Downstream Boundary Conditions Research Articles

Evolution of dispersal in river networks.

Evolution of dispersal is a fascinating topic at the intersection of ecology and evolutionary dynamics that has generated many challenging problems in the analysis of reaction-diffusion equations. Early results indicated that lower random diffusion rates are generally beneficial. However, in riverine environments with downstream drift, high diffusion may be optimal, depending on downstream boundary conditions. Most of these results were obtained from modeling a single river reach, yet many rivers form intricate tree-shaped networks. We study the evolution of dispersal on a metric graph representing the simplest such possible network: two upstream segments joining to form one downstream segment. We first show that the shape of the positive steady state of a single population depends crucially on the geometry of the network, here considered as the relative length of the three segments. We then study the evolution of dispersal by considering the possibility of "invasion" of a second type (invader) at the steady state of the first type (resident). We show that the geometry of the network determines whether higher or intermediate dispersal is favored.

Effects of upstream and downstream boundary conditions on lacustrine shallow-water delta morphologies: A numerical modeling approach

Lacustrine shallow-water deltas exhibit highly variable morphologies, owing to their high sensitivity to changes in the upstream and downstream boundary conditions, where a small change significantly alters their morphology. In this study, we present the results from a numerical model (DELFT3D) used to explore the mechanism of distributary network amalgamation and delta evolution under various boundary conditions. We established a reference case to model the delta building-out process considering the basin water depth difference (shallow and deep). Geological and hydrodynamic models were established by varying the water level under a steady river discharge and sediment supply. Despite similar initial conditions, each modeled delta exhibits a unique morphological evolution, progressing through distinct stages: (i) formation of unstable, narrow channels with quasi-radial shapes; (ii) channel development, shaping the delta based on controlling factors; (iii) reduction of deltaic activity and increased channel avulsion due to delta submergence, and; (iv) new channels emerging, paving the way for reshaping and migration towards new paths, resulting in fewer bifurcations and straighter channels. Quantitative relationships characterizing delta morphology and distributary channels were established, and the following results were noted: (i) a positive correlation between active and abandoned channels, distributary channel network opening angle, and delta area with discharge and sediment grain size, and negative correlation with basin depth and falling water level; (ii) a positive correlation of lobe elongation with basin depth and discharge, and a negative correlation with sediment grain size; and (iii) roughness and length-to-width ratio emerging as key predictors of delta shape. By applying the model predictions to real-world scenarios, including modern deltas (Sile and Chiemsee) and ancient systems (Bohai Bay Basin), this study can provide valuable insights into the dynamics of lacustrine deltaic systems and their responses to changing boundary conditions. This highlights the importance of understanding deltaic systems for both theoretical research and practical applications.

Investigation of river water pollution using Muskingum method and particle swarm optimization (PSO) algorithm

River water pollution is one of the most important environmental issues. Advection–dispersion equations are used to study the temporal changes in pollutant concentration along the study river reach. The use of advection–dispersion equations in investigating how the concentration of pollution is transformed requires a lot of data including river cross-section characteristics, dispersion coefficient, and upstream and downstream boundary conditions, etc. therefore, the corresponding calculations are very costly, difficult and time-consuming. In the present study, instead of using the mentioned equations, the linear Muskingum method (used in previous studies for flood routing) and the particle swarm optimization (PSO) algorithm was used for the first time to calculate the temporal changes in pollution concentration at different stream locations. The presented solution in the presented study is very accurate and only requires the temporal changes in concentration in the upstream and downstream of the study river reach and for this reason, it is very low-cost and easy to use and requires less time to collect data and perform calculations. In the proposed method, the parameters (X, K, ∆t) of the linear Muskingum method were optimized using the PSO algorithm, and by dividing the temporal changes in the input concentration into three areas of the beginning (the input concentration is greater than the output concentration), the peak (the maximum input and output concentrations) and the end (the output concentration is greater than the input concentration) areas, the accuracy of the calculations increased. The mentioned method was studied for different lengths (first case of x = 50 m (up) and x = 75 m (down), second case of x = 50 m (up) and x = 100 m (down), third case of x = 75 m (up) and x = 100 m (down)) and the mean relative error (MRE) of the total, peak area and the relative error of the maximum concentration using constant parameters for the first case were calculated as 7.08, 1.02, and 2.34 percent, for the second case as 7.41, 11.06 and 6.69 percent, and for the third case as 6.75, 3.59 and 5.42 percent, respectively. If three parameters of (X, K, ∆t) are used, the mentioned values improved by 31.3, 63.7 and 65.5 percent, respectively compared to the case of using constant parameters.

