated first with the Lotka–Volterra model, and then with a landscape modelling experiment on the spread of a mosquito-borne disease in the Sahelian region of West Africa. An interesting characteristic of this approach is the possibility of adding new elements into an existing model, and replacing others with more appropriate ones, thus allowing potentially complex models to be built from simpler parts.     

Laboratory measurements and multi-block numerical simulations of the mean flow and turbulence in the non-aerated skimming flow region of steep stepped spillways

We present and discuss the results of a comprehensive study addressing the non-aerated region of the skimming flow in steep stepped spillways. Although flows in stepped spillways are usually characterized by high air concentrations concomitant with high rates of energy dissipation, the non-aerated region becomes important in small dams and/or spillways with high specific discharges. A relatively large physical model of such spillway was used to acquire data on flow velocities and water levels and, then, well-resolved numerical simulations were performed with a commercial code to reproduce those experimental conditions. The numerical runs benefited from the ability of using multi-block grids in a Cartesian coordinate system, from capturing the free surface with the TruVOF method embedded in the code, and from the use of two turbulence models: the k-e{k{-}\varepsilon} and the RNGk-e{k{-}\varepsilon} models. Numerical results are in good agreement with the experimental data corresponding to three volumetric flow rates in terms of the time-averaged velocities measured at diverse steps in the spillway, and they are in very satisfactory agreement for water levels along the spillway. In addition, the numerical results provide information on the turbulence statistics of the flow. This work also discusses important aspects of the flow, such as the values of the exponents of the power-law velocity profiles, and the characteristics of the development of the boundary layer in the spillway.     

Lock-exchange gravity currents over rough bottoms

In nature, density driven currents often flow over or within a bottom roughness: a sea breeze encountering tall buildings, a shallow flow encountering aquatic vegetation, or a dense oceanic current flowing over a rough bottom. Laboratory experiments investigating the mechanisms by which bottom roughness enhances or inhibits entrainment and dilution in a lock-exchange dense gravity current have been conducted. The bottom roughness has been idealized by an array of vertical, rigid cylinders. Both spacing (sparse vs. dense configuration) and height of the roughness elements compared with the height of the current have been varied. Two-dimensional density fields have been obtained. Experimental results suggest that enhancement of the entrainment/dilution of the current can occur due to two different mechanisms. For a sparse configuration, the dense current propagates between the cylinders and the entrainment is enhanced by the vortices generated in the wake of the cylindrical obstacles. For a dense configuration, the dense current rides on top of the cylinders and the dilution is enhanced by the onset of convective instability between the dense current above the cylinders and the ambient lighter water between the cylinders. For low values of the ratio of the cylinder to lock height \(\lambda \) the dense current behavior approaches that of a current over a smooth bottom, while the largest deviations from the smooth bottom case are observed for large values of \(\lambda \).     

3D model for a secondary facultative pond

This paper describes a comprehensive model of wastewater treatment in secondary facultative ponds, which combines 3D hydrodynamics with a mechanistic water quality model. The hydrodynamics are based on the Navier-Stokes equation for incompressible fluids under shallow water and Boussinesq assumptions capturing the flow dynamics along length, breadth and depth of the pond. The water quality sub model is based on the Activated Sludge Model (ASM) concept, describing COD and nutrient removal as function of bacterial growth following Monod kinetics, except for Escherichia coli removal, which was modelled as first order decay. The model was implemented in the Delft3D software and was used to evaluate the effect of wind and the addition of baffles on the water flow pattern, temperature profiles in the pond and treatment efficiency. In contrast to earlier models reported in the literature, our simulation results did not show any significant improvement in COD removal (based on the ASM concept) with addition of baffles or under intermittent wind-induced mixing. However, E. coli removal efficiency, based on a first order decay approach, showed a fair improvement in the presence of baffles or intermittent wind-induced mixing. Furthermore, simulations with continuous wind effect showed a decrease in removal efficiency for COD but a further increase in E. coli removal efficiency. Such contrasting results for two different approaches in modelling could indicate that the first order decay concept might not be appropriate to describe all the interactions between biochemical processes in a pond. However, these interpretations remain theoretical, as the model needs validation with field data.     

Stratification and Circulation in a Shallow Turbid Waterbody

Shallow waterbodies are often assumed to be well mixed in the vertical. However, when they are characterised by high turbidity levels, absoption of solar heating within a relatively thin surface layer can produce thermal stratification. Results from an intensive monitoring program have been combined with three-dimensional circulation modelling to examine the diurnal stratification cycles in a small turbid waterbody. The waterbody, known as Rushy Billabong, is located in southeastern Australia and its high turbidity coupled with forcing by wind and solar radiation resulted in regular diurnal cycles of stratification and overturning. Under conditions of light wind and high solar radiation, the model results were generally consistent with the observed temperature field. However, under stronger winds, preferential cooling and sinking of shallow water around the edge of the lake began to contribute significantly to the interior stratification. Model estimates then became more sensitive to the detailed bathymetry and the choice of turbulence parameterisation. The level of stratification is also shown to influence the circulation in the billabong by trapping the wind-driven flow near the surface. Insights provided by the observations and modelling may have broader implications for the management of small turbid systems such as settling ponds, aquaculture ponds, and some natural wetlands.