Comparison of 1-D analytical solutions and a numerical model for quantifying hyporheic exchange flux using the temperature tracer method

An integrated two-dimensional vertical (2DV) model was developed to investigate wave interactions with permeable submerged breakwaters. The integrated model is capable of predicting the flow field in both surface water and porous media on the basis of the extended volume-averaged Reynolds-averaged Navier–Stokes equations (VARANS). The impact of porous medium was considered by the inclusion of the additional terms of drag and inertia forces into conventional Navier–Stokes equations. Finite volume method (FVM) in an arbitrary Lagrangian–Eulerian (ALE) formulation was adopted for discretization of the governing equations. Projection method was utilized to solve the unsteady incompressible extended Navier–Stokes equations. The time-dependent volume and surface porosities were calculated at each time step using the fraction of a grid open to water and the total porosity of porous medium. The numerical model was first verified against analytical solutions of small amplitude progressive Stokes wave and solitary wave propagation in the absence of a bottom-mounted barrier. Comparisons showed pleasing agreements between the numerical predictions and analytical solutions. The model was then further validated by comparing the numerical model results with the experimental measurements of wave propagation over a permeable submerged breakwater reported in the literature. Good agreements were obtained for the free surface elevations at various spatial and temporal scales, velocity fields around and inside the obstacle, as well as the velocity profiles.

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Analytical solutions to two- and three-dimensional periodic flows for numerical model testing

International Journal for Numerical Methods in Biomedical Engineering ◽

10.1002/cnm.1136 ◽

2010 ◽

Vol 26 (2) ◽

pp. 190-204

Author(s):

Phan Ngoc Vinh ◽

Magnus Larson

Keyword(s):

Numerical Model ◽

Analytical Solutions ◽

Three Dimensional ◽

Model Testing ◽

Periodic Flows

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Interaction of Water Waves and a Submerged Parabolic Obstacle in the Presence of a Following Uniform/Shear Current Using RANS Model

Mathematical Problems in Engineering ◽

10.1155/2014/896723 ◽

2014 ◽

Vol 2014 ◽

pp. 1-9 ◽

Cited By ~ 1

Author(s):

Yen-Lung Chen ◽

Jing-Bo Hung ◽

Shih-Lun Hsu ◽

Shih-Chun Hsiao ◽

Yuan-Chieh Wu

Keyword(s):

Experimental Data ◽

Free Surface ◽

Numerical Model ◽

Analytical Solutions ◽

Water Waves ◽

Surface Deformation ◽

Navier Stokes ◽

Regular Waves ◽

Uniform Shear ◽

Shear Current

This paper simulates regular waves propagating over a submerged parabolic obstacle in the presence of a uniform/shear current using a two-dimensional numerical model, named COBRAS (Cornell Breaking and Structure). The numerical model solves the Reynolds-Averaged Navier-Stokes (RANS) equations and the free surface deformation is tracked using the volume of fluid method (VOF). The capability of the numerical model to simulate regular waves with a uniform or shear current over a constant water depth is first validated with available analytical solutions and experimental data. Comparisons among the experimental data, analytical solutions, and present numerical results show good agreements. Then, regular waves propagating over a submerged parabolic obstacle with a following current are investigated. Detailed discussions including those on the velocity and vorticity fields and the relation between free surface and vorticity are given.

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Bearing capacity of a square shallow foundation on swelling soil using a numerical approach

World Journal of Engineering ◽

10.1108/wje-01-2021-0005 ◽

2021 ◽

Vol ahead-of-print (ahead-of-print) ◽

Author(s):

Abdelaziz Khennouf ◽

Mohamed Baheddi

Keyword(s):