Bifurcation analysis on a river population model with varying boundary conditions

A delayed reaction-diffusion-advection equation subject to constant-flux and free-flow boundary conditions is considered, which models single population dynamics in a river. At first, we show the existence of a nonconstant steady state induced by the change of constant flux value. Then by analyzing the distribution of eigenvalues, the stability of the constant and nonconstant steady states and the existence of Hopf bifurcations are obtained. And an algorithm for determining the direction and stability of Hopf bifurcations is derived by applying the center manifold theory and normal form method for PFDEs. Finally, the effects of advection and downstream boundary condition on periodic oscillations are discussed theoretically and numerically.

Stationary axial model of the Hall thruster plasma discharge: electron azimuthal inertia and far plume effects

One-dimensional axial models of the plasma discharge of a Hall thruster provide a valuable picture of its physical behavior with a small computational effort. Therefore, they are very suitable for quick parametric analyses or as a support tool for analyzing the impact of modeling decisions. This paper extends a well-known drift-diffusion stationary, quasineutral model by adding electron azimuthal inertia (EAI), a nonzero thickness cathode layer, and the far-plume region where electrons demagnetize and cool down. The EAI dominates on the far plume and affects positively to thrust. For a small ion backstreaming current, EAI modifies much the electron velocities and density near the anode, but has no discernible effect on the electron cross-field transport. Electron axial inertia and azimuthal gyrovisosity are estimated. The thick cathode layer connects quasineutrally the near and far plumes but the coupling between these two regions is weak. The far plume region is sensitive to the decay length of the magnetic field, the downstream boundary conditions on the electron currents, and the stray electric currents.

Eikonal Equation Reproduces Natural Landscapes With Threshold Hillslopes

AbstractMany natural landscapes maintain steep planar hillslopes bounded at a typical angle, beyond which shallow landslides or slope failures remove the excess sediment volume by mass wasting. Here we show that the celebrated eikonal equation, derived from a landscape evolution model in conditions of negligible soil diffusion and fluvial erosion, accurately portrays the organization of these topographies. Referred to as “eikonal landscapes,” such solutions feature constant‐slope hillslopes originating from downstream boundary conditions and culminating in sharp upstream ridges. We demonstrate that the eikonal landscapes reproduce well a variety of natural landforms, including small islands, a volcano, and an extended mountain ridge. The boundary condition for the eikonal representation is specified through the natural landscape's slope‐area relation. Going beyond merely representing landscape statistical features, the present results provide a first‐of‐kind direct match of mathematical and natural landscapes.

Flooding in the urban fringes: Analysis of flood inundation and hazard levels within the informal settlement of Kibera in Nairobi, Kenya

Overlapping conditions of rapid urbanisation and climate change across developing countries are threatening the capacity of cities to manage climate risks, especially in the flood-exposed low-income peripheral areas. Limited studies have applied hydrodynamic flood models in ascertaining flooding conditions, supportive of risk-informed decisions in such urban fringes. Against this backdrop, we assessed plausible flooding and hazard conditions in the low-lying villages of Lindi and Silanga in Kibera informal settlement. The coupled one-dimensional and two-dimensional hydrodynamic model, customised from the Hydrological Engineering Centre's River Analysis System (HEC-RAS) was parameterised for flood simulation under different hydrological regimes and scenarios associated with flooding in Kibera. Volumetric flow estimates and a computed energy slope were used to define the upstream and downstream modelling boundary conditions respectively. Trial-and-error adjustment of the flow resistance coefficients from land-use features was applied in model calibration, and the results compared to the surveyed flood of 23rd April 2019. Results show that proximal areas to the Ngong River and Nairobi dam face high flood risks. A flood volume of 11.7×105m3 from a 2.5h, 50 mm rainfall could potentially inundate about 2.0% and 8.3% of areas in Lindi and Silanga respectively, while a volume of 48.9×105m3 from a 100-year storm of 172 mm could inundate about 10.6% of Lindi and 29.1% of Silanga. Upstream steeply sloping topographies of the villages increase flood velocities and risk of drowning, while the lower reaches at relatively flatter topographies, experience attenuated flow and rapid accumulation of flood waters, hence, higher flood depths. These results can support policy interventions for integrated flood risk management in Kibera, as a way of mainstreaming the underserved urban communities in climate risk management.

Assessing the compound flood risk in coastal areas: Framework formulation and demonstration

Storm surge and river runoff can result in compound flooding in coastal areas. The impact of these events can be more significant than that generated by each component individually. This paper describes a framework for characterizing flooding during compound events and quantifying the relative importance of surge and river flows in controlling inundation depth (ID). For the analysis, we considered 1051 simulations of historical flood events covering about 40 years in Connecticut (CT), USA, and several simulated storms associated with synthetic climate scenarios. We simulated river discharge time series for each event using a physically based distributed hydrological model and retrieved the storm surge from tidal stations. These time series are used as upstream and downstream boundary conditions in 2D hydrodynamic simulation. We focused the analysis on seven locations along the coast of Connecticut covered by LiDAR-derived 1 m DEM. To capture the variability of inundation characteristics over the full-scale gradient from river to coast, we introduced a new topographic index, D-Index, that distinguishes topologic variabilities. Results from this study highlight that there is a correlation of ID to different drivers in distinct categories of the D-Index, which can correctly label the main source of hazard, either coast, river, or compound. We identified thresholds of standard deviation (σ) of the D-Index to identify areas where ID strongly correlates with either flow peak and volume, surge peak, or a combination of both. The study also shows that it is possible to use the results obtained from the 1 m analysis to generalize the findings for the entire CT coast to derive zones dominated by surge, river flow, or the compound effect of the two. This study can help coastal communities better understand the risk of the compound impacts of coastal storms, which is essential for increasing climate resilience.

SUITABLE BOUNDARY LOCATION IDENTIFCATION FOR RAINFALL-RUNOFF AND SURGE MODEL COUPLING TO EVALUATE COMPOUND FLOOD HAZARDS IN COASTAL REGIONS

Flooding in many coastal regions is exacerbated due to complex interactions of multiple flood drivers such as rainfall-runoff and coastal surge which can occur simultaneously or sequentially during storm events, leading to compound flooding hazards. The Texas Gulf Coasts (USA) are especially vulnerable from compound flooding due to frequent occurrence of tropical storms which bring strong winds to drive storm surge and heavy rainfall to generate inland flooding. Large scale studies {Coastal Texas Restoration and Protection Study (CTX, 2021), Texas General Land Office’s Texas River Basin Study, Base Level Engineering Study} are being conducted by state and federal agencies for flood hazard assessment and for development of mitigation and abatement strategies for reducing this risk and increasing community resilience. Traditionally, large scale storm surge models do not account for runoff contributions to water levels in the interior of their domain. Riverine models for their part use either normal depth or mean high water levels to assign downstream boundary conditions within tidally influenced area, thus ignoring effects of storm surge. In this Planning Assistance to States (PAS) study, located in the Lower Clear Creek and Dickinson Bayou watersheds (Texas, USA), we have evaluated rainfall-runoff and storm surge interactions to determine suitable locations to use as model boundary conditions for exchanging data between rainfall-runoff and surge models under compound flooding conditions.