Numerical Model ◽

Bearing Capacity ◽

Analytical Solutions ◽

Soil Mass ◽

Numerical Results ◽

Shallow Foundation ◽

Initial State ◽

Elastoplastic Behavior ◽

Content Type ◽

Swelling Soil

Purpose The estimation of bearing capacity for shallow foundations in swelling soil is an important and complex context. The complexity is due to the unsaturated swelling soil related to the drying and humidification environment. Hence, a serious study is needed to evaluate the effect of swelling potential soil on the foundation bearing capacity. The purpose of this paper is to analyze the bearing capacity of a rough square foundation founded on a homogeneous swelling soil mass, subjected to vertical loads. Design/methodology/approach A proposed numerical model based on the simulation of the swelling pressure in the initial state, followed by an elastoplastic behavior model may be used to calculate the foundation bearing capacity. The analyses were carried out using the finite-difference software (FLAC 3 D) with an elastic perfectly plastic Mohr–Coulomb constitutive model. Moreover, the numerical results obtained are compared with the analytical solutions proposed in the literature. Findings The numerical results were in good agreement with the analytical solutions proposed in the literature. Also, reasonable capacity and performance of the proposed numerical model. Originality/value The proposed numerical model is capable to predict the bearing capacity of the homogeneous swelling soil mass loaded by a shallow foundation. Also, it will be of great use for geotechnical engineers and researchers in the field.

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Seasonal variations in surface water groundwater interaction alter the relation of solute transport and biogeochemical processes in the hyporheic zone

10.5194/egusphere-egu21-2949 ◽

2021 ◽

Author(s):

Lara-Maria Schmitgen ◽

Tobias Schuetz

Keyword(s):

Surface Water ◽

Boundary Conditions ◽

Hyporheic Zone ◽

Treatment Plant ◽

Hyporheic Exchange ◽

Waste Water Treatment Plant ◽

Small Scale ◽

Vertical Profiles ◽

Surface Water And Groundwater ◽

Exchange Flux

<p>The hyporheic interstitial as interface between surface water and groundwater offers a unique environment for contaminant attenuation and nutrient cycling, with steep chemical gradients and high retention times. Disentangling the effect of seasonal dynamics in exchange flux intensities and directions, we carried out 19 measurement campaigns where we sampled the continuum surface water - hyporheic zone - groundwater and the climatic and hydraulic boundary conditions of a whole year. Groundwater, surface water and hyporheic zone pore water from four depths were sampled at two vertical profiles in a second order stream about 150 m downstream a municipal waste water treatment plant effluent. Samples were analyzed for physical water parameters, major anions, ammonium, iron, manganese, NPOC and five selected pharmaceuticals (diclofenac, carbamazepine, caffeine, ethinylestradiol and clofibric acid). Surface water and groundwater levels as well as river discharge were measured to quantify the hydraulic boundary conditions. In addition, three vertical profiles, each equipped with five newly developed probes (Truebner AG) allowed a parallel monitoring of continuous bulk water temperatures and bulk electrical conductivity dynamics over two years. Furthermore, continuous hyporheic exchange flux intensities and exchange depths were calculated using analytical and numerical model schemes to allow distinguishing between small scale transport and attenuation processes.</p><p>The typical behavior of the redox sensitive metals and nutrients with depth is visible in each single profile snapshot. The picture is not as clear for the examined pharmaceuticals, because dilution has a major effect on the observable low concentrations. However, a clear seasonal variation driven by hydraulic and climatic processes can be observed for all substances. We were able to trace the organic pollutants down to the groundwater. Furthermore, the influence of hyporheic exchange flux intensities and directions on nutrient and contaminant depth profiles is shown.</p>

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A Mathematical Model of Gas and Water Flow in a Swelling Geomaterial—Part 1. Verification with Analytical Solution

Minerals ◽

10.3390/min10010030 ◽

2019 ◽

Vol 10 (1) ◽

pp. 30 ◽

Cited By ~ 1

Author(s):

Elias Ernest Dagher ◽

Julio Ángel Infante Sedano ◽

Thanh Son Nguyen

Keyword(s):

Mathematical Model ◽

Numerical Model ◽

Analytical Solution ◽

Analytical Solutions ◽

Gas Flow ◽

Numerical Models ◽

Model Verification ◽

Model Complexity ◽

Gas Migration

Gas generation and migration are important processes that must be considered in a safety case for a deep geological repository (DGR) for the long-term containment of radioactive waste. Expansive soils, such as bentonite-based materials, are widely considered as sealing materials. Understanding their long-term performance as barriers to mitigate gas migration is vital in the design and long-term safety assessment of a DGR. Development and the application of numerical models are key to understanding the processes involved in gas migration. This study builds upon the authors’ previous work for developing a hydro-mechanical mathematical model for migration of gas through a low-permeable geomaterial based on the theoretical framework of poromechanics through the contribution of model verification. The study first derives analytical solutions for a 1D steady-state gas flow and 1D transient gas flow problem. Using the finite element method, the model is used to simulate 1D flow through a confined cylindrical sample of near-saturated low-permeable soil under a constant volume boundary stress condition. Verification of the numerical model is performed by comparing the pore-gas pressure evolution and stress evolution to that of the results of the analytical solution. The results of the numerical model closely matched those of the analytical solutions. Future studies will attempt to improve upon the model complexity and investigate processes and material characteristics that can enhance gas migration in a nearly saturated swelling geomaterial.

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Modelling hyporheic processes for regulated rivers under transient hydrological and hydrogeological conditions

Hydrology and Earth System Sciences ◽

10.5194/hess-19-329-2015 ◽

2015 ◽

Vol 19 (1) ◽

pp. 329-340 ◽

Cited By ~ 18

Author(s):

D. Siergieiev ◽

L. Ehlert ◽

T. Reimann ◽

A. Lundberg ◽

R. Liedl

Keyword(s):

Hydraulic Conductivity ◽

Numerical Model ◽

Wave Amplitude ◽

Overland Flow ◽

Analytical Models ◽

Hyporheic Exchange ◽

Groundwater Abstraction ◽

River Bank ◽

Wave Duration ◽

Solute Fluxes

Abstract. Understanding the effects of major hydrogeological controls on hyporheic exchange and bank storage is essential for river water management, groundwater abstraction, restoration and ecosystem sustainability. Analytical models cannot adequately represent complex settings with, for example, transient boundary conditions, varying geometry of surface water–groundwater interface, unsaturated and overland flow, etc. To understand the influence of parameters such as (1) sloping river banks, (2) varying hydraulic conductivity of the riverbed and (3) different river discharge wave scenarios on hyporheic exchange characteristics such as (a) bank storage, (b) return flows and (c) residence time, a 2-D hydrogeological conceptual model and, subsequently, an adequate numerical model were developed. The numerical model was calibrated against observations in the aquifer adjacent to the hydropower-regulated Lule River, northern Sweden, which has predominantly diurnal discharge fluctuations during summer and long-lasting discharge peaks during autumn and winter. Modelling results revealed that bank storage increased with river wave amplitude, wave duration and smaller slope of the river bank, while maximum exchange flux decreased with wave duration. When a homogeneous clogging layer covered the entire river–aquifer interface, hydraulic conductivity positively affected bank storage. The presence of a clogging layer with hydraulic conductivity < 0.001 m d−1 significantly reduced the exchange flows and virtually eliminated bank storage. The bank storage return/fill time ratio was positively related to wave amplitude and the hydraulic conductivity of the interface and negatively to wave duration and bank slope. Discharge oscillations with short duration and small amplitude decreased bank storage and, therefore, the hyporheic exchange, which has implications for solute fluxes, redox conditions and the potential of riverbeds as fish-spawning locations. Based on these results, river regulation strategies can be improved by considering the effect of certain wave event configurations on hyporheic exchange to ensure harmonious hydrogeochemical functioning of the river–aquifer interfaces and related ecosystems.