A PROPOSED TECHNIQUE FOR IMPROVING THE ACCURACY OF TIDAL MODELING OF RIVER NETWORKS CONNECTING TO THE DADAHUP IRRIGATION AREA

Optimizing the operational management of tidal irrigation networks is a significant factor in the reactivation program of the swamp irrigation areas in Central Kalimantan Province. Appropriate water level and flow rate control in a tidal environment would provide a better solution for this effort. Monitoring water parameters and hydraulic modeling is an intelligent technique for evaluating irrigation canals' gate system operations. This paper focuses on providing more accurate hydraulic modeling that requires proper boundary conditions and calibration of the canal roughness coefficient. This study aims to obtain a more precise downstream boundary condition data calibration method with an appropriate river cross-sectional roughness coefficient value to improve the overall hydraulic modeling accuracy of the river network connecting to the Dadahup Irrigation Area. The hydraulic modeling utilized the HEC-RAS Software, where input data preparation used geometric data derived from the National Geospatial Agency's DEM in the form of river channel network chain, cross-section, and long-section data. Boundary condition data evaluation compared and selected data generated from references and the Tides Application Software. The results show that the tide prediction from the Tides Application Software provides the slightest difference between the predicted tide and the measured ones. The river network's channel roughness coefficient calibration utilized the generated boundary condition tide and simultaneously measured water level data at several locations. The results show that the most minor Root Mean Squared Error (RMSE) of the Manning roughness coefficient differences of the river channel network can reach 0.04 with a minimum RMSE value of 0.027.

Establishing a time‐varying flood‐wave impulse function combined with a dynamic machine‐learning technique in response to the disturbance of boundary conditions

AbstractTo seek other alternative approaches besides numerical methods, the linearized Saint Venant equations were utilized to derive the channel response functions for simulating streamflow. This study advocates developing a new approach to make the temporal distribution of response functions more flexible by introducing time‐varying reference parameters which depend on both the upstream inflow and the downstream boundary conditions. Moreover, to expand the model applicability in natural channels with irregular cross‐sectional shapes affected by the unsteady inflow, lateral flow, and the variation of tide level, a dynamic neural network algorithm is jointly applied to determine more appropriate time‐varying hydraulic parameters which are adopted in the channel flow response functions respectively derived from upstream and downstream boundary conditions. The tidal level at the estuary and the upstream inflow discharge are simultaneously considered influential factors to determine an optimal set of reference parameters by applying a machine learning technique, and this prediction can further be provided for updating the channel response functions. The novelty of this study is to propose a complete methodology to combine channel response functions with the machine learning algorithm for ameliorating the accuracy of channel flow simulation and resolving the uncertainty of model parameters. Therefore, by using the proposed method, not only the physical mechanism of Saint Venant equations can be preserved, but also the optimal hydraulic parameters can be specified. The problem of numerical instability during channel flow routing can be eliminated by using the proposed new model and therefore the reliability of real‐time flood forecasting can be reinforced.

A coherent composite approach for the continuous circular hydraulic jump and vortex structure

We examine the structure of the continuous circular hydraulic jump and recirculation for a jet impinging on a disk. We use a composite mean-field thin-film approach consisting of subdividing the flow domain into three regions of increasing gravity strength: a developing boundary layer near impact, an intermediate supercritical viscous layer and a region comprising the jump and subcritical flow. Unlike existing models, the approach does not require any empirically or numerically adjusted boundary conditions. We demonstrate that the stress or corner singularity for a film draining at the edge is equivalent to an infinite slope of the film surface, which we impose as the downstream boundary condition. The model is validated against existing experiment and numerical simulation of the boundary-layer and Navier–Stokes equations. We find that the flow in the supercritical region remains insensitive to the change in gravity level but is greatly affected by viscosity. The existence of the jump is not necessarily commensurate with the presence of recirculation, which is strongly dependent on the upstream curvature and steepness of the jump.

Filling data gaps using citizen science for flood modeling in urbanized catchment of Akaki

Identifying and understanding the value of citizen science to improve flood modeling is of importance to flood risk management. However, there are few studies that explore the value of citizen science data, with most studies focusing on evaluating the accuracy of the data. This research articulates the added value of citizen science data in flood modeling studies. During flood events, citizen scientists measured river water levels at selected sites along a main reach of the Big Akaki River in Addis Ababa, Ethiopia. They also provided information to estimate water discharge of the ungauged tributaries. The data acquired was used to force a one-dimensional (1D) HECRAS flood model, and to evaluate the model's sensitivity to inputs and parameters. Varying the downstream boundary condition caused a significant difference in the simulated water level (up to 3.5 ​km upstream of the downstream boundary site). Correcting the Digital Elevation Model and consideration of river tributary flows in the model simulation resulted in an underestimation of the observed stage by 0.08 ​m. The sensitivity analysis also showed that results were more sensitive to the Manning roughness values of the channel than that of the floodplain. Finally, this study identifies future flood modeling data collection priorities (e.g. flow data for the tributary). The flood modeling of the study area would not have been realized without the citizen science data.

Drawbacks of phase change models in simulating flashing of steam with a subsaturation downstream boundary condition

AbstractThe development of phase change models applicable to a wide range of temperatures, pressures, and mass flow rates is primarily limited by the metastable or partially stable behaviour of the fluid. Due to this, the fluid does not change phase even after crossing saturation conditions. Most liquid–vapour phase change models have been developed primarily for the cavitation process where the phase change is not sustained, occurs in a very narrow region of space, or occurs under equilibrium conditions. In this paper, the mechanism of phase change is discussed along with the review of three different computational fluid dynamics (CFD)‐based phase change methods available in OpenFOAM, which are used to simulate flashing of steam, in applications related to steam assisted gravity drainage (SAGD) systems. The first method is based on barotropic compressibility (BC) used with the realizable turbulence model, the second combination is of mass transfer model (MTM) with the realizable turbulence model, and the third one is based on two fluid (TF) method along with a family of turbulence models. These methods are tested on a converging–diverging nozzle with pressure driven phase change. It is demonstrated that these methods are not able to adjust their physics to different depressurization rates, do not account for liquid to be in superheated conditions, and have significant discrepancies with experimental results. In the end, better approaches to model this category of phase change are discussed.

Adoption of Homotopy Perturbation Method (HPM) for non-Darcy Flow in Porous Media

For non-Darcy flow in coarse porous media, an analytical solution based on the Homotopy Perturbation Method (HPM) is proposed. Subsurface water profile data of a laboratory model are used for six different inlet discharges in both rounded and crushed coarse porous media types. The model slope is S = 0.00001 close to the horizon. Different upstream and downstream water level boundary conditions are considered. The results of the analytical solution of non-Darcy flow by the HPM method are compared with experimental data. The normal objective function (NOF) is used for better comparison between the results of analytical solutions and experimental data. Results depict that the HPM method provides acceptable solutions in both rounded and crushed media types. The analytical results of flow rates q = 26.25 lit/s with NOF of 0.000294586 percent in rounded porous media and q = 30 lit/s with NOF of 0.00028660 percent in crushed one are the most consistent with the experimental data. The proposed HPM solution performs very well, particularly at higher flow rates, in both rounded and crushed porous media.

Hydraulic Analysis of Dredging Impacts in Downstream Reach of The Tulang Bawang River

The Tulang Bawang river is one of the largest rivers in Lampung Province, Indonesia, transporting humans and goods. Changes in upstream land use, climate, and sedimentation are silting the riverbed and disrupting transportation. To this end, investors and government agencies have submitted various proposals to carry out sand mining downstream to assist the local government in revitalizing transportation. However, some government and community assets are likely to be affected in the upstream part that is planned to be dredged. Therefore, this study aimed to conduct a modeling scenario of riverbed dredging in the lower reaches of the Tulang Bawang River from the estuary to 11.8 km upstream. It also aimed to review the impact on the environment, especially the impact of flooding and sedimentation by 17.8 km upstream, using the HEC-RAS software. The scenarios of upstream and downstream boundary conditions were used to determine the significance of the impact. The results showed that dredging would cause water level elevation to drop upstream and sediment deposition along the river section dredged. However, the decrease in river water level was insignificant for the upstream assets and beneficial for reducing flood inundation. The result of sedimentation analysis shows that river dredging leads to morphological changes and may have an environmental impact. Therefore, effective environmental management for dredging needs to be applied to minimize the environmental impact.