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Modelling hyporheic processes for regulated rivers under transient hydrological and hydrogeological conditions

Hydrology and Earth System Sciences Discussions ◽

10.5194/hessd-11-9327-2014 ◽

2014 ◽

Vol 11 (8) ◽

pp. 9327-9359

Author(s):

D. Siergieiev ◽

L. Ehlert ◽

T. Reimann ◽

A. Lundberg ◽

R. Liedl

Keyword(s):

Hydraulic Conductivity ◽

Numerical Model ◽

Wave Amplitude ◽

Overland Flow ◽

Analytical Models ◽

Hyporheic Exchange ◽

Groundwater Abstraction ◽

River Bank ◽

Wave Duration ◽

Solute Fluxes

Abstract. Understanding the effects of major hydrogeological controls on hyporheic exchange and bank storage is essential for river water management, groundwater abstraction, restoration and ecosystem sustainability. Analytical models cannot adequately represent complex settings with, for example, transient boundary conditions, varying geometry of surface water–groundwater interface, unsaturated and overland flow, etc. To understand the influence of parameters such as (1) sloping river banks, (2) varying hydraulic conductivity of the riverbed and (3) different river discharge wave scenarios on hyporheic exchange characteristics such as (a) bank storage, (b) return flows and (c) residence time, a 2-D hydrogeological conceptual model and, subsequently, an adequate numerical model were developed. The numerical model was calibrated against observations in the aquifer adjacent to the hydropower regulated Lule River, Northern Sweden, which has predominantly diurnal discharge fluctuations during summer and long-lasting discharge peaks during autumn and winter. Modelling results revealed that bank storage increased with river wave amplitude, wave duration and smaller slope of the river bank, while maximum exchange flux decreased with wave duration. When a homogeneous clogging layer covered the entire river–aquifer interface, hydraulic conductivity positively affected bank storage. The presence of a clogging layer with hydraulic conductivity < 0.001 m d−1 significantly reduced the exchange flows and virtually eliminated bank storage. The bank storage return/fill time ratio was positively related to wave amplitude and the hydraulic conductivity of the interface and negatively to wave duration and bank slope. Discharge oscillations with short duration and small amplitude decreased bank storage and, therefore, the hyporheic exchange, which has implications for solute fluxes, redox conditions and the spawning potential of riverbeds. Based on these results, river regulation strategies can be improved by considering the effect of certain wave event configurations on hyporheic exchange to ensure harmonious hydrogeochemical functioning of the river–aquifer interfaces and related ecosystems.

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Hyporheic exchange in recirculating flumes under heterogeneous bacterial and morphological conditions

Environmental Earth Sciences ◽

10.1007/s12665-021-09472-2 ◽

2021 ◽

Vol 80 (6) ◽

Author(s):

Andrea Betterle ◽

Anna Jaeger ◽

Malte Posselt ◽

Claudia Coll ◽

Jonathan P. Benskin ◽

...

Keyword(s):

Surface Water ◽

Numerical Model ◽

Hyporheic Zone ◽

Transport Processes ◽

Hyporheic Exchange ◽

Numerical Representation ◽

Experimental Conditions ◽

Riverine Ecosystems ◽

Hyporheic Flow ◽

Intrinsic Complexity

AbstractHyporheic exchange (HE) contributes to the biogeochemical turnover of macro- and micro-pollutants in rivers. However, the spatiotemporal complexity and variability of HE hinder understanding of its role in the overall functioning of riverine ecosystems. The present study focuses on investigating the role of bacterial diversity and sediment morphology on HE using a multi-flume experiment. A fully coupled surface–subsurface numerical model was used to highlight complex exchange patterns between surface water and the underlying flow field in the sediments. Under the experimental conditions, the surface water flow induced by bedforms has a prominent effect on both local trajectories and residence time distributions of hyporheic flow paths, whereas mean hyporheic retention times are mainly modulated by average surface flowrates. In case of complex bedform morphologies, the numerical model successfully reproduces the HE estimated by means of salt dilution tests. However, the 2D numerical representation of the system falls short in predicting HE in absence of bedforms, highlighting the intrinsic complexity of water circulation patterns in real scenarios. Finally, results show that higher bacterial diversities in the stream sediments can significantly reduce hyporheic fluxes. This work provides a framework to interpret micropollutants turnover in light of the underlying physical transport processes in the hyporheic zone. The study emphasizes the importance of better understanding the tradeoff between physically driven transport processes and bacterial dynamics in the hyporheic zone to quantify the fate of pollutants in streams and rivers.

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