Systematic Assessment of the Two-Step, One-Way Coupled Method for Computational Fluid Dynamics

AbstractThis paper assesses the validity of the Two-Step, One-Way (TSOW) coupled method for computational fluid dynamics, which splits a complicated geometry into an upstream and a downstream part. The problem is solved in two steps: first, the upstream part using approximate downstream boundary conditions, followed by a solution of the downstream flow where the inlet boundary conditions are extracted from the upstream solution. The method is based on two assumptions: first, the solution for the upstream part should be identical in the common domain to a complete solution. Second, the solution for the downstream part should be identical in the common domain to a complete solution. The resulting agreement between the upstream solution and the full solution was excellent, except in the vicinity of the outflow boundary. For the assessment of the second assumption, the downstream flow was simulated with two sets of boundary conditions, one that was extracted from the full simulation, and one that came from the upstream part solution. The two solutions in the downstream geometry with slightly different boundary conditions agreed excellently with each other but exhibited small differences from the full solution. Overall, the difference to the full solution is judged to be acceptable for many engineering design situations. The solution time for the TSOW method was about 23 h faster than the full solution, which took about 85 h on the same hardware. For additional design iterations, where the same upstream geometry can be used, a 30-h gain would be obtained for each step.

풍수해 생활권 종합정비계획 수립 시 하류경계조건의 고려

The ‘Comprehensive Maintenance Plan for Neighborhood Unit in storm and flood disaster’ is a meaningful project in that it integrates and implements all storm and flood-related maintenance plans that have been dispersed by ministries. In this paper, we examined whether the 'Comprehensive Maintenance Plan for Neighborhood Unit' can be included in the 'intensive heavy rain' in August 2022 and 'Hinnamnor' in September, and whether it can be applied appropriately in inland areas without unreasonableness. The ‘flooding by Hinnamnor in Pohang’, ‘the claim of flood damage caused by the operation of Lake Sihwa’, and ‘flooding of the Moraenae stream’ had a common cause. In order to solve this problem, 'Pohang flooding by Hinnamnor' requires a separate design that considers sea level rise due to typhoon low pressure rather than dealing with tide forecast alone. There is a need for institutional arrangements (guidelines, etc.) In addition, in the case of the 'Moraenae District', cases caused by the rise of the 'downstream boundary condition' of nearby rivers must be reflected in the design.

Experimental and numerical investigation of flow distribution pattern at a T-shape roadway crossing under extreme storms

ABSTRACT A major drainage systemwhich uses urban roadways as flood passages during extreme storm events has been proven to be effective and low-cost. However, to date, the amount of flow diverted at a bifurcating road crossing still could not be accurately assessed. Previous studies mainly focused on diversion flat bottom channels with no turning radius. Results from these studies are not applicable to the road crossing due to the significant discrepancies between the two flow fields. In this study, the flow distribution pattern at a roadway crossing with a T-shape was studied experimentally and numerically. The three-dimensional computational fluid dynamics (CFD) model was constructed using FLUENT. The numerical model was validated using the experimental results and showed satisfying agreements. Results of the 2k factorial design experiments show that the flow distribution ratio is sensitive to turning radius, longitude slope, flowrate and downstream boundary conditions. Detailed numerical studies were conducted to reveal the relationship between the flow distribution ratio and the individual impacting factor. Findings from this research could provide more accurate flowrate predictions to guide the design of the road crossings to improve the performance of the major drainage system during extreme storms.

Analysis of steady flow in radial porous media

Abstract The outflow depth from the radial porous media (inflow to the well) is very useful as the downstream boundary condition and the starting point for water surface profile calculations. Based on the studies, unlike the Stephenson's hypothesis (the outflow depth is equal to the critical depth), the outflow depth from the rockfill media is a coefficient (Γ) of the critical depth. In the present study, using several (large scale and almost real) experimental data in the radial non-Darcy flow condition, dimensional analysis and the particle swarm optimization (PSO) algorithm, an equation was presented to calculate the mentioned coefficient based on upstream water depth (h) and distance between the well center and the upstream (R). Then, using the calculated outflow depth and the 1D flow analysis equations, the water surface profile in the radial non-Darcy condition was calculated for the first time. The results showed that considering an outflow depth equal to the critical depth and using the proposed solution in the present study, the mean relative error (MRE) values of 83.43% and 3.53% were obtained, respectively. In addition, using the proposed solution for different experimental conditions, an average MRE of 2.58% was calculated for the water surface profile.